数学中国

标题: 《数论小火花》 [打印本页]

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作者: 小草    时间: 2023-6-22 20:13
标题: 《数论小火花》
《数论小火花》


哥德巴赫猜想

哥德巴赫写给欧拉的信的原件：

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作者: 小草    时间: 2023-6-22 20:15
1742年6月7日，哥德巴赫写信给欧拉，提出了著名的哥德巴赫猜想：随便取某一个奇数，比如77，可以把它写成三个素数之和，即77=53+17+7；再任取一个奇数，比如461，可以表示成461=449+7+5，也是三个素数之和，461还可以写成257+199+5，仍然是三个素数之和。例子多了，即发现“任何大于5的奇数都是三个素数之和。”

1742年6月30日欧拉给哥德巴赫回信。这个命题看来是正确的，但是他也给不出严格的证明。同时欧拉又提出了另一个命题：任何一个大于2的偶数都是两个素数之和。但是这个命题他也没能给予证明。[1]

研究途径
研究偶数的哥德巴赫猜想的四个途径。这四个途径分别是：殆素数，例外集合，小变量的三素数定理以及几乎哥德巴赫问题。

殆素数
殆素数就是素因子个数不多的正整数。现设N是偶数，虽然不能证明N是两个素数之和，但足以证明它能够写成两个殆素数的和，即N=A+B，其中A和B的素因子个数都不太多，譬如说素因子个数不超过10。用“a+b”来表示如下命题：每个大偶数N都可表为A+B，其中A和B的素因子个数分别不超过a和b。显然，哥德巴赫猜想就可以写成"1+1"。在这一方向上的进展都是用所谓的筛法得到的。

“a + b”问题的推进

1920年，挪威的布朗证明了“9 + 9”。

1924年，德国的拉特马赫证明了“7 + 7”。

1932年，英国的埃斯特曼证明了“6 + 6”。

1937年，意大利的蕾西先后证明了“5 + 7”,“4 + 9”,“3 + 15”和“2 + 366”。

1938年，苏联的布赫夕太勃证明了“5 + 5”。

1940年，苏联的布赫夕太勃证明了“4 + 4”。

1948年，匈牙利的瑞尼证明了“1 + c”，其中c是一很大的自然数。

1956年，中国的王元证明了“3 + 4”。稍后证明了“3 + 3”和“2 + 3”。

1962年，中国的潘承洞和苏联的巴尔巴恩证明了“1 + 5”，中国的王元证明了“1 + 4”。

1965年，苏联的布赫夕太勃和小维诺格拉多夫，及意大利的朋比利证明了“1 + 3”。

1966年，中国的陈景润证明了“1 + 2”。

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作者: 小草    时间: 2023-6-22 20:16
丘成桐张益唐评价陈景润
1.丘成桐评价陈景润
澎湃新闻：有人说近三十年来中国数学没有大的发展，但过去有过辉煌，我们有华罗庚、苏步青、陈景润……

丘成桐：相对于欧美的数学水平，中国数学界没有辉煌过。中国数学界最伟大的大师只有陈省身、华罗庚和周炜良，应用数学家则有林家翘和冯康，周、林两位学者长期在美国，不能够代表中国。我在伯克利读书时，大师甚多，包括陈省身和Stephen Smale 。一间大学就比得上中国数学最辉煌的时候。

这样说也许会伤很多人的心。中国数学与欧洲相比，还有不小的差距。一味地往脸上贴金是没有用的。

澎湃新闻：改革开放之初，在邓重新提出重视科技人才的背景之下，中国曾有过“陈景润现象”。作家徐迟刊登在《人民文学》上的《哥德巴赫猜想》一文使得数学成为全国上下的热门话题。当时国际数学界对于陈景润先生的研究是如何评价的？

丘成桐：陈景润做的工作很好，但谈不上伟大，对于整个数学潮流的影响有限。徐迟的报告文学是夸张的。但“文革”期间能做出工作不容易。

最近美国有位华人学者张益唐（证明弱化版孪生素数猜想），他的工作比陈景润的工作重要得多。张益唐做的是让人吃惊的工作。

注：丘成桐，美国哈佛大学数学系教授，菲尔兹奖、沃尔夫数学奖得主，证明了卡拉比猜想、正质量猜想等，是几何分析学科的奠基人

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作者: 小草    时间: 2023-6-22 20:17
2.张益唐评价陈景润


张益唐
记者：你刚才提到丘成桐，我好像觉得他把中国人对数学的一点自信都打掉了。为什么这样说呢？这是指他对陈景润的研究成果的评价。对很多中国人来说，那是在天上的一个数学成果。记得徐迟那篇报导文学中，说陈是摘取“数学皇冠上的明珠”的人。但陈的研究成果在丘成桐看来并不怎么样。他在国内接受采访时说：国内“以为陈景润的哥德巴赫猜想是全世界最伟大的问题，事实上不是，在美国没有人在乎哥德巴赫猜想，你问做数论的人。是媒体误导成功的。”　　

记者：究竟中国人能拿出什么样的数学成绩呢？这个时候，你的研究成果出来了，问一个比较外行问题：如果用小学、中学和大学层次来简单对比的话，你的研究成果与陈景润的研究成果相比，究竟如何呢？

张益唐：这两个研究有点不一样。客观地讲，我的研究应该比陈景润好，但陈景润应该也是第一流的，我们的研究成果都是第一流的。

记者：既然都是第一流的，第一流中是不是有超一流的呢？

张益唐：我的研究似乎更有突破性。陈景润是从1＋3进展到1＋2，我的研究是从无限变成了有限，这个跨越应该比他那个更大。

记者：再回头看，丘成桐先生对陈景润的研究成果评价不高，他对你的研究成果评价如何呢？现在似乎还没有看到他对你的研究的评价，只是知道他邀请你去哈佛做演讲。

网络上有人因此分析说，“显然他不会说张的坏话，因为就是他邀请张去哈佛给报告（而且还要张去得越早越好），讲他的研究结果的。丘成桐如果认为这个结果不重要，自然不可能邀请张去哈佛做报告，更不可能催他越早给报告越好。丘成桐的行动已经可以说明一切了。”

张益唐：他对我的这个研究的评价高得不得了。他带我出去的时候，都提到我的这个研究成果，说比陈景润要好得多。

记者：这些评价好像都没有报导出来？

张益唐：真正像他这类人，他反而不能在网上随便乱说话了。

注：张益唐，美国加州大学圣塔芭芭拉分校数学系教授， 2013年5月，张益唐在孪生素数研究方面所取得的突破性进展，他证明了孪生素数猜想的一个弱化形式。

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作者: 小草    时间: 2023-6-22 20:17
知乎用户​
数学话题下的优秀答主
8,085 人赞同了该回答
首先声明我不是搞数论的，我对陈景润的评价不一定全对。

要说陈景润的历史地位的话我觉得应该是比较一般，和张益唐差不多，至少应该在华罗庚之下，和丘成桐、陈省身那就根本不要比了。毕竟第一他没有真的证出哥德巴赫猜想，只是从“1+3”改进到“1+2”，结果的重要程度不如张益唐；第二他的工作还是在用筛法去估计质数密度，是在改进前人的方法，性质和张益唐类似；第三整个过程中他没有开创出什么新的方向。但是和同行比起来，他的水平还是很高的，比如如果陈景润是美国人，凭他那个”1+2”在美国大部分学校拿个正教授绝无问题。菲尔兹不好说有没有戏，小一点的奖拿一堆也没什么问题。

但是我想说的是，陈景润是在像老鼠一样的生存状态下，在33岁抱着病体完成的那个“1+2"的证明；文革开始以后他的生存环境恐怕连老鼠都不如；到了80年代徐迟的那个报告出来以后又被政治潮流卷着到处去作报告给演讲，天天逢场作戏，也没精力去做什么研究了。真要是让他有比如说陶哲轩那样的成长环境，从小有各路牛人提携指点，有一个能够和全世界同行交流的学术环境，没有人知道他这一辈子能够达到什么高度。不知道有没有人看过刘慈欣的小说《朝闻道》，其实在学术圈子里面，那种殉道者一样纯粹的理想主义者是很少很少的，但是陈景润绝对应该算一个。和他比起来，今天的我们都应该感到惭愧。

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作者: 小草    时间: 2023-6-22 20:18
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對篩法略有瞭解的人可能會知道Vinogradov用圓法給出了三素數定理（"1+1+1"）的情況，所以可能會說爲什麼這裏不用圓法。實際上，對於歌德巴赫猜想的進展，主要就是集中在Brun篩法跟Hardy-Littlewood圓法。模糊的印象裏，圓法會給出一個比較差的bound，所以在這裏也就不再贅述。印象裏是會多一個O(N^{1/2})，細節記不清了。篩法理解起來並不難，總的來說是對某一組數A，定義一個集合，集合裏數我們想得知的數字，比如說，在朝着哥德巴赫猜想上，我們需要得知的就是以下數字：令A爲集合{a<=N|a=N-p_1}對於某個質數p_1.   S(A, z)=在A裏面滿足在A的元素n的質因子均大於z的個數。歌德巴赫猜想遂能轉化爲對於S(A,N^{1/2})的研究。通過Buchstab's identity，我們又可以把問題轉回對於一般S(A,z)上下確界的研究。在結果裏，我們會得到一定的主項，但是對於餘項的研究非常困難，涉及到一些其他問題，比如在其中一個確界裏會需求質數在mod n情況下的分佈，跟L方程的零點分佈也有關係，這些相關的問題的解決離結果還有不少距離。所謂篩法方向封死了，仔細算算這邊得到的餘項應該是能看出來的，具體我就不細算了。於是，我們就考慮另外一個比較接近的問題，就是考慮N=pm+p_n，其中p_m(p_n)是一個最多有m(n)個質因子的數，在這個情況下對於餘項的控制就比較好了，陳老前輩做的就是在這方面的工作。從結果上來講，這個不是一個非常非常困難的結果，因爲這個實際上是對Renyi的方法的改進，而Renyi的方法是建立在Brun的方法基礎上的，所以說他的工作並不是開創性的。至於做這個結果難不難，像大家所想的Trivial or not，影響大不大，希望評價的各位別光看別人怎麼看，自己鑽進paper看一眼，包括後面Ross的paper，不看paper卻對於他人的結果品頭論足終歸不可取。不知道具體對大家是個什麼影響，我個人是很受他經歷觸動的。陳老前輩大學畢業分去做高中老師，又因爲表達不是很清楚被踢去做grader，然後又被人踢回家養病。好不容易好了幾年，文革時期又被當作專政對象關起來，就在1966-1973這幾年被專政期間，他還改進了之前paper的數值結果並最終得到了現在我們看到的結論。就這個經歷裏能看出來的對數學的專注和純粹，恐怕並不是每一個人都能有的。飛鳥和蛙的比喻大家都很熟悉了，陳老前輩或許是蛙沒錯，但是蛙也是值得大家去尊敬的，一步一個腳印，腳踏實地，也比很多只會評頭論足的人強得多。至於一些關於他的結果的評論，小小的補充兩個：“Each work of Mr. Chen Jingrun seems as if it is scaling the tallest mountains of the Himalayas. It is perilous [work], but if successful, will certainly affect the world.” (André Weil, Wolf Prize in Mathematics Laureate, 1979)"Our object in this chapter will be to prove the following remarkable result of Jing-run Chen, which came to our attention only after Chapter 1-10 had gone to press; it constitutes a splendid climax to any account of sieve theory." (Heini Halberstam, H.E. Richert, Sieve Methods, 1974)當然了，希望大家做數學能夠認真學術，一心求學，只管打坐，嘴上功夫，沽名釣譽，實不可取。编辑于 2018-03-23 09:49

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作者: 小草    时间: 2023-6-25 21:37


欧几里得的证明

假设p1=2<p2=3<...<pr是全部素数，令P=p1p2p3...pr+1,并且p为除尽P的一个素数，则p不能是
p1,p2,p3,...,pr当中的任何一个。因为否则，将除尽差数P-p1p2p3...pr=1,而这是不可能的。所以p又是一个新的素数。从而p1,p2,p3,...,pr不能为全部素数。


欧拉的证明

对于每一个素数p,1/p<1.于是有几何级数求和
Σ1/pk=1/1-(1/p).将这n个等式相乘，得到
Π(Σ1/n)=Π1/1-(1/p).左边是所有自然数的倒数和，由算数基本定理，每个自然数恰好出现一次.但是级数Σ1/n是发散的，而上式左边有限，这导致矛盾。

欧拉恒等式

Π(1-p^-s)^-1=Σn^s


Γ(s)

Γ(s)=1/sΠ(1+1/n)^s/1+s/n
Γ(s)=∫x^s-1e^-x(dx)
sΓ(s)=Γ(s+1)
Γ(n+1)=n!
Γ(s)Γ(1-s)=π/sin(πs)
Γ(s)Γ(s+1/2)=√π2^1-2sΓ(2s)
Γ(1/2s)π^-s/2


黎曼ζ(s)函数

ζ(s)=1/Γ(s)∫x^s-1/(e^x)-1dx



命题1+4

| Α^[4] |>3.24C(n)N/l0g^2N
其中C(n)=Π(1-1/(p-1)^2)Πp-1/p-2



命题1+3

| Α^[3] |>2.64C(N)N/log^2N
其中C(N)=Π(1-1/(p-1)^2)Πp-1/p-2



命题1+2

| Α^[2] |>0.62C(n)N/log^2N
其中C(N)=Π(1-1/(p-1)^2)Πp-1/p-2



ζ(2)=Σ1/n^2=π^2/6
ζ(4)=Σ1/n^4=π^4/90

ζ(2)=Σ1/n^2=1.644934066848
ζ(3)=Σ1/n^3=1.202056903159
ζ(4)=Σ1/n^4=1.082323233711
ζ(5)=Σ1/n^5=1.036927755143
ζ(6)=Σ1/n^6=1.017343061984



哈代

2C(n)n/lnn
C(n)=Π(1-1/(p-1)^2)Πp-1/p-2

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作者: 小草    时间: 2023-6-27 10:40
对于哥德巴赫猜想的研究：
哥德巴赫的发现；
欧拉的启发；
高斯的参与；
布朗的风暴；
哈代的半成品；
陈景润的牺牲；
民间数学家的闹剧。

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作者: 小草    时间: 2023-6-29 15:48

小草 发表于 2023-6-27 02:40
对于哥德巴赫猜想的研究：
哥德巴赫的发现；
欧拉的启发；

希望你能成功！

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作者: 小草    时间: 2023-6-30 12:45
1、欧拉猜想：每个大于2的整数n，任何n- 1个正整数的n次幂的和都不是某正整数的n次幂，也就是说以下不定方程无正整数解。

2、这猜想在1966年被L. J. Lander和T. R. Parkin推翻。

3、他们找出n= 5的反例：27^5+ 84^5+ 110^5+ 133^5= 144^5。

4、这是错误的。




一、欧拉猜想作为对费马大定理的推广，欧拉于1769年提出以下猜想：对于每个大于 2 的整数 n ，任何 n&#8722;1个正整数的 n 次幂的和都不是某正整数的 n 次幂。当 n=3 时，欧拉猜想是成立的，此时正是费马大定理 n=3的情形。此后欧拉猜想没有任何进展，直至1911年R. Norrie发现以下 n=4的例子（不是反例）：30^4+120^4+272^4+315^4=353^4
1966年，美国Aerospace公司的L. J. Lander和T. R. Parkin用大型计算机CDC 6600找到以下结果：27^5+84^5+110^5+133^5=144^5 ,成为欧拉猜想的第一个反例。这个结果最初发布在《美国数学会快报》时，正文只有五行，此后很长时期都被视为最短的数学论文。

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作者: 小草    时间: 2023-7-2 18:36
1989年3月，陆家羲妻子张淑琴代表陆家羲参加了在北京人民大会堂隆重举行的“1987年国家自然科学奖颁奖大会”，接受了中国自然科学界的最高荣誉——国家自然科学奖一等奖。陆家羲彼时却早已不在人世。他的一生是穷困的一生，却也是幸福的、纯粹的一生，因为他一直孜孜不倦地沉浸在数学的海洋里。数学的魅力是无穷的，而历经磨难达到顶峰者更是世界上最幸福的人，因为他们欣赏到了数学最高境界的美。

一支笔，几张纸，一个夜深人静时在宿舍楼道口借灯光的孤独身影。这就是挑战世界难题的全部条件。整整四年，陆家羲没有一天停止过思考，毕业时，他已经基本破解了“科克曼女生问题”。

这实在是令人惊叹的天才大脑！但谁能料到，他即将会遭遇那么多的不幸……

1961年，他把论文:《寇克曼系列和斯坦纳系列制作方法》寄给中国科学院数学研究所。一年过去了，对方回信“可以投稿”没有肯定，没有建议，就这样将他的成果搁置一边。他苦笑，只继续埋头完善论文。

1963年，他再次把修改过的论文，又投寄给《中国数学通报》。又是一年的等待，而回信只有草率的一句：建议改投其他刊物。

1965年冬，他把“寇克曼系列”推广到四元组，投给《数学学报》。又等了一年，退稿信写着：没价值！三次投稿，三次被退，他耗费多年心血的研究成果，一次次被忽视、一次次被搁浅。他没等来世界数学的宝座，却等来了一场10年浩——

“文化大革命”开始了。

期间，1966年-1976年，在极左思潮日益弥漫的时候，陆家羲被当成“疯子”，扣上了一顶走“白专道路”的帽子，送到干校进行劳动改造。这给他的精神造成了很大伤害，也使他中断了一切思考。

十年动乱，中国科学几乎停滞了，但世界并不会因此停下脚步。1971年，意大利两名数学家向全世界庄严宣布： “寇克曼系列”解决了!这枚世界数学金牌从此永远属于了意大利！意大利人将永远引以为傲！而此时的他，却浑然不知，还在傻傻等着有一天国家能把它公开。

直到1979年，当他看到了从北京借来的《组合论》杂志，他 “啊！”的一声大叫，随即泪流满面，《组合论》杂志白纸黑字的写着：寇克曼问题在国外已于1971年被破解了。破解者是意大利的数学家！

他崩溃发狂，嚎啕大哭，

这样的结果，他怎能接受？！

要知道，从1961年起，

他就已经得到了“寇克曼系列”的成果！

意大利数学家的证明比他的证明晚10年！

但却比他的论文先问世8年！

18年里，他一次次投稿，却一次次被拒，他的青春年华在等待中失去。祖国学术最好的前进岁月在时间上流失。中国问鼎世界数学巅峰的绝佳机会！就这样错过了。

18年的心血苦熬，他与“寇克曼系列”永别了！但他并没有因此一蹶不振，而是很快抬起头，望向数学王国的另一座高峰——“斯坦纳系列”。那是与陈景润“歌德巴赫猜想”，齐名的另一大世界级数学难题！他恳请校方给他多一点时间研究，但却被拒绝了！

长期高强度的脑力劳动和熬夜，使他患上神经性牙痛病，他心一横，索性拔牙。不到一年时间，满口的牙竟然都被他给拔光了……双腮塌陷，瘦的几乎脱相，妻子看他这样忍不住偷偷落泪。

终于，1980年，他完成了“斯坦纳系列”论文。他再次登上了世界数学的巅峰！他激动的目光炯炯，可神情依然肃穆。之前的经验告诉他：能发表，也许比解出这道难题更难！

稿件寄到北京，又是石沉大海！他始终活在权威部门视线的死角里，泱泱中华竟看不到这个数学王者！

论文被苏州大学的朱烈教授看到，他有一双发现天才的慧眼。朱教授找到陆家羲，建议他把论文直接寄给世界权威期刊《组合论》。

1982年5月，陆家羲收到了正式出版通知与版权签约书。1983年3月，陆家羲的前3篇论文正式发表；4月，后3篇论文一并发表。至此，独自闪耀了130多年的“斯坦纳系列”明珠，被中国的陆家羲最先摘取了！

马上，他把相关6篇论文相继寄往美国，仅仅一个月，他就收到了全部回信。一个月啊！在这一个月的时间里，他的学术论文经过中国、美国、加拿大，又从美国返回中国，五段跨国旅程，仅仅用了一个月。相比之前每封信都要等一年的时间，这简直就像是奇迹！

多伦多大学门德尔松教授在信中写：“这是世界上20 多年来，组合设计方面最重大的成果之一。”捧着这篇信纸，他闭上眼睛紧抿着嘴唇，泪水无声的簌簌而下。

1982年5月，他做了一个重要决定：接受哥伦比亚大学的版权签约书，不收取任何报酬。消息传出，各种声音纷至沓来，有人劝他：何不等等？还有机会取得报酬。有人酸溜溜的讽刺：让外国人发表，就是不爱国。但这些声音他统统不在意：决不能让“寇克曼系列”的悲剧重演。

《组合论》杂志

之后的1983年1月，《组合论》杂志给与他的论文极高评价；3月，他的三篇论文出版，撼动了世界组合学领域；4月，《组合论》杂志发表系列论文，他的名字彻底响彻了西方数学界......但讽刺的是，国内竟还对他一无所知！

中国有关单位向加拿大门德尔松教授，和滑铁卢大学郝迪教授发出邀请，请他们到中国讲学，他们却感到十分吃惊。门德尔松惊讶地问道:“请我去讲组合数学？可你们中国不是有陆家羲博士吗？”外国人的话好像特别有分量，主办方马上邀请他参加学术会议。他奋斗半生未能摸进中国科研大门，如今竟被门德尔松这一句话，实现了。

终于，他被自己的国家、自己的同胞看见了。可中国的彗星，为什么偏要等外国人推荐后才被重视呢？！

但即使他已名扬世界，包头九中和教育局领导却不知道。就连参加学术会议的400元路费都是他妻子筹借的。

7月25日，中国首届组合数学学术讨论会在大连开幕。加拿大门德尔松先生向他提出邀请，请他到多伦多大学工作。他婉言谢绝了，说:“我国组合学还不发达，我要留在祖国。”门德尔松笑了，钦佩的望着他，还把多伦多大学的校徽赠给了他。

会议中，他以特邀代表的身份走上讲台，用中文向全世界数学界宣布：我已经证明了“斯坦纳系列”! 顿时，全场沸腾了！

会后，无数惜才的手伸向他:中国应用数学研究所副所长，推荐他到合肥讲学；

华南师院、华中师大、兰州大学、大连工学院、哈工大、黑龙江大学邀请他到本校任教；内蒙古大学陈子歧副教授连拉带劝:“还是留在内蒙大学的好！”这颗金子，终于被人发现了，但并非所有人都发现了......

9 月，包头市九中校长，收到了来自多伦多大学的一封信。斯特兰格威校长和门德尔松教授，诚恳的邀请他去加拿大讲学，这两个外国学者，爱惜人才就像爱惜钻石，不论国界。但九中校长却对此不屑一顾“又不会提高升学率！去什么去？”

1983年，是他几乎被累垮的一年。数学研究、论文发表，教课任务……

他忙着整理讲学稿，忙着思考“斯坦纳系列”完稿论文。连鞋子露出了脚趾头，他都不舍得再去买一双。他明白，时间和金钱他都浪费不起！

武汉会议结束后，他强撑着疲惫不堪的身躯回到家，把衣兜里舍不得吃的桔子，拿出来分给女儿们，便一头栽倒在床，累的再也起不来。妻子帮他盖好被子，他虚弱的勉强挤出一丝笑容，就闭上了眼睛。而所有人都没想到，这个微笑竟是他最后的告别！

1983年10月31日凌晨一点，他永远的离开了。那一年，他才刚刚48岁。他走的太早、太寒碜，躺在土坑上，依然穿着那双露着脚趾头的鞋。一句遗言都没有留，只留下了15箱书和400多元外债，再就是抽屉里尚未完成的，“斯坦纳系列”最后一篇论文。

在他去世当天，妻子收到中国科学院寄来的45元钱。其中28元是从大连到合肥的路费；9元是他买的一部数学新作报销款；剩下的8元，是他为人代审稿件的酬劳。他一生中唯一从出版部门换来的报酬,就是这8元!

他死了，死的一贫如洗，死的不声不响。包头市新市委、市政府的领导同志来了；中国数学学会内蒙古分会主席来了；内蒙古师范大学数学系主任来了；好友和学生们恸哭着走向他……

斯特兰格威校长发来唁电:“门德尔松教授和我对此非常沉痛，这对世界数学无疑将是极大的损失……”12月，《人民日报》、《光明日报》、《文汇报》、《内蒙古日报》，同时刊登了他的讣闻。《人民日报》报道的标题是：“拚博20 多年，耗尽毕生心血，中学教师陆家羲攻克世界难题斯坦纳系列。”

1984年9月，中国组合数学学会组织了“陆家羲学术工作评审委员会”，对他一生的研究成果给予了高度评价。

1984年底，曾“拒绝”过陆家羲的《数学学报》，终于全文刊发了他于23年前投出的，那篇关于“科克曼女生问题”的论文。

1987年，陆家羲的《不相交的斯坦纳三元系大集》研究成果，被国家科委评为国家自然科学一等奖。



他走的不甘、走的憋屈，他解开了世界性数学难题，但却留下了一道更难的现实问题给我们：为什么会出现“寇克曼系列”的悲剧？为什么会有英才早逝的遗憾？

而今，那个时代早已成为历史，他的名字仍旧被很多人所遗忘！世人皆知陈景润的“哥德巴赫猜想”，但如今又有多少人知道，他曾为祖国作出的巨大贡献与牺牲？！这样的默默英才，我们怎能忘记？

陆家羲的研究，究竟有什么价值、地位如何，在数学界自有判断，我们不做过多的评价。但是，价值绝不和经济效益划等号。哪怕陆家羲没有作出直接贡献、没有产生具体价值，单单只是挑战了人类智慧的极限，难道还不值得敬佩、不值得保护吗？

在陆家羲的故事中，我们看到了民族自信的缺乏，我们不仅需要提升对五千年灿烂中华文明的自信，更需要对现在和未来的科学自信。会念经的不是外来和尚，也许就在山后的破庙里。最大的珍珠不在深海，也许就在河边的滩涂中。我们中国历来不缺乏人才和天才，缺乏的是发现人才和天才的眼睛，以及培养、扶持、保护他们的机制。

假设，没有国际期刊的公开发表，没有国外学者的主动提及，或许陆家羲这个土生土长的天才将会一直贫病交加，终其一生都被埋没。如何避免这种“墙内开花墙外香，错把朱砂当红土”的悲剧再次发生，才是我们最应该思考的。

他的逝去鞭策激励着后辈的努力。他走了，但他的精神永不散。

千年中华，雄姿沃土；

逝者一问，纵今穿古。

2020年，正值陆家羲逝世37周年的祭日，让我们向这位伟大的科学家致以崇高的敬意。

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作者: 小草    时间: 2023-7-5 15:54
欧拉Γ(s)函数


Γ(s)=1/sΠ(1+1/n)^s/1+s/n
Γ(s)=∫x^s-1e^-x(dx)
sΓ(s)=Γ(s+1)
Γ(n+1)=n!
Γ(s)Γ(1-s)=π/sin(πs)
Γ(s)Γ(s+1/2)=√π2^1-2sΓ(2s)
Γ(1/2s)π^-s/2

欧拉能构造出这样一个函数，那正是一个数神。


黎曼ζ(s)函数

ζ(s)=1/Γ(s)∫x^s-1/(e^x)-1dx

黎曼能构造出这样一个函数，那正是一个数神之子。

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作者: 小草    时间: 2023-7-7 20:21
π(x)值与x/lnx,Li(x),R(x)的比较
其中R(x）是黎函数
      R(x)=∑[n=_1,^∞]μ(n)Li(x^1/n)/n


x   【】π(x)   【】(x/lnx)-π(x)【】Li(x)-π(x)【】R(x)-π(x)

10^8【】5761455【】-332774     【】754       【】97
10^9【】50847534【】-2592592   【】1701      【】-79
10^10【】455052511【】-20758030【】3104      【】-1828
10^11【】4118054813【】-169923160【】11588   【】-2318
10^12【】37607912018【】-1416705193【】38263 【】-1476
10^13【】346065536839【】-11992858452【】108971【】-5773
10^14【】3204941750802【】-102838308636【】314890【】-19200
10^15【】29844570422669【】-891604962453【】1052619【】73218
10^16【】279238341033925【】-7804289844393【】3214632【】327052
10^17【】2623557157654233【】-68883734693929【】7956589【】-598255
10^18【】24739954287740860【】-612483070893537【】21949555【】-3501366
10^19【】234057667276344607【】-5481624169369961【】99877775【】23884333
10^20【】2220819602560918840【】-49347193044659702【】222744643【】-4891825
10^21【】21127269486018731928【】-446579871578168707【】597394254【】-86432204

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作者: 小草    时间: 2023-7-8 12:56
这里π(x)=x/a,x/lnx,Li(x)=x/b,R(x)=x/c
它们的最终去向都是同一个站点，是同一个终点站。
而这里面π(x)是终点站。x/lnx是普通公交车，Li(x)是豪华公交车，R(x)是豪华小轿车。
虽然Li(x)特别是R(x)计算精度较高，但计算复杂，特别耗时。
经过一番考量，我们最终选择了普通公交车x/lnx.
因为我们还可以利用系数λ来达到平衡的目的。以10^8为例：
10^8/ln10^8=5428681,我们利用λ=1.061299236407517774575444753523，使得
1.061299236407517774575444753523*10^8/ln10^8=π(x)=5761455.

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作者: 小草    时间: 2023-7-9 13:40
2C2=1.3203236316937400

9√18C=1.3165455165540338955695137279859
10√20C=1.2943986152317356820743316315192
11√22C=1.2753899998576349140152604841772

能否有一个适合呢？

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作者: 小草    时间: 2023-7-9 20:52
Li(x)完全可以进行级数展开.根据分部积分法有
          Li(x)=Σ1,k  ck x/(lnx)^k,其中ck=k-1!
          ∫2,x  1/(lnx)^2 =Σ2,k  ck x/(lnx)^k,其中ck=k-1!

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作者: 小草    时间: 2026-5-7 12:37
素数筛法：
因为π(x)与x的根号中的素数有关，因此设素数有p1,p2,p3,...,pn个.
设x^2=x^θ1+x^θ2,其中x^θ1是非素数个数表g(x^2)，x^θ2是素数个数
表π(x^2).
当x^2=p1^2时,2^2=g(2^2)+π(2^2).
g(2^2)=2^1,π(2^2)=2^1,当x大于2时设g(x^2)=偶数个数，π(x^2)=奇数个数.则g(x^2)=2^1+a1,π(x^2)=2^1+b1.
当x^2=p2^2时
令a1=Δ1,b1=δ1,此时a1,b1是不定数，Δ1,δ1是定数.
p2^2=g(3^2)+π(3^2).
g(3^2)=1^1+Δ1+a2,π(3^2)=3^1+δ1+b2
当x^2=p3^2时
令a2=Δ2,b2=δ2,此时a2,b2是不定数，Δ2,δ2是定数.
p3^2=g(5^2)+π(5^2).
g(5^2)=1^1+Δ1+Δ2+a3,π(2^2)=2^1+δ1+δ2+b3.
.
.
.
当x^2=pk^2时
令a1=Δ1,a2=Δ2,a3=Δ3,...,an=Δn,
令b1=δ1,b2=δ2,b3=δ3,...,bn=δn,
此时ak,bk是不定数，Δk,δk是定数.
pn^2=g(pn^2)+π(pn^2).
g(pn^2)=pn^1+Δ1+Δ2+Δ3+...+an
π(pn^2)=pn^1+δ1+δ1+b3+...+bn

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作者: 蔡家雄    时间: 2026-5-7 20:38

http://www.mathchina.com/bbs/for ... 5&fromuid=45368

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作者: 小草    时间: 2026-5-8 07:12
π(2^1)=1=[2]
π(2^2)=2*1=2
maxa=2;mina=2
1.5*2=3
π(2^2)=2
[2,3]
maxb=1.5;minb=1.5
π(2^2)=2
π(2^3)=2*2=4
maxa=2;mina=2
1.66667*3≈5
1.4*5=7,
[2,3,5,7]
maxb=1.66667;minb=1.4
π(2^3)=4
π(2^4)=1.5*4=6
maxa=2;mina=1.5
1.57143*7≈11
1.18182*11≈13
[2,3,5,7,11,13]
maxb=1.57143;minb=1.18182
π(2^4)=6
π(2^5)≈1.83333*6=11
maxa=2;mina=1.83333
1.30769*13≈17
1.11765*17≈19
1.21053*19≈23
1.26087*23≈29
1.06897*29≈31
[2,3,5,7,11,13,17,19,23,29,31]
maxb=1.30769;minb=1.06897
π(2^5)≈1.83333*6=11
π(2^6)≈1.63636*11=18

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作者: 小草    时间: 2026-5-9 07:11
π(2^2)=2=2^1
π(2^3)=4=2^2
π(2^5)=11>2^3=8
π(2^6)=18>2^4=16
π(2^8)=54>2^5=32
π(2^9)=97>2^6=64
π(2^10)=172>2^7=128
π(2^11)=309>2^8=256
π(2^12)=564>2^9=512
π(2^13)=1028>2^10=1024
π(2^15)=3512>2^11=2048
π(2^16)=6542>2^12=4096
π(2^17)=12251>2^13=8192
π(2^18)=23000>2^14=16384
π(2^19)=43390>2^15=32768
π(2^20)=82025>2^16=65536
π(2^21)=155611>2^17=131072
π(2^22)=295947>2^18=262144
π(2^23)=564163>2^19=524288
π(2^24)=1077871>2^20=1048576
π(2^26)=3957809>2^21=2097152
π(2^27)=7603553>2^22=4194304
π(2^28)=14630843>2^23=8388608
π(2^29)=28192750>2^24=16777216
π(2^30)=54400028>2^25=33554432
π(2^31)=105097565>2^26=67108864
π(2^32)=203280221>2^27=134217728
π(2^33)=393615806>2^28=268435456
π(2^34)=762939111>2^29=536870912
π(2^35)=1480206279>2^30=1073741824
π(2^36)=2874398515>2^31=2147483648
π(2^37)=5586502348>2^32=4294967296
π(2^38)=10866266172>2^33=8589934592
π(2^39)=21151907950>2^34=17179869184
π(2^40)=41203088796>2^35=34359738368
π(2^41)=80316571436>2^36=68719476736
π(2^42)=156661034233>2^37=137438953472
π(2^43)=305761713237>2^38=274877906944
π(2^44)=597116381732>2^39=549755813888
π(2^45)=1166746786182>2^40=1099511627776
π(2^46)=2280998753949>2^41=2199023255552
π(2^47)=4461632979717>2^42=4398046511104
π(2^49)=17094432576778>2^43=8796093022208
π(2^50)=33483379603407>2^44=17592186044416
π(2^51)=65612899915304>2^45=35184372088832
π(2^52)=128625503610475>2^46=70368744177664
π(2^53)=252252704148404>2^47=140737488355328
π(2^54)=494890204904784>2^48=281474976710656
π(2^55)=971269945245201>2^49=562949953421312
π(2^56)=1906879381028850>2^50=1125899906842624
π(2^57)=3745011184713964>2^51=2251799813685248
π(2^58)=7357400267843990>2^52=4503599627370496
π(2^59)=14458792895301660>2^53=9007199254740992
π(2^60)=28423094496953330>2^54=18014398509481984
π(2^61)=55890484045084135>2^55=36028797018963968
π(2^62)=109932807585469973>2^56=72057594037927936
π(2^63)=216289611853439384>2^57=144115188075855872
π(2^64)=425656284035217743>2^58=288230376151711744
π(2^65)=837903145466607212>2^59=576460752303423488
π(2^66)=1649819700464785589>2^60=1152921504606846976
π(2^67)=3249254387052557215>2^61=2305843009213693952
π(2^68)=6400771597544937806>2^62=4611686018427387904
π(2^69)=12611864618760352880>2^63=9223372036854775808
π(2^70)=24855455363362685793>2^64=18446744073709551616
π(2^71)=48995571600129458363>2^65=36893488147419103232
π(2^72)=96601075195075186855>2^66=73786976294838206464
π(2^73)=190499823401327905601>2^67=147573952589676412928
π(2^74)=375744164937699609596>2^68=295147905179352825856
π(2^75)=741263521140740113483>2^69=590295810358705651712
π(2^76)=1462626667154509638735>2^70=1180591620717411303424
π(2^77)=2886507381056867953916>2^71=2361183241434822606848
π(2^78)=5697549648954257752872>2^72=4722366482869645213696
π(2^79)=11248065615133675809379>2^73=9444732965739290427392
π(2^80)=22209558889635384205844>2^74=18889465931478580854784
π(2^81)=43860397052947409356492>2^75=37778931862957161709568
π(2^82)=86631124695994360074872>2^76=75557863725914323419136
π(2^83)=171136408646923240987028>2^77=151115727451828646838272
π(2^84)=338124238545210097236684>2^78=302231454903657293676544
π(2^85)=668150111666935905701562>2^79=604462909807314587353088
π(2^86)=1320486952377516565496055>2^80=1208925819614629174706176
π(2^87)=2610087356951889016077639>2^81=2417851639229258349412352
π(2^88)=5159830247726102115466054>2^82=4835703278458516698824704
π(2^89)=10201730804263125133012340>2^83=9671406556917033397649408
π(2^90)=20172933541156002700963336>2^84=19342813113834066795298816
π(2^91)=39895115987049029184882256>2^85=38685626227668133590597632
π(2^92)=78908656317357166866404346>2^86=77371252455336267181195264

---

作者: 被遗弃的草根    时间: 2026-5-9 08:38


在我证明并发表的数学文章中，就有2012年11月发表在数学杂志"Advances in Theoretical and Applieed Mathematics"第4期上的哥德巴赫猜想证明，到目前都还没有得到数学界的普遍认可，但也未见有人否定。

关于张益唐先生对孪生素数猜想的预想证明，在他向“Annals of Mathematics"投稿之前，我对该猜想及以素数数目和间隔不同而命名的猜想的证明就已经发表在2013年1月数学杂志"Advances in Theoretical and Applieed Mathematics"第1期上了，到目前都还没有得到数学界的普遍认可，但也未见有人否定。

---

作者: 小草    时间: 2026-5-9 10:29

被遗弃的草根 发表于 2026-5-9 00:38
在我证明并发表的数学文章中，就有2012年11月发表在数学杂志"Advances in Theoretical and Applieed Mathem ...

是金子总会发光，蒙上灰尘也仍然发光。

---

作者: 小草    时间: 2026-5-10 07:06
T(2^3)=2=2^1
T(2^5)=5>2^2=4
T(2^7)=10>2^3=8
T(2^8)=17>2^4=16
T(2^10)=36>2^5=32
T(2^12)=107>2^6=64
T(2^13)=177>2^7=128
T(2^14)=290>2^8=256
T(2^16)=860>2^9=512
T(2^17)=1526>2^10=1024
T(2^18)=2679>2^11=2048
T(2^19)=4750>2^12=4096
T(2^20)=8535>2^13=8192
T(2^22)=27995>2^14=16384
T(2^23)=50638>2^15=32768
T(2^24)=92246>2^16=65536
T(2^25)=168617>2^17=131072
T(2^26)=309561>2^18=262144
T(2^27)=571313>2^19=524288
T(2^28)=1056281>2^20=1048576
T(2^30)=3650557>2^21=2097152
T(2^31)=6810670>2^22=4194304
T(2^32)=12739574>2^23=8388608
T(2^33)=23878645>2^24=16777216
T(2^34)=44849427>2^25=33554432
T(2^35)=84384508>2^26=67108864
T(2^36)=159082253>2^27=134217728
T(2^37)=300424743>2^28=268435456
T(2^38)=568237005>2^29=536870912
T(2^39)=1076431099>2^30=1073741824
T(2^41)=3879202049>2^31=2147483648
T(2^42)=7378928530>2^32=4294967296
T(2^43)=14053179903>2^33=8589934592
T(2^44)=26795709320>2^34=17179869184
T(2^45)=51149458583>2^35=34359738368
T(2^46)=97741674629>2^36=68719476736
T(2^47)=186965900951>2^37=137438953472
T(2^48)=357988002871>2^38=274877906944
T(2^49)=686087457349>2^39=549755813888
T(2^50)=1316068371494>2^40=1099511627776
T(2^51)=2526674510802>2^41=2199023255552
T(2^52)=4854867527890>2^42=4398046511104
T(2^53)=9335730886226>2^43=8796093022208
T(2^54)=17965892577331>2^44=17592186044416
T(2^56)=66678992679955>2^45=35184372088832
T(2^57)=128589588118191>2^46=70368744177664
T(2^58)=248145307510177>2^47=140737488355328
T(2^59)=479159158312507>2^48=281474976710656
T(2^60)=925800651712810>2^49=562949953421312
T(2^61)=1789823239135382>2^50=1125899906842624

---

作者: 小草    时间: 2026-5-10 20:52

小草 发表于 2026-5-9 02:29
是金子总会发光，蒙上灰尘也仍然发光。

要被别人认可，也许比自己证明命题更难，许多大数学家也曾遭受过同样的磨难。

---

作者: 小草    时间: 2026-5-11 06:40
10^n内素数个数
主项a_k^(k+1)
余项π(10^(k+1))-a_k^(k+1)=(b_k+1)^(k+1)


π(10^1)=4
π(10^2)=25=4^2+3^2=5^2
π(10^3)=168≈5^3+3.50340^3≈5.51785^3
π(10^4)=1229≈5.51785^4+4.16871≈5.92090^4
π(10^5)=9592≈5.92090^5+4.70889^5≈6.25723^5
π(10^6)=78498≈6.25723^6+5.14175^6≈6.54349^6
π(10^7)=664579≈6.54349^7+5.49320^7≈6.78879^7
π(10^8)=5761455≈6.78879^8+5.78234^8≈6.99949^8
π(10^9)=50847534≈6.99949^9+6.02873^9≈7.18211^9
π(10^10)=455052511≈7.18211^10+6.24248^10≈7.34186^10
π(10^11)=4118054813≈7.34186^11+6.43023^11≈7.48278^11
π(10^12)=37607912018≈7.48278^12+6.59691^12≈7.60805^12
π(10^13)=346065536839≈7.60805^13+6.74615^13≈7.72018^13
π(10^14)=3204941750802≈7.72018^14+6.88080^14≈7.82119^14
π(10^15)=29844570422669≈7.82119^15+7.00300^15≈7.91269^15
π(10^16)=279238341033925≈7.91269^16+7.11456^16≈7.99601^16
π(10^17)=2623557157654233≈7.99601^17+7.21686^17≈8.07223^17
π(10^18)=24739954287740860≈8.07223^18+7.31111^18≈8.14225^18
π(10^19)=234057667276344607≈8.14225^19+7.39826^19
≈8.20682^19
π(10^20)=2220819602560918840≈8.20682^20+7.47915^20
≈8.26658^20
π(10^21)=21127269486018731928≈8.26658^21+7.55444^21
≈8.32206^21
π(10^22)=201467286689315906290≈8.32206^22+7.62476^22
≈8.37372^22
π(10^23)=1925320391606803968923≈8.37372^23+7.69061^23
≈8.42196^23
π(10^24)=18435599767349200867866≈8.42196^24+7.75241^24
≈8.46712^24
π(10^25)=176846309399143769411680≈8.46712^25+7.81053^25
≈8.50950^25
π(10^26)=1699246750872437141327603≈8.50950^26+7.86530^26
≈8.54935^26
π(10^27)=16352460426841680446427399≈8.54935^27+7.91706^27
≈8.58690^27
π(10^28)=157589269275973410412739598≈8.58690^28+7.96607^28
≈8.62236^28
π(10^29)=1520698109714272166094258063≈8.62236^29+8.01246^29
≈8.65589^29

---

作者: 小草    时间: 2026-5-12 07:23
方程z^n=x^n+y^n        （1）
(1)=z^n-x^n-y^n=0       (2)
计算方程(2)
令n=1
3-2-1=0
4-3-1=0
5-4-1=0
6-5-1=0
7-6-1=0
8-7-1=0
9-8-1=0
10-9-1=0

令n=2
取最小非负余项
3^2-2^2-1^2=4
4^2-3^2-2^2=3
【2^2+5=3^2】
5^2-4^2-3^2=0
6^2-5^2-3^2=2
7^2-6^2-3^2=4
8^2-7^2-3^2=6
9^2-8^2-4^2=1
10^2-9^2-4^2=3
11^2-10^2-4^2=5
12^2-11^2-4^2=7
【4^2+9=5^2】
13^2-12^2-5^2=0

---

作者: 晋源泉    时间: 2026-5-12 07:30

小草 发表于 2026-5-12 07:23
方程z^n=x^n+y^n        （1）
(1)=z^n-x^n-y^n=0       (2)
计算方程(2)

四色猜想成立的终极证明：地图4CC成立的终极证明2024
http://www.mathchina.com/bbs/for ... &fromuid=124943
(出处: 数学中国)

---

作者: 小草    时间: 2026-5-12 07:46

晋源泉 发表于 2026-5-11 23:30
四色猜想成立的终极证明：地图4CC成立的终极证明2024
http://www.mathchina.com/bbs/forum.php?mod=view ...

谢谢你的参与！你的作品值得一读，慢慢品味。

---

作者: 小草    时间: 2026-5-20 12:46
T(10^1)=2
(ln10)^2=5.30190
10/5.30190=1.88612
1.88612*1.32032=2.49028
2/2.49028=0.80312

T(10^2)=8
(ln10^2)^2=21.20759
10^2/21.20759=4.71529
4.71529*1.32032=6.22569
8/6.22569=1.28500

T(10^3)=35
(ln10^3)^2=47.71708
10^3/47.71708=20.95686
20.95686*1.32032=27.66976
35/27.66976=1.26492

T(10^4)=205
(ln10^4)^2=84.83037
10^4/84.83037=117.88231
117.88231*1.32032=155.64237
205/155.64237=1.31712

T(10^5)=1224
(ln10^5)^2=132.54745
10^5/132.54745=754.44680
754.44680*1.32032=996.11120
1224/996.11120=1.22878

T(10^6)=8169
(ln10^6)^2=190.86833
10^6/190.86833=5239.21386
5239.21386*1.32032=6917.43884
8169/6917.43884=1.18093

T(10^7)=58980
(ln10^7)^2=259.79301
10^7/259.79301=38492.18268
38492.18268*1.32032=50821.99864
58980/50821.99864=1.16052

T(10^8)=440312
(ln10^8)^2=339.32148
10^8/339.32148=294705.77577
294705.77577*1.32032=389105.92986
440312/389105.92986=1.13160

T(10^9)=3424506
(ln10^9)^2=429.45375
10^9/429.45375=2328539.45274
2328539.45274*1.32032=3074417.21024
3424506/3074417.21024=1.11387

T(10^10)=27412679
(ln10^10)^2=530.18981
10^10/530.18981=18861169.73844
18861169.73844*1.32032=24902779.62906
27412679/24902779.62906=1.10079

T(10^11)=224376048
(ln10^11)^2=641.52967
10^11/641.52967=155877435.87915
155877435.87915*1.32032=205808096.13996
224376048/205808096.13996=1.09022

T(10^12)=1870585220
(ln10^12)^2=763.47333
10^12/763.47333=1309803447.88206
1309803447.88206*1.32032=1729359688.30764
1870585220/1729359688.30764=1.08166

T(10^13)=15834664872
(ln10^13)^2=896.02078
10^13/896.02078=11160455452.83001
11160455452.83001*1.32032=14735372543.48052
15834664872/14735372543.48052=1.07460

T(10^14)=135780321665
(ln10^14)^2=1039.17203
10^14/1039.17203=96230457626.92439
96230457626.92439*1.32032=127054997813.98081
135780321665/127054997813.98081=1.06867

T(10^15)=1177209242304
(ln10^15)^2=1192.92707
10^15/1192.92707=838274212353.98741
838274212353.98741*1.32032=1106790208055.21666
1177209242304/1106790208055.21666=1.06362

T(10^16)=10304195696798
(ln10^16)^2=1,357.28592
10^16/1,357.28592=7367644394336.60374
7367644394336.60374*1.32032=9727648246730.50465
10304195696798/9727648246730.50465=1.05927

T(10^17)=90948889353159
(ln10^17)^2=1532.24855
10^17/1532.24855=65263563147114.74193
65263563147114.74193*1.32032=86168787694398.53607
90948889353159/86168787694398.53607=1.05547

T(10^18)=808675888577435
(ln10^18)^2=1717.81499
10^18/1717.81499=582134866572563.78931
582134866572563.78931*1.32032=768604307033087.42230
808675888577435/768604307033087.42230=1.05214

---

作者: 小草    时间: 2026-5-21 13:46
T(18)=4
(ln18)^2=8.35425
18/8.35425=2.15459
2.15459*1.32032=2.84474
4/2.84474=1.40610
4/3=1.33333

T(50)=6
(ln50)^2=15.30392
50/15.30392=3.26714
3.26714*1.32032=4.31367
6/4.31367=1.39093
6/8=0.75

T(242)=17
(ln242)^2=30.12844
242/30.12844=8.03228
8.03228*1.32032=10.60518
17/10=1.7
17/19=0.89474

T(578)=26
(ln578)^2=40.44418
578/40.44418=14.29130
14.29130*1.32032=18.86909
26/18.86909=1.37791
26/36=0.72222

T(1682)=53
(ln1682)^2=55.17130
1682/55.17130=30.48687
30.48687*1.32032=40.25242
53/40.25242=1.31669
53/65=0.81538

T(3362)=89
(ln3362)^2=65.93913
3362/65.93913=50.98642
50.98642*1.32032=67.31839
89/67.31839=1.32208
89/106=0.83962

T(6962)=162
(ln6962)^2=78.29103
6962/78.29103=88.92462
88.92462*1.32032=117.40895
162/117.40895=1.37979
162/165=0.98182

T(10082)=208
(ln10082)^2=84.98087
10082/84.98087=118.63847
118.63847*1.32032=156.64074
208/156.64074=1.32788
208/236=0.88135

T(20402)=346
(ln20402)^2=98.47363
20402/98.47363=207.18237
207.18237*1.32032=273.54703
346/273.54703=1.26486
346/337=1.02671

T(22898)=387
(ln22898)^2=100.77760
22898/100.77760=227.21319
227.21319*1.32032=299.99412
387/299.99412=1.29003
387/444=0.87162

T(37538)=564
(ln37538)^2=110.94638
37538/110.94638=338.34362
338.34362*1.32032=446.72185
564/446.72185=1.26253
564/581=0.97074

T(44402)=641
(ln44402)^2=114.51225
44402/114.51225=387.74890
387.74890*1.32032=511.95263
641/511.95263=1.25207
641/730=0.87808

T(64082)=845
(ln64082)^2=122.49883
64082/122.49883=523.12336
523.12336*1.32032=690.69023
845/690.69023=1.22341
845/909=0.92959

T(72962)=942
(ln72962)^2=125.38835
72962/125.38835=581.88819
581.88819*1.32032=768.27862
942/768.27862=1.22612
942/1100=0.85636

T(77618)=985
(ln77618)^2=126.77757
77618/126.77757=612.23764
612.23764*1.32032=808.34960
985/808.34960=1.21853
985/1297=0.75944

T(103058)=1252
(ln103058)^2=133.24194
103058/133.24194=773.46517
773.46517*1.32032=1021.22153
1252/1021.22153=1.22598
1252/1524=0.82152

T(114242)=1362
(ln114242)^2=135.63105
114242/135.63105=842.29975
842.29975*1.32032=1112.10521
1362/1112.10521=1.22470
1362/1763=0.77255

T(144722)=1649
(ln144722)^2=141.19547
144722/141.19547=1024.97623
1024.97623*1.32032=1353.29662
1649/1353.29662=1.21851
1649/2032=0.81152

T(157922)=1784
(ln157922)^2=143.27747
157922/143.27747=1102.21098
1102.21098*1.32032=1455.27120
1784/1455.27120=1.22589
1784/2313=0.77129

T(193442)=2105
(ln193442)^2=148.17543
193442/148.17543=1305.49309
1305.49309*1.32032=1723.66864
2105/1723.66864=1.22123
2105/2624=0.80221

T(240818)=2508
(ln240818)^2=153.55663
240818/153.55663=1568.26833
1568.26833*1.32032=2070.61604
2508/2070.61604=1.21123
2508/2971=0.84416

T(351122)=3429
(ln351122)^2=163.04452
351122/163.04452=2153.53450
2153.53450*1.32032=2843.35467
3429/2843.35467=1.20597
3429/3390=1.01150

T(371522)=3585
(ln371522)^2=164.48995
371522/164.48995=2258.63039
2258.63039*1.32032=2,982.11488
3585/2,982.11488=1.20217
3585/3821=0.93824

T(425042)=4003
(ln425042)^2=167.96013
425042/167.96013=2530.61247
2530.61247*1.32032=3341.21826
4003/3341.21826=1.19807
4003/4282=0.93484

T(542882)=4898
(ln542882)^2=174.36271
542882/174.36271=3113.52123
3113.52123*1.32032=4110.84435
4898/4110.84435=1.19148
4898/4803=1.01978

T(647522)=5688
(ln647522)^2=179.04870
647522/179.04870=3616.45742
3,616.45742*1.32032=4774.88106
5688/4774.88106=1.19123
5688/5372=1.05882

T(717602)=
(ln717602)^2=181.80937
717602/181.80937=3947.00229
3947.00229*1.32032=5211.30606
6189/5,211.30606=1.18761
6189/5971=1.03651

T(761378)=6483
(ln761378)^2=183.40974
761378/183.40974=4151.24082
4151.24082*1.32032=5480.96628
6483/5480.96628=1.18282
6483/6588=0.98406

T(821762)=6906
(ln821762)^2=185.48277
821762/185.48277=4430.39534
4430.39534*1.32032=5,849.53958
6906/5,849.53958=1.18061
6906/7229=0.95532

T(868562)=7242
(ln868562)^2=186.99453
868562/186.99453=4644.85245
4644.85245*1.32032=6132.69159
7242/6132.69159=1.18088
7242/7888=0.91810

---

作者: 小草    时间: 2026-5-22 14:04
施承忠素数个数π(x)分段系数法

(pk)^2≤x<(pk+1)^2；π(x)≈bk*x/lnx

2
ln4=1.3862943611
4/1.3862943611=2.8853900818
3/2.8853900818=1.0397207708
b1=1.0397207708

3
ln9=2.1972245773
9/2.1972245773=4.0960765198
6/4.0960765198=1.4648163849
b2=1.4648163849

5
ln25=3.2188758248
25/3.2188758248=7.7666866822
11/7.7666866822=1.4163053629
b3=1.4163053629

7
ln49=3.8918202981
49/3.8918202981=12.5905093881  
18/12.5905093881=1.4296482728  
b4=1.4296482728  

11
ln121=4.7957905456
121/4.7957905456=25.2304596812
29/25.2304596812=1.1494043456
b5=1.1494043456

13
ln169=5.1298987149
169/5.1298987149=32.9441202239
42/32.9441202239=1.2748860712
b6=1.2748860712

17
ln289=5.6664266881
289/5.6664266881=51.0021598986
59/51.0021598986=1.1568137529
b7=1.1568137529

19
ln361=5.8888779583
361/5.8888779583=61.3020005774
78/61.3020005774=1.2723891433
b8=1.2723891433

23
ln529=6.2709884319
529/6.2709884319=84.3567175645
101/84.3567175645=1.1972964681
b9=1.1972964681

29
ln841=6.7345916600
841/6.7345916600=124.8776529385
130/124.8776529385=1.0410189249
b10=1.0410189249

31
ln961=6.8679744090
961/6.8679744090=139.9248079231
161/139.9248079231=1.1506179811
b11=1.1506179811

37
ln1369=7.2218358253
1369/7.2218358253=189.5639880381
198/189.5639880381=1.0445021866
b12=1.0445021866

41
ln1681=7.4271441334
1681/7.4271441334=226.3319480284
239/226.3319480284=1.0559711171
b13=1.0559711171

43
ln1849=7.5224002314
1849/7.5224002314=245.7992054560
282/245.7992054560=1.1472779152
b14=1.1472779152

47
ln2209=7.7002952034
2209/7.7002952034=286.8721187500
329/286.8721187500=1.1468524771
b15=1.1468524771

53
ln2809=7.9405838271
2809/7.9405838271=353.75232 61720
382/353.75232 61720=1.07985155641
b16=1.07985155641

59
ln3481=8.1550748878
3481/8.1550748878=426.8507705806
441/426.8507705806=1.0331479533
b17=1.0331479533

61
ln3721=8.2217477283
3721/8.2217477283=452.5801718766
502/452.5801718766=1.1091957430
b18=1.1091957430

67
ln4489=8.4093852388
4489/8.4093852388=533.8083430033
569/533.8083430033=1.0659256406
b19=1.0659256406

71
ln5041=8.5253597541
5041/8.5253597541=591.2946955201
640/591.2946955201=1.0823706095
b20=1.0823706095

73
ln5329=8.5809188823
5329/8.5809188823=621.0290614671
713/621.0290614671=1.1480944198
b21=1.1480944198

79
ln6241=8.7388957049
6241/8.7388957049=714.1634607792
792/714.1634607792=1.1089898090
b22=1.1089898090

83
ln6889=8.8376812156
6889/8.8376812156=779.5031108205
875/779.5031108205=1.1225099526
b23=1.1225099526

89
ln7921=8.9772727395
7921/8.9772727395=882.3392393046
964/882.3392393046=1.0925502993
b24=1.0925502993

97
ln9409=9.1494219570
9409/9.1494219570=1028.3709773382
1061/1028.3709773382=1.0317288443
b25=1.0317288443

101
ln10201=9.2302410337
10201/9.2302410337=1105.1715727418
1162/1105.1715727418=1.0514204569
b26=1.0514204569

---

作者: 小草    时间: 2026-5-23 10:12
施承忠孪生素数对数T(x)分段系数法

2(qk)^2≤x<2(qk+1)^2；T(x)≈ck*x/ln^2x

3
(ln18)^2=8.3542488988
18/8.3542488988=2.1545922581
3/2.1545922581=1.3923748165
c1=1.3923748165

5
(ln50)^2=15.3039239950
50/15.3039239950=3.2671359330
8/3.2671359330=2.4486278392
c2=2.4486278392

11
(ln242)^2=30.1284373616
242/30.1284373616=8.0322785113
19/8.0322785113=2.3654558259
c3=2.3654558259

17
(ln578)^2=40.4441797911
578/40.4441797911=14.2913023082
36/14.2913023082=2.5190146583
c4=2.5190146583

29
(ln1682)^2=55.1713042832
1682/55.1713042832=30.4868630868
65/30.4868630868=2.1320658611
c5=2.1320658611

41
(ln3362)^2=65.9391310237
3362/65.9391310237=50.9864165300
106/50.9864165300=2.07898509474
c6=2.07898509474

59
(ln6962)^2=78.2910337712
6962/78.2910337712=88.9246145395
165/88.9246145395=1.8555042477
c7=1.8555042477

71
(ln10082)^2=84.9808701041
10082/84.9808701041=118.6384651940
236/118.6384651940=1.9892367928
c8=1.9892367928

101
(ln20402)^2=98.4736336506
20402/98.4736336506=207.1823618532
337/207.1823618532=1.6265863415
c9=1.6265863415

107
(ln22898)^2=100.7776028060
22898/100.7776028060=227.2131839063
444/227.2131839063=1.9541119594
c10=1.9541119594

137
(ln37538)^2=110.9463858846
37538/110.9463858846=338.3436035406
581/338.3436035406=1.7171892535
c11=1.7171892535

149
(ln44402)^2=114.5122526396
44402/114.5122526396=387.7489000216
730/387.7489000216=1.8826616915
c12=1.8826616915

179
(ln64082)^2=122.4988263917
64082/122.4988263917=523.1233791179
909/523.1233791179=1.7376397926
c13=1.7376397926

191
(ln72962)^2=125.3883517385
72962/125.3883517385=581.8881817042
1100/581.8881817042=1.8903975619
c14=1.8903975619

197
(ln77618)^2=126.7775706469
77618/126.7775706469=612.2376348115
1297/612.2376348115=2.1184584649
c15=2.1184584649

227
(ln103058)^2=133.2419390198
103058/133.2419390198=773.4651773920
1524/773.4651773920=1.97035 37335
c16=1.97035 37335

239
(ln114242)^2=135.6310462383
114242/135.6310462383=842.2997769941
1763/842.2997769941=2.0930790298
c17=2.0930790298

269
(ln144722)^2=141.1954683734
144722/141.1954683734=1024.9762380282
2032/1024.9762380282=1.9824849832
c18=1.9824849832

281
(ln157922)^2=143.2774650909
157922/143.2774650909=1102.2110134333
2313/1102.2110134333=2.0985092435
c19=2.0985092435

311
(ln193442)^2=175.5035992586
193442/175.5035992586=1102.2110134332
2624/1102.2110134332=2.3806693709
c20=2.3806693709

---

作者: 小草    时间: 2026-5-23 13:52
施承忠哥德巴赫偶数素数对数D(x)分段系数法

4(qk)^2≤x<4(qk+1)^2；D(2n)≈dk*2n/ln^2(2n)

3
(ln36)^2=12.8416079823
36/12.8416079823=2.8033872432
3/2.8033872432=1.0701339985
d1=1.0701339985

5
(ln100)^2=35.6711332844
100/35.6711332844=2.8033872432
8/2.8033872432=2.8536906628
d2=2.8536906628

11
(ln484)^2=38.2181737939
484/38.2181737939=12.6641320595
19/12.6641320595=1.5003002109
d3=1.5003002109

17
(ln1156)^2=49.7408741983
1156/49.7408741983=23.2404439735
36/23.2404439735=1.5490237640
d4=1.5490237640

29
(ln3364)^2=65.9487897676
3364/65.9487897676=51.0092757101
65/51.0092757101=1.2742780425
d5=1.2742780425

41
(ln6724)^2=77.6766980968
6724/77.6766980968=86.5639266955
106/86.5639266955=1.2245285542
d6=1.2245285542

59
(ln13924)^2=91.0377271445
13924/91.0377271445=152.9475793909
165/152.9475793909=1.0788009896
d7=1.0788009896

71
(ln20164)^2=98.2408872994
20164/98.2408872994=205.2505891824
236/205.2505891824=1.1498139954
d8=1.1498139954

101
(ln40804)^2=112.7108237891
40804/112.7108237891=362.0237935298
337/362.0237935298=0.9308780418
d9=0.9308780418

107
(ln45796)^2=115.1747943752
45796/115.1747943752=397.6217213882
444/397.6217213882=1.1166391978
d10=1.1166391978

137
(ln75076)^2=126.0288285549
75076/126.0288285549=595.7049737021
581/595.7049737021=0.9753150060
d11=0.9753150060

149
(ln88804)^2=129.8274967760
88804/129.8274967760=684.0153450175
730/684.0153450175=1.0672275196
d12=1.0672275196

179
(ln128164)^2=138.3226728166
128164/138.3226728166=926.5581512434
909/926.5581512434=0.9810501357
d13=0.9810501357

191
(ln145924)^2=141.3921048530
145924/141.3921048530=1032.0519674823
1100/1032.0519674823=1.0658378014
d14=1.0658378014

197
(ln155236)^2=142.8670807643
155236/142.8670807643=1086.5764119315
1297/1086.5764119315= 1.1936574232
d15=1.1936574232

227
(ln206116)^2=149.7244532987
206116/149.7244532987=1376.6355158352
1524/1376.6355158352=1.1070468417
d16=1.1070468417

239
(ln228484)^2=152.2563863619
228484/152.2563863619=1500.6529805385
1763/1500.6529805385=1.1748219094
d17=1.1748219094

269
(ln289444)^2=158.1486610904
289444/158.1486610904=1830.2020263994
2032/1830.2020263994=1.1102599444
d18=1.1102599444

281
(ln315844)^2=160.3516627008
315844/160.3516627008=1969.6958215478
2313/1969.6958215478=1.1742929922
d19=1.1742929922

311
(ln386884)^2=165.5308729471
386884/165.5308729471=2337.2316783688
2624/2337.2316783688=1.1226957192
d20=1.1226957192

---

作者: 小草    时间: 2026-5-24 15:47
103
ln10609=9.2694579765
10609/9.2694579765=1144.5113648388
1265/1144.5113648388=1.1052751758
b27=1.1052751758

107
ln11449=9.3456576689
11449/9.3456576689=1225.0609219402
1372/1225.0609219402=1.1199443027
b28=1.1199443027

109
ln11881=9.3826957645
11881/9.3826957645=1266.2672112798
1481/1266.2672112798=1.1695793643
b29=1.1695793643

113
ln12769=9.4547756374
12769/9.4547756374=1350.5344272253
1594/1350.5344272253=1.1802735035
b30=1.1802735035

127
ln16129=9.6883741729
16129/9.6883741729=1664.7788072756
1721/1664.7788072756=1.0337709685
b31=1.0337709685

131
ln17161=9.7503946464
17161/9.7503946464=1760.0313240999
1852/1760.0313240999=1.0522539995
b32=1.0522539995

137
ln18769=9.8399618517
18769/9.8399618517=1907.4260940105
1989/1907.4260940105=1.0427664832
b33=1.0427664832

139
ln19321=9.8689478663
19321/9.8689478663=1957.7568208640
2128/1957.7568208640=1.0869582868
b34=1.0869582868

149
ln22201=10.0078926119
22201/10.0078926119=2218.3491431155
2277/2218.3491431155=1.0264389657
b35=1.0264389657

151
ln22801=10.0345596736
22801/10.0345596736=2272.2471878848
2428/2272.2471878848=1.0685457167
b36=1.0685457167

157
ln24649=10.1124916107
24649/10.1124916107=2437.4803904825
2585/2437.4803904825=1.0605213523
b37=1.0605213523

163
ln26569=10.1875004016
26569/10.1875004016=2607.9998971904
2748/2607.9998971904=1.0536810231
b38=1.0536810231

167
ln27889=10.2359876248
27889/10.2359876248=2724.6027469230
2915/2724.6027469230=1.0698807389
b39=1.0698807389

173
ln29929=10.3065831890
29929/10.3065831890=2903.8721612360
3088/2903.8721612360=1.0634076945
b40=1.0634076945

179
ln32041=10.3747716117
32041/10.3747716117=3088.3571416518
3267/3088.3571416518=1.0578439766
b41=1.0578439766

181
ln32761=10.3969940625
32761/10.3969940625=3151.0068970956
3448/3151.0068970956=1.0942533966
b42=1.0942533966

191
ln36481=10.5045468561
36481/10.5045468561=3472.8770788257
3639/3472.8770788257=1.0478343798
b43=1.0478343798

193
ln37249=10.5253803778
37249/10.5253803778=3538.9694873703
3832/3538.9694873703=1.0828010848
b44=1.0828010848

197
ln38809=10.5664074575
38809/10.5664074575=3672.86612 37130
4029/3672.86612 37130=1.0969634787
b45=1.0969634787

199
ln39601=10.5866096494
39601/10.5866096494=3740.6687609611
4228/3740.6687609611=1.1302791747
b46=1.1302791747

211
ln44521=10.7037162670
44521/10.7037162670=4159.3965020598
4439/4159.3965020598=1.06722 21313
b47=1.06722 21313

223
ln49729=10.8143435429
49729/10.8143435429=4598.4298355907
4662/4598.4298355907=1.0138243198
b48=1.0138243198

227
ln51529=10.8499000350
51529/10.8499000350=4749.2603465263
4889/4749.2603465263=1.0294234561
b49=1.0294234561

229
ln52441=10.8674440071
52441/10.8674440071=4825.5137054986
5351/4825.5137054986=1.1088974825
b50=1.1088974825

233
ln54289=10.9020769071
54289/10.9020769071=4979.6933614222
5351/4979.6933614222=1.0745641572
b51=1.0745641572

239
ln57121=10.9529271039
57121/10.9529271039=5215.1355941793
5590/5215.1355941793=1.0718800881
b52=1.0718800881

241
ln58081=10.9695938670
58081/10.9695938670=5294.72655999834
5831/5294.7265599983=1.10128444480
b53=1.10128444480

251
ln63001=11.0509058783
63001/11.0509058783=5700.9805977726
6082/5700.9805977726=1.0668340114
b54=1.0668340114

257
ln66049=11.0981521698
66049/11.0981521698=5951.3510888534
6339/5951.3510888534=1.0651362868
b55=1.0651362868

263
ln69169=11.1443080644
69169/11.1443080644=6206.6661833369
6602/6206.6661833369=1.0636950345
b56=1.0636950345

269
ln72361=11.1894227592
72361/11.1894227592=6466.9108994478
6871/6466.9108994478=1.0624856453
b57=1.0624856453

271
ln73441=11.2042376418
73441/11.2042376418=6554.7520811243
7142/6554.7520811243=1.0895911717
b58=1.0895911717

277
ln76729=11.2480350124
76729/11.2480350124=6821.5470449205
7419/6821.5470449205=1.0875832053
b59=1.0875832053

281
ln78961=11.2767093387
78961/11.2767093387=7002.1313512992
7700/7002.1313512992=1.0996651753
b60=1.0996651753

283
ln80089=11.2908937953
80089/11.2908937953=7093.2382725394
7983/7093.2382725394=1.1254380148
b61=1.1254380148

293
ln85849=11.3603452180
85849/11.3603452180=7556.9006357286
8276/7556.9006357286=1.0951579753
b62=1.0951579753

307
ln94249=11.4536954952
94249/11.4536954952=8228.6978940114
8583/8228.6978940114=1.0430568859
b63=1.0430568859

311
ln96721=11.4795858244
96721/11.4795858244=8425.4781905475
8894/8425.4781905475=1.0556077411
b64=1.0556077411

313
ln97969=11.4924063811
97969/11.4924063811=8524.6724446776
9207/8524.6724446776=1.0800414983
b65=1.0800414983

317
ln100489=11.5178035478
100489/11.5178035478=8724.6669543339
9524/8724.6669543339=1.0916175998
b66=1.0916175998

331
ln109561=11.6042367508
109561/11.6042367508=9441.4654192958
9855/9441.4654192958=1.0437998300
b67=1.0437998300

337
ln113569=11.6401658607
113569/11.6401658607=9756.6479171432
10192/9756.6479171432=1.0446210714
b68=1.0446210714

347
ln120409=11.6986495599
120409/11.6986495599=10292.5555110849
10539/10292.5555110849=1.0239439553
b69=1.0239439553

349
ln121801=11.7101438444
121801/11.7101438444=10401.3239818781
10888/10401.3239818781=1.0467898144
b70=1.0467898144

---

作者: 小草    时间: 2026-5-26 16:33
D(6)=1
1*2=2
ln6=1.79176
(1.79176)^2=3.21040
6/3.21040=1.86893
1.86893*1.32032=2.46759
2.46759*2=4.93518
【】
D(36)=4
4*2=8
ln36=3.58352
(3.58352)^2=12.84162
36/12.84162=2.80338
2.80338*1.32032=3.70135
3.70135*2=7.4027
【】
D(30)=3
3*2=6
ln30=3.40120
(3.40120)^2=11.56816
30/11.56816=2.59333
2.59333*1.32032=3.42403
3.42403*2.66667=9.13075
【】
D(900)=48
48*2=96
(ln900)^2=46.27257
900/46.27257=19.44997
19.44997*1.32032=25.68018
25.68018*2.66667=68.48057
【】
D(210)=19
19*2=38
(ln210)^2=28.59156
210/28.59156=7.34482
7.34482*1.32032=9.69751
9.69751*3.2=31.03203
【】
D(44100)=1007
1007*2=2014
(ln44100)^2=114.36624
44100/114.36624=385.60330
385.60330*1.32032=509.11975
509.11975*3.2=1629.1832
【】
D(2310)=114
114*2=228
(ln2310)^2=59.98507
2310/59.98507=38.50958
38.50958*1.32032=50.84497
50.84497*3.55556=180.78234
【】
D(36960)=980
980*2=1960
(ln36960)^2=110.61973
36960/110.61973=334.11761
334.11761*1.32032=441.14216
441.14216*3.55556=1568.50742
【】
D(30030)=905
905*2=1810
(ln30030)^2=106.29511
30030/106.29511=282.51535
282.51535*1.32032=373.01067
373.01067*3.87878=492.49345

---

作者: 小草    时间: 2026-5-26 16:34
5D(30)=3
7D(210)=19
11D(2310)=114
13D(30030)=905
17D(510510)=9493
19D(9699690)=124180
23D(223092870)=2044847
29D(6469693230)≈44128292
31D(200560490130)≈1015462775

---

作者: 小草    时间: 2026-5-29 15:13
哥德巴赫偶数素数对的真值上限中值与下限
【4(q1)^2】
D(48)=5
(ln48)^2=14.9861972669
48/14.9861972669=3.2029472951
5/3.2029472951=1.5610622153

D(36)=4
(ln36)^2=12.8416079823
36/12.8416079823=2.8033872432
4/2.8033872432=1.4268453314

D(68)=2
(ln68)^2=17.8042452740
68/17.8042452740=3.8193138183
2/3.8193138183=0.5236542728
【4(q2)^2】
D(114)=10
(ln114)^2=22.4315757426
114/22.4315757426=5.0821217960
10/5.0821217960=1.9676820827

D(100)=6
(ln100)^2=21.2075924419
100/21.2075924419=4.7152924253
6/4.7152924253=1.2724555465

D(128)=3
(ln128)^2=23.5421976820
128/23.5421976820=5.4370455014
3/5.4370455014=0.5517702582
【4(q3)^2】
D(510)=32
(ln510)^2=38.8678770970
510/38.8678770970=13.1213752356
32/13.1213752356=2.4387687590

D(484)=14
(ln484)^2=38.2181737939
484/38.2181737939=12.6641320595
14/12.6641320595=1.1054843659

D(488)=9
(ln488)^2=38.3200048239
488/38.3200048239=12.7348626975
9/12.7348626975=0.7067214004
【4(q4)^2】
D(1260)=68
(ln1260)^2=50.9634220429
1260/50.9634220429=24.7236144963
68/24.7236144963=2.7504069039

D(1156)=22
(ln1156)^2=49.7408741983
1156/49.7408741983=23.2404439735
22/23.2404439735=0.9466256335

D(1412)=18
(ln1412)^2=52.6025626927
1412/52.6025626927=26.8427986722
18/26.8427986722=0.6705709125
【4(q5)^2】
D(3570)=154
(ln3570)^2=66.9176496143
3570/66.9176496143=53.3491540809
154/53.3491540809=2.8866437088

D(3364)=47
(ln3364)^2=65.9487897676
3364/65.9487897676=51.0092757100
47/51.0092757100=0.9214010461

D(3632)=40
(ln3632)^2=67.1996413892
3632/67.1996413892=54.0479074727
40/54.0479074727=0.7400841563
【4(q6)^2】
D(6930)=268
(ln6930)^2=78.2095278987
6930/78.2095278987=88.6081298045
268/88.6081298045=3.0245531713

D(6724)=71
(ln6724)^2=77.6766980968
6724/77.6766980968=86.5639266955
71/86.5639266955=0.8202030882

D(7292)=67
(ln7292)^2=79.1127197038
7292/79.1127197038=92.1722831335
67/92.1722831335=0.7268996462
【4(q7)^2】
D(15330)=447
(ln15330)^2=92.8826971372
15330/92.8826971372=165.0468867991
447/165.0468867991=2.7083213060

D(13924)=131
(ln13924)^2=91.0377271445
13924/91.0377271445=152.9475793909
131/152.9475793909=0.8565026038

D(14138)=117
(ln14138)^2=91.3290142406
14138/91.3290142406=154.8029409663
117/154.8029409663=0.7557995944
【4(q8)^2】
D(20790)=615
(ln20790)^2=98.8478852926
20790/98.8478852926=210.3231641067
615/210.3231641067=2.9240716429

D(20164)=175
(ln20164)^2=98.2408872994
20164/98.2408872994=205.2505891824
175/205.2505891824=0.8526163101

D(20348)=155
(ln20348)^2=98.4210405984
20348/98.4210405984=206.7444103038
155/206.7444103038=0.7497179719
【4(q9)^2】
D(43680)=1083
(ln43680)^2=114.1616518202
43680/114.1616518202=382.6153467786
1083/382.6153467786=2.8305189771

D(40804)=309
(ln40804)^2=112.7108237891
40804/112.7108237891=362.0237935298
309/362.0237935298=0.8535350591

D(40814)=280
(ln40814)^2=112.7160268855
40814/112.7160268855=362.0958006394
280/362.0958006394=0.7732760212
【4(q10)^2】
D(46410)=1205
(ln46410)^2=115.4608323638
46410/115.4608323638=401.9544901060
1205/401.9544901060=2.9978518207

D(45796)=333
(ln45796)^2=115.1747943752
45796/115.1747943752=397.6217213882
333/397.6217213882=0.8374793984

D(45998)=296
(ln45998)^2=115.2692799550
45998/115.2692799550=399.0482114398
296/399.0482114398=0.7417650086
【4(q11)^2】
D(76230)=1692
(ln76230)^2=126.3715552860
76230/126.3715552860=603.2211903025
1692/603.2211903025=2.8049412507

D(75076)=483
(ln75076)^2=126.0288285549
75076/126.0288285549=595.7049737021
483/595.7049737021=0.8108040411

D(75188)=447
(ln75188)^2=126.0623009610
75188/126.0623009611=596.4352500848
447/596.4352500848=0.7494526857
【4(q12)^2】
D(90090)=2135
(ln90090)^2=130.1553428017
90090/130.1553428017=692.1728917211
2135/692.1728917211=3.0844894759

D(88804)=549
(ln88804)^2=129.8274967759
88804/129.8274967759=684.0153450181
549/684.0153450181=0.8026135729

D(89372)=521
(ln89372)^2=129.9728301730
89372/129.9728301730=687.6206348745
521/687.6206348745=0.7576852316
【4(q13)^2】
D(131670)=2810
(ln131670)^2=138.95821878901
131670/138.95821878901=947.5510059605
2810/947.5510059605=2.9655395671

D(128164)=755
(ln128164)^2=138.3226728166
128164/138.3226728166=926.5581512434
755/926.5581512434=0.8148436221

D(129524)=704
(ln129524)^2=138.5710720597
129524/138.5710720597=934.711683144
704/934.711683144=0.7531734252
【4(q14)^2】
D(150150)=3215
(ln150150)^2=142.0718597221
150150/142.0718597221=1056.8595377980
3215/1056.8595377980=3.0420314952

D(145924)=841
(ln145924)^2=141.3921048530
145924/141.3921048530=1032.0519674823
841/1032.0519674823=0.8148814464

D(147248)=790
(ln147248)^2=142.6749859886
147248/142.6749859886=1032.0519674820
790/1032.0519674820=0.7654653301
【4(q15)^2】
D(157080)=3320
(ln157080)^2=143.1495117126
157080/143.1495117126=1097.3142564074
3320/1097.3142564074=3.0255690023

D(155236)=852
(ln155236)^2=142.8670807643
155236/142.8670807643=1086.5764119315
852/1086.5764119315=0.7841142055

D(158428)=826
(ln158428)^2=143.3540582555
158428/143.3540582555=1105.1518312627
826/1105.1518312627=0.7474086154
【4(q16)^2】
D(207480)=4033
(ln207480)^2=149.8859125782
207480/149.8859125782=1384.2528389167
4033/1384.2528389167=2.9134850850

D(206116)=1083
(ln206116)^2=149.7244532987
206116/149.7244532987=1376.6355158352
1083/1376.6355158352=0.7867006100

D(206498)=1042
(ln206498)^2=149.7697700476
206498/149.7697700476=1378.7695603350
1042/1378.7695603350=0.7557463045
【4(q17)^2】
D(232050)=4470
(ln232050)^2=152.6388133400
232050/152.6388133400=1520.2555295232
4470/1520.2555295232=2.9402951762

D(228484)=1195
(ln228484)^2=152.2563863619
228484/152.2563863619=1500.6529805385
1195/1500.6529805385=0.7963200124

D(230228)=1142
(ln230228)^2=152.4440974886
230228/152.4440974886=1510.2454197495
1142/1510.2454197495=0.7561684909
【4(q18)^2】5240/2032
D(297990)=5398
(ln297990)^2=158.8813664247
297990/158.8813664247=1875.5503348546
5398/1875.5503348546=2.8780885800

D(289444)=1439
(ln289444)^2=154.3248371537
289444/154.3248371537=1875.5503348546
1439/1875.5503348546=0.7672414721

D(291008)=1385
(ln291008)^2=158.2842291189
291008/158.2842291189=1838.5154454106
1385/1838.5154454106=0.7533251915
【4(q19)^2】
D(324870)=5926
(ln324870)^2=161.0660594705
324870/161.0660594705=2016.9984978089
5926/2016.9984978089=2.9380289606

D(315844)=1544
(ln315844)^2=156.5910933216
315844/156.5910933216=2016.9984978094
1544/2016.9984978094=0.7654938770

D(317972)=1494
(ln317972)^2=160.5217695950
317972/160.5217695950=1980.8652795334
1494/1980.8652795334=0.7542158548
【4(q20)^2】
D(390390)=7094
(ln390390)^2=165.7630891095
390390/165.7630891095=2355.1081371445
7094/2355.1081371445=3.0121759116

D(386884)=1830
(ln386884)^2=165.53087294708465
386884/165.53087294708465=2337.2316783690
1830/2337.2316783690=0.7829775785

D(388142)=1774
(ln388142)^2=165.6144176717
388142/165.6144176717=2343.6486113752
1774/2343.6486113752=0.7569394112
【4(q21)^2】
D(510510)=9493
(ln510510)^2=172.7427994927
510510/172.7427994927=2955.3185516226
9493/2955.3185516226=3.2121748753

D(481636)=2219
(ln481636)^2=171.2157574161
481636/171.2157574161=2813.0354779759
2219/2813.0354779759=0.7888275912

D(482072)=2119
(ln482072)^2=171.2394377557
482072/171.2394377557=2815.1926116912
2119/2815.1926116912=0.7527016060
【4(q22)^2】
D(746130)=12684
(ln746130)^2=182.8622016767
746130/182.8622016767=4080.2855546886
12684/4080.2855546886=3.10860596151781

D(702244)=2977
(ln702244)^2=181.2264186761
702244/181.2264186761=3874.9538016038
2977/3874.9538016038=0.7682672239

D(705542)=2911
(ln705542)^2=181.3525901334
705542/181.3525901334=3890.4434697129
2911/3890.4434697129=0.7482437472
【4(q23)^2】
D(746130)=12684
(ln746130)^2=182.8622016767
746130/182.8622016767=4080.2855546886
12684/4080.2855546886=3.1086059615

D(743044)=3214
(ln743044)^2=182.7501272560
743044/182.7501272560=4065.9014095193
3214/4065.9014095193=0.7904766192

D(744428)=3076
(ln744428)^2=182.8004432598
744428/182.8004432598=4072.3533637279
3076/4072.3533637279=0.7553372032
【4(q24)^2】
D(863940)=13626
(ln863940)^2=212.1476018498
863940/212.1476018498=4072.3533637287
13626/4072.3533637287=3.3459768303

D(850084)=3499
(ln850084)^2=186.4068787571
850084/186.4068787571=4560.3681884922
3499/4560.3681884922=0.7672626102

D(850118)=3443
(ln850118)^2=186.4079708761
850118/186.4079708761=4560.5238660371
3443/4560.5238660371=0.7549571280
【4(q25)^2】
D(1111110)=17629
(ln1111110)^2=193.7906236067
1111110/193.7906236067=5733.5591336710
17629/5733.5591336710=3.0747044879

D(1085764)=4343
(ln1085764)^2=193.1486904251
1085764/193.1486904251=5621.3893949286
4343/5621.3893949286=0.7725847998

D(1086728)=4244
(ln1086728)^2=193.1733586908
1086728/193.1733586908=5625.6618788694
4244/5625.6618788694=0.7544001206
【4(q26)^2】
D(1345890)=20104
(ln1345890)^2=199.1645208606
1345890/199.1645208606=6757.6795012703
20104/6757.6795012703=2.9749857175

D(1295044)=5060
(ln1295044)^2=198.0790305994
1295044/198.0790305994=6538.0166496227
5060/6538.0166496227=0.7739350129

D(1295642)=4938
(ln1295642)^2=198.0920254945
1295642/198.0920254945=6540.6065527659
4938/6540.6065527659=0.7549758513
【4(q27)^2】

D(1452990)=21618
(ln1452990)^2=201.3315253788
1452990/201.3315253788=7216.9025554554
21618/7216.9025554554=2.9954679080

D(1435204)=5492
(ln1435204)^2=200.9821560544
1435204/200.9821560544=7140.9523520662
5492/7140.9523520662=0.7690850925

D(1436924)=5381
(ln1436924)^2=201.0161171580
1436924/201.0161171580=7148.3024362199
5381/7148.3024362199=0.7527661355
【4(q28)^2】
D(1531530)=24044
(ln1531530)^2=202.8282347252
1531530/202.8282347252=7550.8718106973
24044/7550.8718106973=3.1842680690

D(1522756)=5857
(ln1522756)^2=202.6646187481
1522756/202.6646187481=7513.6746088507
5857/7513.6746088507=0.7795120637

D(1525532)=5648
(ln1525532)^2=202.7164796811
1525532/202.7164796811=7525.4463889658
5648/7525.4463889658=0.7505202626
【4(q29)^2】
D(1651650)=24111
(ln1651650)^2=204.9846596848
1651650/204.9846596848=8057.4322124383
24111/8057.4322124383=2.9923925345

D(1643524)=6210
(ln1643524)^2=204.8434562673
1643524/204.8434562673=8023.3170731867
6210/8023.3170731867=0.7739940904

D(1644044)=6062
(ln1644044)^2=204.8525116006
1644044/204.8525116006=8025.5008208315
6062/8025.5008208315=0.7553422690
【4(q30)^2】
D(1806420)=26597
(ln1806420)^2=207.5575442949
1806420/207.5575442949=8703.2249593078
26597/8703.2249593078=3.0559936259

D(1737124)=6507
(ln1737124)^2=206.4319938029
1737124/206.4319938029=8414.9940520295
6507/8414.9940520295=0.7732625787

D(1737686)=6348
(ln1737686)^2=206.4412890008
1737686/206.4412890008=8417.3374832651
6348/8417.3374832651=0.7541577147
【4(q31)^2】
D(2709630)=37527
(ln2709630)^2=219.4049023520
2709630/219.4049023520=12349.9063646847
37527/12349.9063646847=3.0386465202

D(2617924)=9154
(ln2617924)^2=218.3860977340
2617924/218.3860977340=11987.5945729325
9154/11987.5945729325=0.7636227555

D(2619728)=9023
(ln2619728)^2=218.4064579565
2619728/218.4064579565=11994.7368979436
9023/11994.7368979436=0.7522465959
【4(q32)^2】
D(2709630)=37527
(ln2709630)^2=219.4049023520
2709630/219.4049023520=12349.9063646847
37527/12349.9063646847=3.0386465202

D(2696164)=9361
(ln2696164)^2=219.2573350528
2696164/219.2573350528=12296.8018349340
9361/12296.8018349340=0.7612548470

D(2704766)=9251
(ln2704766)^2=219.3516792134
2704766/219.3516792134=12330.7284890608
9251/12330.7284890608=0.7502395344
【4(q33)^2】
D(2762760)=39092
(ln2762760)^2=219.9805333200
2762760/219.9805333200=12559.1112918209
39092/12559.1112918209=3.1126406233

D(2735716)=9551
(ln2735716)^2=219.6888308089
2735716/219.6888308089=12452.6858735923
9551/12452.6858735923=0.7669831309

D(2741798)=9390
(ln2741798)^2=219.7546662290
2741798/219.7546662290=12476.6315412063
9390/12476.6315412063=0.7526069812

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作者: 小草    时间: 2026-5-30 08:39
施承忠哥德巴赫偶数素数对数D(x)分段系数法

4(qk)^2≤x<4(qk+1)^2；D(2n)≈dk*2n/ln^2(2n)

d1=1.0701339985
d2=1.6966073953
d3=1.5003002109
d4=1.5490237640
d5=1.2742780425
d6=1.2245285542
d7=1.0788009896
d8=1.1498139954
d9=0.9308780418
d10=1.1166391978
d11=0.9753150060
d12=1.0672275196
d13=0.9810501357
d14=1.0658378014
d15=1.1936574232
d16=1.1070468417
d17=1.1748219094
d18=1.1102599444
d19=1.1742929922
d20=1.1226957192



比如D(100)=6，4(q2)^2=100,4(q3)^2=484.100=100<484,取密度系数
d2=1.6966073953.
100/(ln100)^2=4.7152924253
4.7152924253*1.6966073953=7.9999999998
4.7152924253*0.6601618158=3.1128560095
7.9999999998*1.3333333333=10.66666666613
3.1128560095*1.3333333333=4.1504746792

比如D(1000)=28，4(q3)^2=484,4(q4)^2=1156.484<1000<1156,取密度系数d3=1.5003002109
1000/(ln1000)^2=20.9568552235
20.9568552235*1.5003002109=31.4415743116
20.9568552235*0.6601618158=13.8349155978
31.4415743116*1.3333333333=41.9220990811
13.8349155978*1.3333333333=18.4465541299

比如D(10000)=127，4(q6)^2=6724,4(q7)^2=13924.
6724<10000<13924,取密度系数d6=1.2245285542
10000/(ln10000)^2=117.8823106323
117.8823106323*1.2245285542=144.3502554043
117.8823106323*0.6601618158=77.8214002377
144.3502554043*1.3333333333=192.4670072009
77.8214002377*1.3333333333=103.7618669810

比如D(100000)=810，4(q12)^2=75188,4(q13)^2=128164.
75188<100000<128164,取密度系数1.0672275196
100000/(ln100000)^2=754.4467880462
754.4467880462*1.0672275196=805.1663742767
754.4467880462*0.6601618158=498.0569615211
805.1663742767*1.3333333333=1073.5551656754
498.0569615211*1.3333333333=664.0759486782

比如D(10^6)=5402，4(q24)^2=850084,4(q25)^2=1085764.
850084<10^6<1085764,取密度系数d24=0.8172981975
10^6/(ln10^6)^2=5239.2138058788
5239.2138058788*0.8172981975=4281.9999998619
5239.2138058788*0.6601618158=3458.7288994534
4281.9999998619*1.3333333333=5709.3333330065
3458.7288994534*1.3333333333=4611.6385324892

比如D(10^7)=38807，4(q50)^2=8844676,4(q)^2=10329796.
8844676<10^7<10329796,取密度系数d50=0.7987595806
10^7/ln10^7=38492.1830636008
38492.1830636008*0.7987595806=30746.0000002602
38492.1830636008*0.6601618158=25411.0694653727
30746.0000002602*1.3333333333=40994.6666659887
25411.0694653727*1.3333333333=33881.4259529832

比如D(10^8)=291400，4(q126)^2=98684356,4(q127)^2=100360324.
98684356<10^8<100360324,取密度系数d126=0.9404091200
10^8/ln10^8=294705.7765806619
294705.7765806619*0.9404091200=277144.0000131369
294705.7765806619*0.6601618158=194553.5005942389
277144.0000131369*1.3333333333=369525.3333416111
194553.5005942389*1.3333333333=259404.6674525001

比如D(10^9)=2274205，4(q282)^2=990612676,
4(q283)^2=1009587076.
990612676<10^9<1009587076,取密度系数d282=0.7919290286
10^9/ln10^9=2328539.4692789145
2328539.4692789145*0.7919290286=1844037.9999628103
2328539.4692789145*0.6601618158=1537212.8442011365
1844037.9999628103*1.3333333333=2458717.3332222791
1537212.8442011365*1.3333333333=2049617.1255502749

比如D(10^10)=18200488，4(q705)^2=9996400324,
4(q706)^2=10008401764.
9996400324<10^9<10008401764,取密度系数d705=0.8201615936
10^10/ln10^10=18861169.7011628088
18861169.7011628088*0.8201615936=15469206.9992657250
18861169.7011628088*0.6601618158=12451424.0380315832
15469206.999265725038*1.3333333333=20625609.3318386598
12451424.038031583229*1.3333333333=16601898.7169603968

---

作者: 小草    时间: 2026-5-30 08:41
施承忠哥德巴赫偶数素数对数D(x)真值分段系数法

d1=1.4268453314
d2=1.2724555465
d3=1.1054843659
d4=0.9466256335
d5=0.9214010461
d6=0.8202030882
d7=0.8565026038
d8=0.8526163101
d9=0.8535350591
d10=0.8374793984
d11=0.8108040411
d12=0.8026135729
d13=0.8148436221
d14=0.8148814464
d15=0.7841142055
d16=0.7867006100
d17=0.7963200124
d18=0.7862519980
d19=0.7838773800
d20=0.7829775785









比如D(100)=6，4(q2)^2=100,4(q3)^2=484.100=100<484,取密度系数
d2=1.2724555465.
100/(ln100)^2=4.7152924253
4.7152924253*1.2724555465=5.9999999999
4.7152924253*0.6601618158=3.1128560095
3.1128560095*1.3333333333=4.1504746792

比如D(1000)=28，4(q3)^2=484,4(q4)^2=1156.484<1000<1156,取密度系数d3=1.1054843659
1000/(ln1000)^2=20.9568552235
20.9568552235*1.1054843659=23.1674758080
20.9568552235*0.6601618158=13.8349155978
23.1674758080*1.3333333333=30.8899677432
13.8349155978*1.3333333333=18.4465541299

比如D(10000)=127，4(q6)^2=6724,4(q7)^2=13924.
6724<10000<13924,取密度系数d6=0.8202030882
10000/(ln10000)^2=117.8823106323
117.8823106323*0.8202030882=96.6874352248
117.8823106323*0.6601618158=77.8214002377
96.6874352248*1.3333333333=128.9165802965
77.8214002377*1.3333333333=103.7618669810

比如D(100000)=810，4(q12)^2=75188,4(q13)^2=128164.
75188<100000<128164,取密度系数d12=0.8026135729
100000/(ln100000)^2=754.4467880462
754.4467880462*0.8026135729=605.5292321167
754.4467880462*0.6601618158=498.0569615211
605.5292321167*1.3333333333=807.3723094687
498.0569615211*1.3333333333=664.0759486782

比如D(10^6)=5402，4(q24)^2=850084,4(q25)^2=1085764.
850084<10^6<1085764,取密度系数d24=0.6678482936
10^6/(ln10^6)^2=5239.2138058788
5239.2138058788*0.6678482936=3499.0000000617
5239.2138058788*0.6601618158=3458.7288994534
3499.0000000617*1.3333333333=4665.3333332990
3458.7288994534*1.3333333333=4611.6385324892

比如D(10^7)=38807，4(q50)^2=8844676,4(q)^2=10329796.
8844676<10^7<10329796,取密度系数d50=0.6845285952
10^7/ln10^7=38492.1830636008
38492.1830636008*0.6845285952=26348.9999987079
38492.1830636008*0.6601618158=25411.0694653727
26348.9999987079*1.3333333333=35131.9999973989
25411.0694653727*1.3333333333=33881.4259529832

比如D(10^8)=291400，4(q126)^2=98684356,4(q127)^2=100360324.
98684356<10^8<100360324,取密度系数d126=0.7327104426
10^8/ln10^8=294705.7765806619
294705.7765806619*0.7327104426=215933.9999951935
294705.7765806619*0.6601618158=194553.5005942389
215933.9999951935*1.3333333333=287911.9999863935
194553.5005942389*1.3333333333=259404.6674525001

---

作者: 小草    时间: 2026-5-30 08:44
【3】1-(1/4)=0.75
【5】1-(1/16)=0.9375=0.703125
【7】1-(1/36)=0.9722222222=0.6835937500
【11】1-(1/100)=0.99=0.6767578125
【13】1-(1/144)=0.9930555556=0.6720581055
【17】1-(1/256)=0.99609375=0.6694328785
【19】1-(1/324)=0.99691358=0.6673667275=1.334733455

---

作者: 小草    时间: 2026-6-6 08:36
夹逼定理
提出者
拉格朗日

提出时间
1835年

1、函数夹逼定理

f(x)与g(x)在x0处连续且存在相同的极限A，即x→ x0时, lim f(x)=lim g(x)=A,则若有函数k(x)在x0 的某邻域内(如x0∈(x1,x2))，恒有f(x)≤k(x)≤g(x),则当X趋近x0时 ,有lim f(x)≤lim k(x)≤lim g(x)，即A≤lim k(x)≤A

故 lim k(x)=A。

简单地说：函数A>B,函数B>C，函数A的极限是X，函数C的极限也是X ，那么函数B的极限就一定是X，这个就是夹逼定理。[1]

2、数列夹逼定理

夹逼定理的极限定义是：

如果数列{Xn},{Yn}及{Zn}满足下列条件：

(1)当n>N0时，其中N0∈N*，有Yn≤Xn≤Zn，

(2){Yn}、{Zn}有相同的极限a，设-∞

则，数列{Xn}的极限存在，且当 n→+∞，limXn =a。[2]

---

作者: 小草    时间: 2026-6-6 08:36
夹逼定理
提出者
拉格朗日

提出时间
1835年

1、函数夹逼定理

f(x)与g(x)在x0处连续且存在相同的极限A，即x→ x0时, lim f(x)=lim g(x)=A,则若有函数k(x)在x0 的某邻域内(如x0∈(x1,x2))，恒有f(x)≤k(x)≤g(x),则当X趋近x0时 ,有lim f(x)≤lim k(x)≤lim g(x)，即A≤lim k(x)≤A

故 lim k(x)=A。

简单地说：函数A>B,函数B>C，函数A的极限是X，函数C的极限也是X ，那么函数B的极限就一定是X，这个就是夹逼定理。[1]

2、数列夹逼定理

夹逼定理的极限定义是：

如果数列{Xn},{Yn}及{Zn}满足下列条件：

(1)当n>N0时，其中N0∈N*，有Yn≤Xn≤Zn，

(2){Yn}、{Zn}有相同的极限a，设-∞

则，数列{Xn}的极限存在，且当 n→+∞，limXn =a。[2]

---

作者: 小草    时间: 2026-6-6 09:16
【4(q34)^2】
D(2984520)=41084
(ln2984520)^2=222.2767748315
2984520/222.2767748315=13427.0438387567
41084/13427.0438387567=3.0597948806

D(2937796)=10020
(ln2984520)^2=221.8065185560
2937796/221.8065185560=13244.8587134660
10020/13244.8587134660=0.7565199612
【4(q35)^2】
D(3273270)=43574
(ln3273270)^2=225.0390029863
3273270/225.0390029863=14545.3452804324
43574/14545.3452804324=2.9957350039

D(3104644)=10608
(ln3104644)^2=223.4549499578
3104644/223.4549499578=13893.8251338192
10608/13893.8251338192=0.7635046431
【4(q36)^2】
D(4354350)=56891
(ln4354350)^2=233.6827659091
4354350/233.6827659091=18633.5949211325
56891/18633.5949211325=3.0531413955

D(4153444)=13708
(ln4153444)^2=232.2407883764
4153444/232.2407883764=17884.2141771771
13708/17884.2141771771=0.7664860119
【4(q37)^2】
D(4354350)=56891
(ln4354350)^2=233.6827659091
4354350/233.6827659091=18633.5949211325
56891/18633.5949211325=3.0531413955

D(4251844)=14018
(ln4251844)^2=232.9549970044
4251844/232.9549970044=18251.7827678094
14018/18251.7827678094=0.7680345629
【4(q38)^2】
D(4444440)=57591
(ln4444440)^2=234.3092830322
4444440/234.3092830322=18968.2625565852
57591/18968.2625565852=3.0361768680

D(4401604)=14451
(ln4401604)^2=234.0128814366
4401604/234.0128814366=18809.2380768898
14451/18809.2380768898=0.7682926837
【4(q39)^2】
D(4564560)=60707
(ln4564560)^2=235.1264247142
4564560/235.1264247142=19413.2157010778
60707/19413.2157010778=3.1270965581

D(4502884)=14736
(ln4502884)^2=234.7094055313
4502884/234.7094055313=19184.9320644268
14736/19184.9320644268=0.7681027981
【4(q40)^2】
D(4834830)=63128
(ln4834830)^2=236.8938557093
4834830/236.8938557093=20409.2672033376
63128/20409.2672033376=3.0931046848

D(4761124)=15350
(ln4761124)^2=236.4212017219
4761124/236.4212017219=20138.3123227690
15350/20138.3123227690=0.7622287188
【4(q41)^2】
D(5419260)=68139
(ln5419260)^2=240.4195947337
5419260/240.4195947337=22540.8415898988
68139/22540.8415898988=3.0229128637

D(5299204)=16768
(ln5299204)^2=239.7253692559
5299204/239.7253692559=22105.3116591229
16768/22105.3116591229=0.7585507166
【4(q42)^2】
D(6096090)=76090
(ln6096090)^2=244.0830702680
6096090/244.0830702680=24975.4724623325
76090/24975.4724623325=3.0465890130

D(6041764)=18859
(ln6041764)^2=243.8034471308
6041764/243.8034471308=24781.2903020957
18859/24781.2903020957=0.7610176779
【4(q43)^2】
D(6636630)=84638
(ln6636630)^2=246.7448725333
6636630/246.7448725333=26896.7291269825
84638/26896.7291269825=3.1467766806

D(6522916)=20045
(ln6522916)^2=246.2022111489
6522916/246.2022111489=26494.1406072711
20045/26494.1406072711=0.7565823816
【4(q44)^2】
D(6846840)=85946
(ln6846840)^2=247.7254949202
6846840/247.7254949202=27638.8185326084
85946/27638.8185326084=3.1096119358

D(6646084)=20440
(ln6646084)^2=246.7895957042
6646084/246.7895957042=26930.1628418969
20440/26930.1628418969=0.7590002378
【4(q45)^2】
D(6846840)=85946
(ln6846840)^2=247.7254949202
6846840/247.7254949202=27638.8185326084
85946/27638.8185326084=3.1096119358

D(6770404)=20856
(ln6770404)^2=247.3722273887
6770404/247.3722273887=27369.2971578477
20856/27369.2971578477=0.7620217604
【4(q46)^2】
D(7147140)=90159
(ln7147140)^2=249.0785576025
7147140/249.0785576025=28694.3206544740
90159/28694.3206544740=3.1420503411

D(6959044)=21321
(ln6959044)^2=248.2374398286
6959044/248.2374398286=28033.8211867033
21321/28033.8211867033=0.7605456230
【4(q47)^2】
D(8168160)=100898
(ln8168160)^2=253.3112326230
8168160/253.3112326230=32245.5499324681
100898/32245.5499324681=3.1290519222

D(8145316)=24354
(ln8145316)^2=253.2220921508
8145316/253.2220921508=32166.6878699875
24354/32166.6878699875=0.7571186719
【4(q48)^2】
D(8558550)=104491
(ln8558550)^2=254.7995335727
8558550/254.7995335727=33589.3472016818
104491/33589.3472016818=3.1108374739

D(8421604)=25173
(ln8421604)^2=254.2848302634
8421604/254.2848302634=33118.7825529211
25173/33118.7825529211=0.7600822874
【4(q49)^2】
D(8978970)=107736
(ln8978970)^2=256.3327715711
8978970/256.3327715711=35028.5683136285
107736/35028.5683136285=3.0756609587

D(8773444)=26088
(ln8773444)^2=255.5918424868
8773444/255.5918424868=34325.9937979167
26088/34325.9937979167=0.7600071291
【4(q50)^2】
D(8978970)=107736
(ln8978970)^2=256.3327715711
8978970/256.3327715711=35028.5683136285
107736/35028.5683136285=3.0756609587

D(8844676)=26349
(ln8844676)^2=255.8504619732
8844676/255.8504619732=34569.7089299236
26349/34569.7089299236=0.7621990701
【4(q51)^2】
D(10720710)=127810
(ln10720710)^2=262.0412409321
10720710/262.0412409321=40912.3005289764
127810/40912.3005289764=3.1239993437

D(10329796)=29943
(ln10329796)^2=260.8400421858
10329796/260.8400421858=39602.0331596249
29943/39602.0331596249=0.7560975438
【4(q52)^2】
D(10720710)=127810
(ln10720710)^2=262.0412409321
10720710/262.0412409321=40912.3005289764
127810/40912.3005289764=3.1239993437

D(10484644)=30407
(ln10484644)^2=261.3208771181
10484644/261.3208771181=40121.7235898899
30407/40121.7235898899=0.7578687374
【4(q53)^2】
D(11231220)=133240
(ln11231220)^2=263.5495080363
11231220/263.5495080363=42615.2189912381
133240/42615.2189912381=3.1265825485

D(11115556)=31904
(ln11115556)^2=263.2135076173
11115556/263.2135076173=42230.1883388200
31904/42230.1883388200=0.7554785156
【4(q54)^2】
D(11741730)=145183
(ln11741730)^2=264.9947623109
11741730/264.9947623109=44309.2908614708
145183/44309.2908614708=3.2765814387

D(11519236)=32960
(ln11519236)^2=264.3722797764
11519236/264.3722797764=43572.0265745815
32960/43572.0265745815=0.7564486344
【4(q55)^2】
D(12552540)=145249
(ln12552540)^2=267.1731993596
12552540/267.1731993596=46982.7813197124
145249/46982.7813197124=3.0915368550

D(11847364)=33606
(ln11847364)^2=265.2864334501
11847364/265.2864334501=44658.7631561961
33606/44658.7631561961=0.7525062860
【4(q56)^2】
D(13123110)=158471
(ln13123110)^2=268.6283419852
13123110/268.6283419852=48852.2912475223
158471/48852.2912475223=3.2438806032

D(12773476)=36202
(ln12773476)^2=267.7438874303
12773476/267.7438874303=47707.8155643245
36202/47707.8155643245=0.7588274494
【4(q57)^2】
D(14264250)=162542
(ln14264250)^2=271.3685245006
14264250/271.3685245006=52564.1285268825
162542/52564.1285268825=3.0922609117

D(14002564)=38868
(ln14002564)^2=270.7588309218
14002564/270.7588309218=51716.0011081751
38868/51716.0011081751=0.7515662303
【4(q58)^2】
D(14264250)=162542
(ln14264250)^2=271.3685245006
14264250/271.3685245006=52564.1285268825
162542/52564.1285268825=3.0922609117

D(14092516)=38985
(ln14092516)^2=270.9696053096
14092516/270.9696053096=52007.7371183325
38985/52007.7371183325=0.7496000049
【4(q59)^2】
D(15825810)=185193
(ln15825810)^2=274.8019919547
15825810/274.8019919547=57589.8663886280
185193/57589.8663886280=3.2157219944

D(14915044)=41034
(ln14915044)^2=272.8403902848
14915044/272.8403902848=54665.8212313477
41034/54665.8212313477=0.7506335600
【4(q60)^2】
D(15825810)=185193
(ln15825810)^2=274.8019919547
15825810/274.8019919547=57589.8663886280
185193/57589.8663886280=3.2157219944

D(15194404)=41717
(ln15194404)^2=273.4537737948
15194404/273.4537737948=55564.7990852081
41717/55564.7990852081=0.7507810824
【4(q61)^2】
D(16546530)=191899
(ln16546530)^2=276.2804777330
16546530/276.2804777330=59890.3336774693
191899/59890.3336774693=3.2041731648

D(15952036)=43664
(ln15952036)^2=275.0654434266
15952036/275.0654434266=57993.6025451948
43664/57993.6025451948=0.7529106330
【4(q62)^2】
D(16546530)=191899
(ln16546530)^2=276.2804777330
16546530/276.2804777330=59890.3336774693
191899/59890.3336774693=3.2041731648

D(16434916)=44722
(ln16434916)^2=276.0555218798310
16434916/276.0555218798310=59534.8207059384
44722/59534.8207059384=0.7511906389
【4(q63)^2】
D(17687670)=202765
(ln17687670)^2=278.5019717735
17687670/278.5019717735=63510.0350901107
202765/63510.0350901107=3.1926450633

D(17322244)=46950
(ln17322244)^2=277.8056233836
17322244/277.8056233836=62353.8277916033
46950/62353.8277916033=0.7529609915
【4(q64)^2】
D(17687670)=202765
(ln17687670)^2=278.5019717735
17687670/278.5019717735=63510.0350901107
202765/63510.0350901107=3.1926450633

D(17422276)=47556
(ln17422276)^2=277.9976048724
17422276/277.9976048724=62670.5974966826
47556/62670.5974966826=0.7588247424
【4(q65)^2】
D(18378360)=204319
(ln18378360)^2=279.7819724721
18378360/279.7819724721=65688.1493743586
204319/65688.1493743586=3.1104392793

D(17825284)=48013
(ln17825284)^2=271.3622498088
17825284/271.3622498088=65688.1493743495
48013/65688.1493743495=0.7309233166
【4(q66)^2】
D(18378360)=204319
(ln18378360)^2=279.7819724721
18378360/279.7819724721=65688.1493743586
204319/65688.1493743586=3.1104392793

D(18130564)=48769
(ln18130564)^2=279.3280355403
18130564/279.3280355403=64907.7847303452
48769/64907.7847303452=0.7513582570
【4(q67)^2】
D(18378360)=204319
(ln18378360)^2=279.7819724721
18378360/279.7819724721=65688.1493743586
204319/65688.1493743586=3.1104392793

D(18335524)=49551
(ln18335524)^2=279.7039143074
18335524/279.7039143074=65553.3335863470
49551/65553.3335863470=0.7558883323
【4(q68)^2】
D(20930910)=234553
(ln20930910)^2=284.1496015624
20930910/284.1496015624=73661.5849007394
234553/73661.5849007394=3.1841970318

D(20016676)=53081
(ln20016676)^2=282.6459089824
20016676/282.6459089824=70818.9128654482
53081/70818.9128654482=0.7495314154
【4(q69)^2】
D(20930910)=234553
(ln20930910)^2=284.1496015624
20930910/284.1496015624=73661.5849007394
234553/73661.5849007394=3.1841970318

D(20557156)=54331
(ln20557156)^2=283.5424798600
20557156/283.5424798600=72501.1504806975
54331/72501.1504806975=0.7493812117
【4(q70)^2】
D(21411390)=236952
(ln21411390)^2=284.9152780286
21411390/284.9152780286=75150.0240638226
236952/75150.0240638226=3.1530528826

D(21325924)=56251
(ln21325924)^2=284.7802720076
21325924/284.7802720076=74885.5384176010
56251/74885.5384176010=0.7511597191
【4(q71)^2】
D(21951930)=244226
(ln21951930)^2=285.7575770392
21951930/285.7575770392=76820.1152440086
244226/76820.1152440086=3.1791933561

D(21883684)=57457
(ln21883684)^2=285.6523155942
21883684/285.6523155942=76609.5102519251
57457/76609.5102519251=0.7499982680
【4(q72)^2】
D(22822800)=244926
(ln22822800)^2=287.0744184302
22822800/287.0744184302=79501.3367084437
244926/79501.3367084437=3.0807783886

D(22676644)=59359
(ln22676644)^2=286.8567542601
22676644/286.8567542601=79052.1529063894
59359/79052.1529063894=0.7508840407
【4(q73)^2】
D(26036010)=276536
(ln26036010)^2=291.5553223545
26036010/291.5553223545=89300.4106038682
276536/89300.4106038682=3.0966934881

D(25989604)=67155
(ln25989604)^2=291.4944030654
25989604/291.4944030654=89159.8731457254
67155/89159.8731457254=0.7531975723
【4(q74)^2】
D(27057030)=291909
(ln27057030)^2=292.8704248177
27057030/292.8704248177=92385.6685660285
291909/92385.6685660285=3.1596783844

D(26853124)=68708
(ln26853124)^2=292.6115658249
26853124/292.6115658249=91770.5488650063
68708/91770.5488650063=0.7486933537
【4(q75)^2】
D(28318290)=300072
(ln28318290)^2=294.4319139482
28318290/294.4319139482=96179.4175782931
300072/96179.4175782931=3.1199190799

D(28238596)=71695
(ln28238596)^2=294.3352071087
28238596/294.3352071087=95940.2589903942
71695/95940.2589903942=0.7472879556
【4(q76)^2】
D(29099070)=323202
(ln29099070)^2=295.3660469640
29099070/295.3660469640=98518.6696274087
323202/98518.6696274087=3.2806167727

D(28879876)=73339
(ln28879876)^2=295.1062074796
28879876/295.1062074796=97862.6517098811
73339/97862.6517098811=0.7494074473
【4(q77)^2】
D(31141110)=329308
(ln31141110)^2=297.7018745541
31141110/297.7018745541=104605.0181801622
329308/104605.0181801622=3.1481090079

D(29398084)=74518
(ln29398084)^2=295.7175507412
29398084/295.7175507412=99412.7129969638
74518/99412.7129969638=0.7495821988
【4(q78)^2】
D(31141110)=329308
(ln31141110)^2=297.7018745541
31141110/297.7018745541=104605.0181801622
329308/104605.0181801622=3.1481090079

D(29789764)=75308
(ln29789764)^2=296.1729274607
29789764/296.1729274607=100582.3329478785
75308/100582.3329478785=0.7487199570
【4(q79)^2】
D(31141110)=329308
(ln31141110)^2=297.7018745541
31141110/297.7018745541=104605.0181801622
329308/104605.0181801622=3.1481090079

D(31114084)=78355
(ln31114084)^2=297.6719142610
31114084/297.6719142610=104524.7553073450
78355/104524.7553073450=0.7496310302
【4(q80)^2】
D(31651620)=339780
(ln31651620)^2=298.2632582933
31651620/298.2632582933=106119.7419390996
339780/106119.7419390996=3.2018547519

D(31382404)=78988
(ln31382404)^2=297.9682862001
31382404/297.9682862001=105321.2890546520
78988/105321.2890546520=0.7499718310
【4(q81)^2】
D(37267230)=384496
(ln37267230)^2=303.9312787641
37267230/303.9312787641=122617.2908281856
384496/122617.2908281856=3.1357404604

D(35259844)=87432
(ln35259844)^2=302.0037576420
35259844/302.0037576420=116752.9976292466
87432/116752.9976292466=0.7488629995
【4(q82)^2】
D(37267230)=384496
(ln37267230)^2=303.9312787641
37267230/303.9312787641=122617.2908281856
384496/122617.2908281856=3.1357404604

D(35976004)=88830
(ln35976004)^2=302.7030252886
35976004/302.7030252886=118849.1722727255
88830/118849.1722727255=0.7474179105
【4(q83)^2】
D(41351310)=415542
(ln41351310)^2=307.5679279523
41351310/307.5679279523=134446.1052077351
415542/134446.1052077351=3.0907700848

D(38912644)=95230
(ln38912644)^2=305.4395796602
38912644/305.4395796602=127398.8264497028
95230/127398.8264497028=0.7474951116
【4(q84)^2】
D(41351310)=415542
(ln41351310)^2=307.5679279523
41351310/307.5679279523=134446.1052077351
415542/134446.1052077351=3.0907700848

D(40119556)=97802
(ln40119556)^2=306.5081602795
40119556/306.5081602795=130892.2932538423
97802/130892.2932538423=0.7471944877
【4(q85)^2】
D(42822780)=435182
(ln42822780)^2=308.7955946353
42822780/308.7955946353=138676.7840732165
435182/138676.7840732165=3.1381027683

D(42276004)=102291
(ln42276004)^2=308.3441247575
42276004/308.3441247575=137106.5657023572
102291/137106.5657023572=0.7460693037
【4(q86)^2】
D(42822780)=435182
(ln42822780)^2=308.7955946353
42822780/308.7955946353=138676.7840732165
435182/138676.7840732165=3.1381027683

D(42432196)=102770
(ln42432196)^2=308.4736508477
42432196/308.4736508477=137555.3337647943
102770/137555.3337647943=0.7471175213
【4(q87)^2】
D(43903860)=448522
(ln43903860)^2=309.6724567915
43903860/309.6724567915=141775.1531889067
448522/141775.1531889067=3.1636149911

D(43533604)=105168
(ln43533604)^2=309.3744584063
43533604/309.3744584063=140714.9259323390
105168/140714.9259323390=0.7473834016
【4(q88)^2】
D(44414370)=458051
(ln44414370)^2=310.0794738845
44414370/310.0794738845=143235.4403972696
458051/143235.4403972696=3.1978887259

D(44328964)=106720
(ln44328964)^2=310.0116901426
44328964/310.0116901426=142991.2658442314
106720/142991.2658442314=0.7463392912
【4(q89)^2】
D(46260060)=460404
(ln46260060)^2=311.5150698103
46260060/311.5150698103=148500.2315559581
460404/148500.2315559581=3.1003588020

D(45131524)=108242
(ln45131524)^2=310.6438518055
45131524/310.6438518055=145283.8153328645
108242/145283.8153328645=0.7450382532
【4(q90)^2】
D(46260060)=460404
(ln46260060)^2=311.5150698103
46260060/311.5150698103=148500.2315559581
460404/148500.2315559581=3.1003588020

D(45454564)=109170
(ln45454564)^2=310.8953158366
45454564/310.8953158366=146205.3678026142
109170/146205.3678026142=0.7466894112
【4(q91)^2】
D(46260060)=460404
(ln46260060)^2=311.5150698103
46260060/311.5150698103=148500.2315559581
460404/148500.2315559581=3.1003588020

D(45941284)=110484
(ln45941284)^2=311.2710278328
45941284/311.2710278328=147592.5476259791
110484/147592.5476259791=0.7485743811
【4(q92)^2】
D(48498450)=505193
(ln48498450)^2=313.1853095883
48498450/313.1853095883=154855.4434553587
505193/154855.4434553587=3.2623522217

D(47914084)=114347
(ln47914084)^2=312.7563971180
47914084/312.7563971180=153199.3731911500
114347/153199.3731911500=0.7463933933
【4(q93)^2】
D(48498450)=505193
(ln48498450)^2=313.1853095883
48498450/313.1853095883=154855.4434553587
505193/154855.4434553587=3.2623522217

D(48080356)=115029
(ln48080356)^2=312.8789374637
48080356/312.8789374637=153670.7980081857
115029/153670.7980081857=0.7485416975
【4(q94)^2】
D(51111060)=505971
(ln51111060)^2=315.0451574276
51111060/315.0451574276=162234.0759570182
505971/162234.0759570182=3.1187714234

D(49758916)=118090
(ln49758916)^2=314.0941031444
49758916/314.0941031444=158420.4080938256
118090/158420.4080938256=0.7454216374
【4(q95)^2】
D(51111060)=505971
(ln51111060)^2=315.0451574276
51111060/315.0451574276=162234.0759570182
505971/162234.0759570182=3.1187714234

D(50098084)=118748
(ln50098084)^2=314.3349334481
50098084/314.3349334481=159378.0349210589
118748/159378.0349210589=0.7450713021
【4(q96)^2】
D(51111060)=505971
(ln51111060)^2=315.0451574276
51111060/315.0451574276=162234.0759570182
505971/162234.0759570182=3.1187714234

D(50608996)=119926
(ln50608996)^2=314.6948239597
50608996/314.6948239597=160819.2831493187
119926/160819.2831493187=0.7457190310
【4(q97)^2】
D(51482970)=512328
(ln51482970)^2=315.3025836321
51482970/315.3025836321=163281.1549050646
512328/163281.1549050646=3.1377044111

D(51294244)=121070
(ln51294244)^2=315.1721726322
51294244/315.1721726322=162749.9140282902
121070/162749.9140282902=0.7439020827
【4(q98)^2】
D(54114060)=536203
(ln54114060)^2=317.0751673503
54114060/317.0751673503=170666.3453092672
536203/170666.3453092672=3.1418203690

D(53904964)=126979
(ln53904964)^2=316.9373068308
53904964/316.9373068308=170080.8419779300
126979/170080.8419779300=0.7465802646
【4(q99)^2】
D(58198140)=593605
(ln58198140)^2=319.6716553791
58198140/319.6716553791=182055.9909541638
593605/182055.9909541638=3.2605628460

D(56761156)=132909
(ln56761156)^2=318.7782701550
56761156/318.7782701550=178058.4227789458
132909/178058.4227789458=0.7464347821
【4(q100)^2】
D(62192130)=595688
(ln62192130)^2=322.0495490591
62192130/322.0495490591=193113.5447377602
595688/193113.5447377602=3.0846515754

D(58400164)=135695
(ln58400164)^2=319.7955821997
58400164/319.7955821997=182617.1693751897
135695/182617.1693751897=0.7430571860

---

作者: 小草    时间: 2026-6-6 09:22
【4(q101)^2】
D(62192130)=595688
(ln62192130)^2=322.0495490591
62192130/322.0495490591=193113.5447377602
595688/193113.5447377602=3.0846515754

D(59320804)=138255
(ln59320804)^2=320.3552508482
59320804/320.3552508482=185171.9422201982
138255/185171.9422201982=0.7466303930
【4(q102)^2】
D(62192130)=595688
(ln62192130)^2=322.0495490591
62192130/322.0495490591=193113.5447377602
595688/193113.5447377602=3.0846515754

D(61371556)=142217
(ln61371556)^2=321.5730150773
61371556/321.5730150773=190847.9664727075
142217/190847.9664727075=0.7451847805
【4(q103)^2】
D(62192130)=595688
(ln62192130)^2=322.0495490591
62192130/322.0495490591=193113.5447377602
595688/193113.5447377602=3.0846515754

D(61748164)=143181
(ln61748164)^2=321.7924658637
61748164/321.7924658637=191888.1594516708
143181/191888.1594516708=0.7461690206
【4(q104)^2】
D(65615550)=648273
(ln65615550)^2=323.9756381242
65615550/323.9756381242=202532.3582350519
648273/202532.3582350519=3.2008366744

D(64032004)=147390
(ln64032004)^2=323.0967991704
64032004/323.0967991704=198182.1056860107
147390/198182.1056860107=0.7437099303
【4(q105)^2】
D(65615550)=648273
(ln65615550)^2=323.9756381242
65615550/323.9756381242=202532.3582350519
648273/202532.3582350519=3.2008366744

D(64609444)=148727
(ln64609444)^2=323.4196215405
64609444/323.4196215405=199769.7099893159
148727/199769.7099893159=0.7444922456
【4(q106)^2】
D(65615550)=648273
(ln65615550)^2=323.9756381242
65615550/323.9756381242=202532.3582350519
648273/202532.3582350519=3.2008366744

D(65577604)=151024
(ln65577604)^2=323.9548141302
65577604/323.9548141302=202428.2435069597
151024/202428.2435069597=0.7460619002
【4(q107)^2】
D(67897830)=679311
(ln67897830)^2=325.2076500278
67897830/325.2076500278=208783.0037030059
679311/208783.0037030059=3.2536700208

D(66945124)=153784
(ln66945124)^2=324.6981924228
66945124/324.6981924228=206176.4603630087
153784/206176.4603630087=0.7458853437
【4(q108)^2】
D(70450380)=696184
(ln70450380)^2=326.5400497092
70450380/326.5400497092=215748.0531491911
696184/215748.0531491911=3.2268379243

D(68128516)=155849
(ln68128516)^2=325.3299932264
68128516/325.3299932264=209413.5721221030
155849/209413.5721221030=0.7442163295
【4(q109)^2】
D(70450380)=696184
(ln70450380)^2=326.5400497092
70450380/326.5400497092=215748.0531491911
696184/215748.0531491911=3.2268379243

D(69122596)=158003
(ln69122596)^2=325.8527617888
69122596/325.8527617888=212128.3110216555
158003/212128.3110216555=0.7448463585
【4(q110)^2】
D(73603530)=701709
(ln73603530)^2=328.1243700518
73603530/328.1243700518=224315.9506512132
701709/224315.9506512132=3.1282171329

D(71132356)=161973
(ln71132356)^2=326.8883117318
71132356/326.8883117318=217604.4644213572
161973/217604.4644213572=0.7443459418
【4(q111)^2】
D(73603530)=701709
(ln73603530)^2=328.1243700518
73603530/328.1243700518=224315.9506512132
701709/224315.9506512132=3.1282171329

D(71537764)=162219
(ln71537764)^2=327.0938479662
71537764/327.0938479662=218707.1522280428
162219/218707.1522280428=0.7417178558
【4(q112)^2】
D(73603530)=701709
(ln73603530)^2=328.1243700518
73603530/328.1243700518=224315.9506512132
701709/224315.9506512132=3.1282171329

D(71944324)=163597
(ln71944324)^2=327.2988661292
71944324/327.2988661292=219812.3227582470
163597/219812.3227582470=0.7442576374
【4(q113)^2】
D(73603530)=701709
(ln73603530)^2=328.1243700518
73603530/328.1243700518=224315.9506512132
701709/224315.9506512132=3.1282171329

D(72556324)=165094
(ln72556324)^2=327.6054279909
72556324/327.6054279909=221474.7308827112
165094/221474.7308827112=0.7454304125
【4(q114)^2】
D(73603530)=701709
(ln73603530)^2=328.1243700518
73603530/328.1243700518=224315.9506512132
701709/224315.9506512132=3.1282171329

D(72965764)=165841
(ln72965764)^2=327.8091629414
72965764/327.8091629414=222586.1026741450
165841/222586.1026741450=0.7450644852
【4(q115)^2】
D(75555480)=726870
(ln75555480)^2=329.0733059575
75555480/329.0733059575=229600.7565249247
726870/229600.7565249247=3.1657996733

D(75238276)=170065
(ln75238276)^2=328.9206858021
75238276/328.9206858021=228742.9135584018
170065/228742.9135584018=0.7434765841
【4(q116)^2】
D(81171090)=766681
(ln81171090)^2=331.6794830219
81171090/331.6794830219=244727.4979460833
766681/244727.4979460833=3.1327946652

D(78180964)=175322
(ln78180964)^2=330.3137860325
78180964/330.3137860325=236686.9543625638
175322/236686.9543625638=0.7407336854
【4(q117)^2】
D(81171090)=766681
(ln81171090)^2=331.6794830219
81171090/331.6794830219=244727.4979460833
766681/244727.4979460833=3.1327946652

D(80317444)=180169
(ln80317444)^2=331.2945072634
80317444/331.2945072634=242435.1815049640
180169/242435.1815049640=0.7431635907
【4(q118)^2】
D(82192110)=796096
(ln82192110)^2=332.1349469472
82192110/332.1349469472=247466.0096911338
796096/247466.0096911338=3.2169912991

D(81613156)=183192
(ln81613156)^2=331.8773438666
81613156/331.8773438666=245913.6108815095
183192/245913.6108815095=0.7449445329
【4(q119)^2】
D(85645560)=801432
(ln85645560)^2=333.6368172698476
85645560/333.6368172698476=256702.9643216184
801432/256702.9643216184=3.1220208232

D(82700836)=184654
(ln82700836)^2=332.3598907473
82700836/332.3598907473=248829.1707343204
184654/248829.1707343204=0.7420914495
【4(q120)^2】
D(87297210)=849395
(ln87297210)^2=334.3349738096
87297210/334.3349738096=261107.0239086467
849395/261107.0239086467=3.2530530481

D(86007076)=191575
(ln86007076)^2=333.7907123502
86007076/333.7907123502=257667.6726396293
191575/257667.6726396293=0.7434964504
【4(q121)^2】
D(87297210)=849395
(ln87297210)^2=334.3349738096
87297210/334.3349738096=261107.0239086467
849395/261107.0239086467=3.2530530481

D(86452804)=192362
(ln86452804)^2=333.9796164364
86452804/333.9796164364=258856.5281991192
192362/258856.5281991192=0.7431220736
【4(q122)^2】
D(91861770)=872089
(ln91861770)^2=336.2013968059
91861770/336.2013968059=273234.3496271516
872089/273234.3496271516=3.1917253493

D(89151364)=197852
(ln89151364)^2=335.1040051791
89151364/335.1040051791=266040.8787186894
197852/266040.8787186894=0.7436902214
【4(q123)^2】
D(91861770)=872089
(ln91861770)^2=336.2013968059
91861770/336.2013968059=273234.3496271516
872089/273234.3496271516=3.1917253493

D(91661476)=202578
(ln91661476)^2=336.1213560968
91661476/336.1213560968=272703.5171594461
202578/272703.5171594461=0.7428507051
【4(q124)^2】
D(93933840)=896142
(ln93933840)^2=337.0198819694
93933840/337.0198819694=278718.9866992144
896142/278718.9866992144=3.2152169130

D(92121604)=203245
(ln92121604)^2=336.3049851489
92121604/336.3049851489=273922.8024205853
203245/273922.8024205853=0.7419791204
【4(q125)^2】
D(102222120)=932057
(ln102222120)^2=340.1316581052
102222120/340.1316581052=300536.9172909612
932057/300536.9172909612=3.1013061836

D(97259044)=213383
(ln97259044)^2=338.2983486083
97259044/338.2983486083=287494.8825499936
213383/287494.8825499936=0.7422149504
【4(q126)^2】
D(102222120)=932057
(ln102222120)^2=340.1316581052
102222120/340.1316581052=300536.9172909612
932057/300536.9172909612=3.1013061836

D(98684356)=215934
(ln98684356)^2=338.8337365900
98684356/338.8337365900=291247.1378828824
215934/291247.1378828824=0.7414115777
【4(q127)^2】
D(102222120)=932057
(ln102222120)^2=340.1316581052
102222120/340.1316581052=300536.9172909612
932057/300536.9172909612=3.1013061836

D(100360324)=219991
(ln100360324)^2=339.4540016857
100360324/339.4540016857=295652.2047217563
219991/295652.2047217563=0.7440871283
【4(q128)^2】
D(102222120)=932057
(ln102222120)^2=340.1316581052
102222120/340.1316581052=300536.9172909612
932057/300536.9172909612=3.1013061836

D(100841764)=220145
(ln100841764)^2=339.6303687042
100841764/339.6303687042=296916.2162522275
220145/296916.2162522275=0.7414381160
【4(q129)^2】
D(104984880)=981419
(ln104984880)^2=341.1160360561
104984880/341.1160360561=307768.8202929697
981419/307768.8202929697=3.1888187993

D(103999204)=226728
(ln103999204)^2=340.7676792265
103999204/340.7676792265=305190.9272500995
226728/305190.9272500995=0.7429054397
【4(q130)^2】
D(110780670)=1024574
(ln110780670)^2=343.1038576627
110780670/343.1038576627=322877.9494193468
1024574/322877.9494193468=3.1732547913

D(109453444)=237004
(ln109453444)^2=342.6574855876
109453444/342.6574855876=319425.2237399855
237004/319425.2237399855=0.7419702089
【4(q131)^2】
D(113333220)=1040115
(ln113333220)^2=343.9482883858
113333220/343.9482883858=329506.5677805507
1040115/329506.5677805507=3.1565835152

D(111471364)=240828
(ln111471364)^2=343.3341539767
111471364/343.3341539767=324673.0996869157
240828/324673.0996869157=0.7417553232
【4(q132)^2】
D(122672550)=1101850
(ln122672550)^2=346.8917115190
122672550/346.8917115190=353633.5574661920
1101850/353633.5574661920=3.1157959326

D(117375556)=252003
(ln117375556)^2=345.2494446680
117375556/345.2494446680=339973.1927530574
252003/339973.1927530574=0.7412437374
【4(q133)^2】
D(122672550)=1101850
(ln122672550)^2=346.8917115190
122672550/346.8917115190=353633.5574661920
1101850/353633.5574661920=3.1157959326

D(118417924)=254071
(ln118417924)^2=345.5780857917
118417924/345.5780857917=342666.1841960007
254071/342666.1841960007=0.7414533786
【4(q134)^2】
D(122672550)=1101850
(ln122672550)^2=346.8917115190
122672550/346.8917115190=353633.5574661920
1101850/353633.5574661920=3.1157959326

D(119990116)=256750
(ln119990116)^2=346.0686299476
119990116/346.0686299476=346723.4693250536
256750/346723.4693250536=0.7405036656
【4(q135)^2】
D(122672550)=1101850
(ln122672550)^2=346.8917115190
122672550/346.8917115190=353633.5574661920
1101850/353633.5574661920=3.1157959326

D(121044004)=259082
(ln121044004)^2=346.3940631610
121044004/346.3940631610=349440.1806295974
259082/349440.1806295974=0.7414201754
【4(q136)^2】
D(122672550)=1101850
(ln122672550)^2=346.8917115190
122672550/346.8917115190=353633.5574661920
1101850/353633.5574661920=3.1157959326

D(121837444)=260609
(ln121837444)^2=346.6373074912
121837444/346.6373074912=351483.9325339874
260609/351483.9325339874=0.7414535228
【4(q137)^2】
D(129159030)=1188327
(ln129159030)^2=348.8137064350
129159030/348.8137064350=370280.8336290772
1188327/370280.8336290772=3.2092587357

D(127193284)=270926
(ln127193284)^2=348.2410724985
127193284/348.2410724985=365244.9238323198
270926/365244.9238323198=0.7417652713
【4(q138)^2】
D(129159030)=1188327
(ln129159030)^2=348.8137064350
129159030/348.8137064350=370280.8336290772
1188327/370280.8336290772=3.2092587357

D(127735204)=271210
(ln127735204)^2=348.3997688418
127735204/348.3997688418=366634.0090426452
271210/366634.0090426452=0.7397295213
【4(q139)^2】
D(129159030)=1188327
(ln129159030)^2=348.8137064350
129159030/348.8137064350=370280.8336290772
1188327/370280.8336290772=3.2092587357

D(128006596)=271931
(ln128006596)^2=348.4790042132
128006596/348.4790042132=367329.4357834120
271931/367329.4357834120=0.7402918838
【4(q140)^2】
D(133243110)=1209437
(ln133243110)^2=349.9775121954
133243110/349.9775121954=380719.0615310377
1209437/380719.0615310377=3.1767177486

D(131836324)=279185
(ln131836324)^2=349.5804917051
131836324/349.5804917051=377127.2342943405
279185/377127.2342943405=0.7402939237
【4(q141)^2】
D(140900760)=1284544
(ln140900760)^2=352.0714229496
140900760/352.0714229496=400205.0459521968
1284544/400205.0459521968=3.2097146525

D(136843204)=288684
(ln136843204)^2=350.9757324875
136843204/350.9757324875=389893.6346115430
288684/389893.6346115430=0.7404173199
【4(q142)^2】
D(140900760)=1284544
(ln140900760)^2=352.0714229496
140900760/352.0714229496=400205.0459521968
1284544/400205.0459521968=3.2097146525

D(137686756)=290488
(ln137686756)^2=351.2060321177
137686756/351.2060321177=392039.8381820985
290488/392039.8381820985=0.7409655135
【4(q143)^2】
D(140900760)=1284544
(ln140900760)^2=352.0714229496
140900760/352.0714229496=400205.0459521968
1284544/400205.0459521968=3.2097146525

D(138250564)=291383
(ln138250564)^2=351.3592148172
138250564/351.3592148172=393473.5682737877
291383/393473.5682737877=0.7405402128
【4(q144)^2】
D(151110960)=1340153
(ln151110960)^2=354.7016623947
151110960/354.7016623947=426022.7002597153
1340153/426022.7002597153=3.1457314345

D(148303684)=310010
(ln148303684)^2=353.9956698086
148303684/353.9956698086=418942.0850265923
310010/418942.0850265923=0.7399829501
【4(q145)^2】
D(151110960)=1340153
(ln151110960)^2=354.7016623947
151110960/354.7016623947=426022.7002597153
1340153/426022.7002597153=3.1457314345

D(150356644)=314377
(ln150356644)^2=354.5131901177
150356644/354.5131901177=424121.4380488379
314377/424121.4380488379=0.7412428889
【4(q146)^2】
D(155195040)=1414540
(ln155195040)^2=355.7068877842
155195040/355.7068877842=436300.3510186556
1414540/436300.3510186556=3.2421243684

D(153611236)=320100
(ln153611236)^2=355.3200693737
153611236/355.3200693737=432317.9275259085
320100/432317.9275259085=0.7404273097
【4(q147)^2】
D(162342180)=1416289
(ln162342180)^2=357.4072255753
162342180/357.4072255753=454221.8746100786
1416289/454221.8746100786=3.1180554684

D(157201444)=326571
(ln157201444)^2=356.1915868905
157201444/356.1915868905=441339.5761880437
326571/441339.5761880437=0.7399540345
【4(q148)^2】
D(162342180)=1416289
(ln162342180)^2=357.4072255753
162342180/357.4072255753=454221.8746100786
1416289/454221.8746100786=3.1180554684

D(158709604)=329111
(ln158709604)=356.5520804968
158709604/356.5520804968=445123.2026997649
329111/445123.2026997649=0.7393705788
【4(q149)^2】
D(162342180)=1416289
(ln162342180)^2=357.4072255753
162342180/357.4072255753=454221.8746100786
1416289/454221.8746100786=3.1180554684

D(161747524)=335192
(ln161747524)=357.2684859359
161747524/357.2684859359=452733.8132729127
335192/452733.8132729127=0.7403732396
【4(q150)^2】
D(170600430)=1510757
(ln170600430)=359.2857590174
170600430/359.2857590174=474832.1516181718
1510757/474832.1516181718=3.1816653419

D(166358404)=343332
(ln166358404)=358.3318414152
166358404/358.3318414152=464257.9440972428
343332/464257.9440972428=0.7395285409

---

作者: 小草    时间: 2026-6-6 09:27
【4(q151)^2】
D(174083910)=1529998
(ln174083910)=360.0524459312
174083910/360.0524459312=483495.9794531281
1529998/483495.9794531281=3.1644482375

D(171662404)=353959
(ln171662404)=359.5210507214
171662404/359.5210507214=477475.2511864030
353959/477475.2511864030=0.7413138149
【4(q152)^2】
D(174083910)=1529998
(ln174083910)=360.0524459312
174083910/360.0524459312=483495.9794531281
1529998/483495.9794531281=3.1644482375

D(172607044)=355006
(ln172607044)=359.7291899473
172607044/359.7291899473=479824.9595071414
355006/479824.9595071414=0.7398656384
【4(q153)^2】
D(182011830)=1582503
(ln182011830)=361.7445086955
182011830/361.7445086955=503150.2223941407
1582503/503150.2223941407=3.1451899047

D(177369124)=362899
(ln177369124)=360.7622946259
177369124/360.7622946259=491650.9475690264
362899/491650.9475690264=0.7381232596
【4(q154)^2】
D(182011830)=1582503
(ln182011830)=361.7445086955
182011830/361.7445086955=503150.2223941407
1582503/503150.2223941407=3.1451899047

D(178970884)=366136
(ln178970884)=361.1038877446
178970884/361.1038877446=495621.5927716119
366136/495621.5927716119=0.7387410180
【4(q155)^2】
D(182011830)=1582503
(ln182011830)=361.7445086955
182011830/361.7445086955=503150.2223941407
1582503/503150.2223941407=3.1451899047

D(179613604)=368137
(ln179613604)=361.2401412914
179613604/361.2401412914=497213.8571253406
368137/497213.8571253406=0.7403997188
【4(q156)^2】
D(183723540)=1613856
(ln183723540)=362.1006597352
183723540/362.1006597352=507382.5055562033
1613856/507382.5055562033=3.1807482172

D(182844484)=373577
(ln182844484)=361.9181513966
182844484/361.9181513966=505209.4880967546
373577/505209.4880967546=0.7394496913
【4(q157)^2】
D(184294110)=1647287
(ln184294110)=362.2186783915
184294110/362.2186783915=508792.3980574182
1647287/508792.3980574182=3.2376407476

D(183819364)=374651
(ln183819364)=362.1205045414
183819364/362.1205045414=507619.3192451066
374651/507619.3192451066=0.7380550460
【4(q158)^2】
D(187867680)=1656883
(ln187867680)=362.9500672446
187867680/362.9500672446=517613.0188547172
1656883/517613.0188547172=3.2010071997

D(184470724)=376530
(ln184470724)=362.2551396791
184470724/362.2551396791=509228.7280269136
376530/509228.7280269136=0.7394123294
【4(q159)^2】
D(187867680)=1656883
(ln187867680)=362.9500672446
187867680/362.9500672446=517613.0188547172
1656883/517613.0188547172=3.2010071997

D(186431716)=379648
(ln186431716)=362.6577714789
186431716/362.6577714789=514070.6491404856
379648/514070.6491404856=0.7385132776
【4(q160)^2】
D(192462270)=1674865
(ln192462270)=363.8712930868
192462270/363.8712930868=528929.5244131526
1674865/528929.5244131526=3.1665182651

D(188732644)=384480
(ln188732644)=363.1251139306
188732644/363.1251139306=519745.5002687320
384480/519745.5002687320=0.7397466641
【4(q161)^2】
D(193993800)=1723190
(ln193993800)=364.1737418098
193993800/364.1737418098=532695.7375782429
1723190/532695.7375782429=3.2348484856

D(193043236)=391303
(ln193043236)=363.9862906555
193043236/363.9862906555=530358.5353512902
391303/530358.5353512902=0.7378084332
【4(q162)^2】
D(193993800)=1723190
(ln193993800)=364.1737418098
193993800/364.1737418098=532695.7375782429
1723190/532695.7375782429=3.2348484856

D(193710724)=393290
(ln193710724)=364.1180104105
193710724/364.1180104105=531999.8419787422
393290/531999.8419787422=0.7392671369
【4(q163)^2】
D(203693490)=1800905
(ln203693490)=366.0382805566
203693490/366.0382805566=556481.3868381811
1800905/556481.3868381811=3.2362358249

D(203176516)=409754
(ln203176516)=365.9410489053
203176516/365.9410489053=555216.5208243118
409754/555216.5208243118=0.7380075784
【4(q164)^2】
D(209969760)=1816227
(ln209969760)=367.2004128020
209969760/367.2004128020=571812.4290704947
1816227/571812.4290704947=3.1762635922

D(207994084)=419187
(ln207994084)=366.8381825883
207994084/366.8381825883=566991.3707794980
419187/566991.3707794980=0.7393181301
【4(q165)^2】
D(221561340)=1895511
(ln221561340)=369.2627282681
221561340/369.2627282681=600010.0281963397
1895511/600010.0281963397=3.1591321993

D(213568996)=428764
(ln213568996)=367.8520888407
213568996/367.8520888407=580583.8881412116
428764/580583.8881412116=0.7385048203
【4(q166)^2】
D(221561340)=1895511
(ln221561340)=369.2627282681
221561340/369.2627282681=600010.0281963397
1895511/600010.0281963397=3.1591321993

D(214974244)=431255
(ln214974244)=368.1037004839
214974244/368.1037004839=584004.5718567897787
431255/584004.5718567897787=0.7384445615
【4(q167)^2】
D(221561340)=1895511
(ln221561340)=369.2627282681
221561340/369.2627282681=600010.0281963397
1895511/600010.0281963397=3.1591321993

D(216031204)=433482
(ln216031204)=368.2919254609
216031204/368.2919254609=586575.9987261386
433482/586575.9987261386=0.7390039840
【4(q168)^2】
D(223092870)=2044847
(ln223092870)=369.52752363490825
223092870/369.52752363490825=603724.6368159977
2044847/603724.6368159977=3.3870524330

D(222427396)=444357
(ln222427396)=369.4126782386
222427396/369.4126782386=602110.8887235764
444357/602110.8887235764=0.7379986118
【4(q169)^2】
D(242492250)=2102651
(ln242492250)=372.7401819244
242492250/372.7401819244=650566.4314162481
2102651/650566.4314162481=3.2320311938

D(224220676)=447286
(ln224220676)=369.7214172983
224220676/369.7214172983=606458.4454924705
447286/606458.4454924705=0.7375377544
【4(q170)^2】
D(242492250)=2102651
(ln242492250)=372.7401819244
242492250/372.7401819244=650566.4314162481
2102651/650566.4314162481=3.2320311938

D(227828836)=454141
(ln227828836)=370.3355843979
227828836/370.3355843979=615195.6376819940
454141/615195.6376819940=0.7382058197
【4(q171)^2】
D(242492250)=2102651
(ln242492250)=372.7401819244
242492250/372.7401819244=650566.4314162481
2102651/650566.4314162481=3.2320311938

D(228553924)=455837
(ln228553924)=370.4578925541603
228553924/370.4578925541603=616949.8034559645
455837/616949.8034559645=0.7388558963
【4(q172)^2】
D(242492250)=2102651
(ln242492250)=372.7401819244
242492250/372.7401819244=650566.4314162481
2102651/650566.4314162481=3.2320311938

D(230371684)=458317
(ln230371684)=370.7629034149
230371684/370.7629034149=621345.0209774734
458317/621345.0209774734=0.7376207816
【4(q173)^2】
D(242492250)=2102651
(ln242492250)=372.7401819244
242492250/372.7401819244=650566.4314162481
2102651/650566.4314162481=3.2320311938

D(240684196)=476757
(ln240684196)=372.4512559527
240684196/372.4512559527=646216.6314471122
476757/646216.6314471122=0.7377665272
【4(q174)^2】
D(249339090)=2115014
(ln249339090)=373.8160975002
249339090/373.8160975002=667010.0396087587
2115014/667010.0396087587=3.1708878044

D(248188516)=489930
(ln248188516)=373.6372696365
248188516/373.6372696365=664249.8919913820
489930/664249.8919913820=0.7375688064
【4(q175)^2】
D(258318060)=2199323
(ln258318060)=375.1853623219
258318060/375.1853623219=688507.8309061784
2199323/688507.8309061784=3.1943325860

D(252746404)=497640
(ln252746404)=374.3411256077
252746404/374.3411256077=675176.6950256804
497640/675176.6950256804=0.7370515062
【4(q176)^2】
D(258318060)=2199323
(ln258318060)=375.1853623219
258318060/375.1853623219=688507.8309061784
2199323/688507.8309061784=3.1943325860

D(256576324)=504747
(ln256576324)=374.9233191108
256576324/374.9233191108=684343.4668414816
504747/684343.4668414816=0.7375638469
【4(q177)^2】
D(261891630)=2250278
(ln261891630)=375.7177985768
261891630/375.7177985768=697043.4485457762
2250278/697043.4485457762=3.2283181266

D(261598276)=513241
(ln261598276)=375.6743513493
261598276/375.6743513493=696343.1894150456
513241/696343.1894150456=0.7370517983
【4(q178)^2】
D(271591320)=2325936
(ln271591320)=377.1289813780
271591320/377.1289813780=720154.9957991200
2325936/720154.9957991200=3.2297713875

D(270207844)=528437
(ln270207844)=376.9306542698
270207844/376.9306542698=716863.5422434765
528437/716863.5422434765=0.7371514505




【4(q179)^2】
D(271591320)=2325936
(ln271591320)=377.1289813780
271591320/377.1289813780=720154.9957991200
2325936/720154.9957991200=3.2297713875

D(270997444)=529835
(ln270997444)=378.0321191281
270997444/378.0321191281=716863.5422435356
529835/716863.5422435356=0.7391016125
【4(q180)^2】
D(281291010)=2487602
(ln281291010)=378.4931462349
281291010/378.4931462349=743186.5353393361
2487602/743186.5353393361=3.3472108034

D(274962724)=537333
(ln274962724)=377.6083019488
274962724/377.6083019488=728169.1704894832
537333/728169.1704894832=0.7379233038
【4(q181)^2】
D(300690390)=2632923
(ln300690390)=381.0925420597
300690390/381.0925420597=789021.9744916850
2632923/789021.9744916850=3.3369450853

D(281367076)=548773
(ln281367076)=378.5036667750
281367076/378.5036667750=743366.8434373650
548773/743366.8434373650=0.73822636
【4(q182)^2】
D(300690390)=2632923
(ln300690390)=381.0925420597
300690390/381.0925420597=789021.9744916850
2632923/789021.9744916850=3.3369450853

D(284192164)=553095
(ln284192164)=378.8925005854
284192164/378.8925005854=750060.1451887139
553095/750060.1451887139=0.7374008652
【4(q183)^2】
D(300690390)=2632923
(ln300690390)=381.0925420597
300690390/381.0925420597=789021.9744916850
2632923/789021.9744916850=3.3369450853

D(291521476)=565432
(ln291521476)=379.8844330754
291521476/379.8844330754=767395.1618389649
565432/767395.1618389649=0.7368198656
【4(q184)^2】
D(300690390)=2632923
(ln300690390)=381.0925420597
300690390/381.0925420597=789021.9744916850
2632923/789021.9744916850=3.3369450853

D(295633636)=572606
(ln295633636)=380.4306511003
295633636/380.4306511003=777102.5682209203
572606/777102.5682209203=0.7368473911
【4(q185)^2】
D(300690390)=2632923
(ln300690390)=381.0925420597
300690390/381.0925420597=789021.9744916850
2632923/789021.9744916850=3.3369450853

D(297700516)=575952
(ln297700516)=380.7024783382
297700516/380.7024783382=781976.8268898303
575952/781976.8268898303=0.7365333347
【4(q186)^2】
D(317026710)=2640593
(ln317026710)=383.1609166332
317026710/383.1609166332=827398.3494602862
2640593/827398.3494602862=3.1914409809

D(311099044)=599329
(ln311099044)=382.4223474615
311099044/382.4223474615=813495.9843875745
599329/813495.9843875745=0.7367325857
【4(q187)^2】
D(317026710)=2640593
(ln317026710)=383.1609166332
317026710/383.1609166332=827398.3494602862
2640593/827398.3494602862=3.1914409809

D(312370276)=601259
(ln312370276)=382.5818572111
312370276/382.5818572111=816479.5849888960
601259/816479.5849888960=0.7364042054
【4(q188)^2】
D(317026710)=2640593
(ln317026710)=383.1609166332
317026710/383.1609166332=827398.3494602862
2640593/827398.3494602862=3.1914409809

D(314069284)=604418
(ln314069284)=382.7940837568
314069284/382.7940837568=820465.3554665102
604418/820465.3554665102=0.7366770528
【4(q189)^2】
D(328077750)=2701949
(ln328077750)=384.5035150512
328077750/384.5035150512=853250.3271298146
2701949/853250.3271298146=3.1666545140

D(321771844)=617197
(ln321771844)=383.7427624519
321771844/383.7427624519=838509.2188946034
617197/838509.2188946034=0.7360646563
【4(q190)^2】
D(328077750)=2701949
(ln328077750)=384.5035150512
328077750/384.5035150512=853250.3271298146
2701949/853250.3271298146=3.1666545140

D(323928004)=620992
(ln323928004)=384.0044638422
323928004/384.0044638422=843552.7044631247
620992/843552.7044631247=0.7361626567
【4(q191)^2】
D(328077750)=2701949
(ln328077750)=384.5035150512
328077750/384.5035150512=853250.3271298146
2701949/853250.3271298146=3.1666545140

D(324792484)=623141
(ln324792484)=384.1089251009
324792484/384.1089251009=845573.9056692879
623141/845573.9056692879=0.7369444537
【4(q192)^2】
D(328077750)=2701949
(ln328077750)=384.5035150512
328077750/384.5035150512=853250.3271298146
2701949/853250.3271298146=3.1666545140

D(326958724)=626286
(ln326958724)=384.3695327517
326958724/384.3695327517=850636.4218290242
626286/850636.4218290242=0.7362558009
【4(q193)^2】
D(358888530)=3066431
(ln358888530)=388.0317846190
358888530/388.0317846190=924894.6715856921
3066431/924894.6715856921=3.3154380647

D(341436484)=651294
(ln341436484)=386.0703203415
341436484/386.0703203415=884389.3612385978
651294/884389.3612385978=0.7364335535
【4(q194)^2】
D(358888530)=3066431
(ln358888530)=388.0317846190
358888530/388.0317846190=924894.6715856921
3066431/924894.6715856921=3.3154380647

D(344547844)=655813
(ln344547844)=386.4268802317
344547844/386.4268802317=891624.9402562537
655813/891624.9402562537=0.7355256346
【4(q195)^2】
D(358888530)=3066431
(ln358888530)=388.0317846190
358888530/388.0317846190=924894.6715856921
3066431/924894.6715856921=3.3154380647

D(349017124)=664455
(ln349017124)=386.9337453739
349017124/386.9337453739=902007.4577954926
664455/902007.4577954926=0.7366402509
【4(q196)^2】
D(358888530)=3066431
(ln358888530)=388.0317846190
358888530/388.0317846190=924894.6715856921
3066431/924894.6715856921=3.3154380647

D(354870244)=673853
(ln354870244)=387.5883154052
354870244/387.5883154052=915585.5063097162
673853/915585.5063097162=0.7359804140
【4(q197)^2】
D(358888530)=3066431
(ln358888530)=388.0317846190
358888530/388.0317846190=924894.6715856921
3066431/924894.6715856921=3.3154380647

D(355775044)=675497
(ln355775044)=387.6885859468
355775044/387.6885859468=917682.5341172688
675497/917682.5341172688=0.7360900692
【4(q198)^2】
D(358888530)=3066431
(ln358888530)=388.0317846190
358888530/388.0317846190=924894.6715856921
3066431/924894.6715856921=3.3154380647

D(356227876)=675909
(ln356227876)=387.7386782407
356227876/387.7386782407=918731.8572816232
675909/918731.8572816232=0.7356977933
【4(q199)^2】
D(358888530)=3066431
(ln358888530)=388.0317846190
358888530/388.0317846190=924894.6715856921
3066431/924894.6715856921=3.3154380647

D(358042084)=679159
(ln358042084)=387.9387617041
358042084/387.9387617041=922934.5436563937
679159/922934.5436563937=0.7358690870
【4(q200)^2】
D(378287910)=3126278
(ln378287910)=390.1085635079
378287910/390.1085635079=969699.0668402473
3126278/969699.0668402473=3.2239672151

D(370870564)=701234
(ln370870564)=389.3267124988
370870564/389.3267124988=952594.7028387966
701234/952594.7028387966=0.7361304844

---

作者: 小草    时间: 2026-6-6 09:54
【4(q201)^2】
D(378287910)=3126278
(ln378287910)=390.1085635079
378287910/390.1085635079=969699.0668402473
3126278/969699.0668402473=3.2239672151
【4(q202)^2】
D(378287910)=3126278
(ln378287910)=390.1085635079
378287910/390.1085635079=969699.0668402473
3126278/969699.0668402473=3.2239672151
【4(q203)^2】
D(397687290)=3350671
(ln397687290)=392.0865928001
397687290/392.0865928001=1014284.3374467421
3350671/1014284.3374467421=3.3034829350
【4(q204)^2】
D(397687290)=3350671
(ln397687290)=392.0865928001
397687290/392.0865928001=1014284.3374467421
3350671/1014284.3374467421=3.3034829350
【4(q205)^2】
D(397687290)=3350671
(ln397687290)=392.0865928001
397687290/392.0865928001=1014284.3374467421
3350671/1014284.3374467421=3.3034829350
【4(q206)^2】
D(406816410)=3387779
(ln406816410)=392.9859232972
406816410/392.9859232972=1035193.3386996677
3387779/1035193.3386996677=3.2726051003
【4(q207)^2】
D(406816410)=3387779
(ln406816410)=392.9859232972
406816410/392.9859232972=1035193.3386996677
3387779/1035193.3386996677=3.2726051003
【4(q208)^2】
D(406816410)=3387779
(ln406816410)=392.9859232972
406816410/392.9859232972=1035193.3386996677
3387779/1035193.3386996677=3.2726051003
【4(q209)^2】
D(417086670)=3492745
(ln417086670)=393.9750440448
417086670/393.9750440448=1058662.6648173480
3492745/1058662.6648173480=3.2992048516
【4(q210)^2】
D(417086670)=3492745
(ln417086670)=393.9750440448
417086670/393.9750440448=1058662.6648173480
3492745/1058662.6648173480=3.2992048516
【4(q211)^2】
D(434444010)=3599690
(ln434444010)=395.5952984433
434444010/395.5952984433=1098203.1680092581
3599690/1098203.1680092581=3.2777996867
【4(q212)^2】
D(434444010)=3599690
(ln434444010)=395.5952984433
434444010/395.5952984433=1098203.1680092581
3599690/1098203.1680092581=3.2777996867
【4(q213)^2】
D(434444010)=3599690
(ln434444010)=395.5952984433
434444010/395.5952984433=1098203.1680092581
3599690/1098203.1680092581=3.2777996867
【4(q214)^2】
D(446185740)=3792532
(ln446185740)=396.6568499801
446185740/396.6568499801=1124865.8381227624
3792532/1124865.8381227624=3.3715416288
【4(q215)^2】
D(446185740)=3792532
(ln446185740)=396.6568499801
446185740/396.6568499801=1124865.8381227624
3792532/1124865.8381227624=3.3715416288
【4(q216)^2】
D(446185740)=3792532
(ln446185740)=396.6568499801
446185740/396.6568499801=1124865.8381227624
3792532/1124865.8381227624=3.3715416288
【4(q217)^2】
D(446185740)=3792532
(ln446185740)=396.6568499801
446185740/396.6568499801=1124865.8381227624
3792532/1124865.8381227624=3.3715416288
【4(q218)^2】
D(475284810)=3833104
(ln475284810)=399.1774146320
475284810/399.1774146320=1190660.5749179549
3833104/1190660.5749179549=3.2193087440
【4(q219)^2】
D(475284810)=3833104
(ln475284810)=399.1774146320
475284810/399.1774146320=1190660.5749179549
3833104/1190660.5749179549=3.2193087440
【4(q220)^2】
D(475284810)=3833104
(ln475284810)=399.1774146320
475284810/399.1774146320=1190660.5749179549
3833104/1190660.5749179549=3.2193087440
【4(q221)^2】
D(481410930)=3932461
(ln481410930)=399.6893318518
481410930/399.6893318518=1204462.7955656855
3932461/1204462.7955656855=3.2649086501
【4(q222)^2】
D(494684190)=3971605
(ln494684190)=400.7775822064
494684190/400.7775822064=1234311.0292661983
3971605/1234311.0292661983=3.2176695386
【4(q223)^2】
D(494684190)=3971605
(ln494684190)=400.7775822064
494684190/400.7775822064=1234311.0292661983
3971605/1234311.0292661983=3.2176695386
【4(q224)^2】
D(494684190)=3971605
(ln494684190)=400.7775822064
494684190/400.7775822064=1234311.0292661983
3971605/1234311.0292661983=3.2176695386
【4(q225)^2】
D(504383880)=4040159
(ln504383880)=401.5554372941
504383880/401.5554372941=1256075.3339534243
4040159/1256075.3339534243=3.2164941790
【4(q226)^2】
D(504383880)=4040159
(ln504383880)=401.5554372941
504383880/401.5554372941=1256075.3339534243
4040159/1256075.3339534243=3.2164941790

---

作者: 小草    时间: 2026-6-8 08:04
【1】
T(18)=3
(ln)^2=8.3542488988
18/8.3542488988=2.1545922581
3/2.1545922581=1.3923748165
【2】
T(50)=6
(ln)^2=15.3039239950
50/15.3039239950=3.2671359330
6/3.2671359330=1.8364708794
【3】
T(242)=17
(ln)^2=30.1284373616
242/30.1284373616=8.0322785113
17/8.0322785113=2.1164604758
【4】
T(578)=26
(ln578)^2=
578/40.4441797911=14.2913023082
26/14.2913023082=1.8192883643
【5】
T(1682)=53
(ln1682)^2=55.1713042832
1682/55.1713042832=30.4868630868
53/30.4868630868=1.7384537021
【6】
T(3362)=89
(ln3362)^2=65.9391310237
3362/65.9391310237=50.9864165300
89/50.9864165300=1.7455629569
【7】
T(6962)=162
(ln6962)^2=78.2910337712
6962/78.2910337712=88.9246145395
162/88.9246145395=1.8217678068
【8】
T(10082)=208
(ln10082)^2=84.9808701041
10082/84.9808701041=118.6384651940
208/118.6384651940=1.7532256479
【9】
T(20402)=346
(ln20402)^2=98.4736336506
20402/98.4736336506=207.1823618532
346/207.1823618532=1.6700263329
【10】
T(22898)=387
(ln22898)^2=100.7776028060
22898/100.7776028060=227.2131839063
387/227.2131839063=1.7032462349
【11】
T(37538)=564
(ln37538)^2=110.9463858846
37538/110.9463858846=338.3436035406
564/338.3436035406=1.6669444733
【12】
T(44402)=641
(ln44402)^2=114.5122526396
44402/114.5122526396=387.7489000216
641/387.7489000216=1.6531317045
【13】
T(64082)=845
(ln64082)^2=122.4988263917
64082/122.4988263917=523.1233791179
845/523.1233791179=1.6152977170
【14】
T(72962)=942
(ln72962)^2=125.3883517385
72962/125.3883517385=581.8881817042
942/581.8881817042=1.6188677303
【15】
T(77618)=985
(ln77618)^2=126.7775706469
77618/126.7775706469=612.2376348115
985/612.2376348115=1.6088524194
【16】
T(103058)=1252
(ln103058)^2=133.2419390198
103058/133.2419390198=773.4651773920
1252/773.4651773920=1.6186895501
【17】
T(114242)=1362
(ln114242)^2=135.6310462383
114242/135.6310462383=842.2997769941
1362/842.2997769941=1.6170014966
【18】
T(144722)=1649
(ln144722)^2=141.1954683734
144722/141.1954683734=1024.9762380282
1649/1024.9762380282=1.6088177841
【19】
T(157922)=1784
(ln157922)^2=143.2774650909
157922/143.2774650909=1102.2110134333
1784/1102.2110134333=1.6185648467
【20】
T(193442)=2105
(ln193442)^2=148.1754288090
193442/148.1754288090=1305.4931006767
2105/1305.4931006767=1.6124175600
【21】
T(240818)=2508
(ln240818)^2=153.5566264567
240818/153.5566264567=1568.2683682029574
2508/1568.2683682029574=1.5992160850
【22】
T(351122)=3429
(ln351122)^2=163.0445268154
351122/163.0445268154=2153.5344169973
3429/2153.5344169973=1.5922661709
【23】
T(371522)=3585
(ln371522)^2=164.4899453357
371522/164.4899453357=2258.6304545349
3585/2258.6304545349=1.58724504613050
【24】
T(425042)=4003
(ln425042)^2=167.9601294723
425042/167.9601294723=2530.6124812800
4003/2530.6124812800=1.5818304974
【25】
T(542882)=4898
(ln542882)^2=174.3627093684
542882/174.3627093684=3113.5212452622
4898/3113.5212452622=1.5731384546
【26】
T(647522)=5688
(ln647522)^2=179.0487002108
647522/179.0487002108=3616.4574176615
5688/3616.4574176615=1.5728098919
【27】
T(717602)=6189
(ln717602)^2=181.8093668300
717602/181.8093668300=3947.0023602854
6189/3947.0023602854=1.5680254115
【28】
T(761378)=6483
(ln761378)^2=183.4097403088
761378/183.4097403088=4151.2408158809
6483/4151.2408158809=1.5617017387
【29】
T(821762)=6906
(ln821762)^2=185.4827746418
821762/185.4827746418=4430.3952298911
6906/4430.3952298911=1.5587774096
【30】
T(868562)=7242
(ln868562)^2=186.9945278902
868562/186.9945278902=4644.8524980902
7242/4644.8524980902=1.5591453126

---

作者: 小草    时间: 2026-6-12 07:03
【31】
T(1308962)=10313
(ln1308962)^2=198.3800421285
1308962/198.3800421285=6598.2544713451
10313/6598.2544713451=1.5629891276
【32】
T(1348082)=10589
(ln1348082)^2=199.2104553175
1348082/199.210455317495=6767.1247367588
10589/6767.1247367588=1.5647709200
【33】
T(1367858)=10728
(ln1367858)^2=199.6217622315
1367858/199.6217622315=6852.2488966594
10728/6852.2488966594=1.5656173852
【34】
T(1468898)=11393
(ln1468898)^2=201.6406537048
1468898/201.6406537048=7284.7313922640
11393/7284.7313922640=1.5639560866
【35】
T(1552322)=11951
(ln1552322)^2=203.212507018
1552322/203.212507018=7638.9097441847
11951/7638.9097441847=1.5644902742
【36】
T(2076722)=15373
(ln2076722)^2=211.5948799686
2076722/211.5948799686=9814.6136631858
15373/9814.6136631858=1.5663377620
【37】
T(2125922)=15662
(ln2125922)^2=212.2766286506
2125922/212.2766286506=10014.8660430216
15662/10014.8660430216=1.5638751365
【38】
T(2200802)=16122
(ln2200802)^2=213.2865247724
2200802/213.2865247724=10318.5234151501
16122/10318.5234151501=1.5624328551
【39】
T(2251442)=16452
(ln2251442)^2=213.9515119728
2251442/213.9515119728=10523.1413381469
16452/10523.1413381469=1.5634114825
【40】
T(2380562)=17246
(ln2380562)^2=215.5860004956
2380562/215.5860004956=11042.2847240890
17246/11042.2847240890=1.5618144642
【41】
T(2649602)=18845
(ln2649602)^2=218.7417335474
2649602/218.7417335474=12112.9240270277
18845/12112.9240270277=1.5557762897
【42】
T(3020882)=21056
(3020882ln)^2=222.6380136091
3020882/222.6380136091=13568.5813533351
21056/13568.5813533351=1.5518203010
【43】
T(3261458)=22508
(ln3261458)^2=224.9305521385
3261458/224.9305521385=14499.8443697047
22508/14499.8443697047=1.5522925230
【44】
T(3323042)=22878
(ln3323042)^2=225.4920042641
3323042/225.4920042641=14736.8506960805
22878/14736.8506960805=1.5524348093
【45】
T(3385202)=23234
(ln3385202)^2=226.0489438229
3385202/226.0489438229=14975.5267277522
23234/14975.5267277522=1.5514646277
【46】
T(3479522)=23795
(ln3479522)^2=226.8760590245
3479522/226.8760590245=15336.6644984971
23795/15336.6644984971=1.5515107605
【47】
T(4072658)=27297
(ln4072658)^2=231.6425073257
4072658/231.6425073257=17581.6522063183
27297/17581.6522063183=1.5525844602
【48】
T(4210802)=28087
(ln4210802)^2=232.6590024419
4210802/232.6590024419=18098.5990475547
28087/18098.5990475547=1.5518880730
【49】
T(4386722)=29054
(ln4386722)^2=233.9092748532
4386722/233.9092748532=18753.9463869189
29054/18753.9463869189=1.5492205961
【50】
T(4422338)=29267
(ln4422338)^2=234.1566843969
4422338/234.1566843969=18886.2342810767
29267/18886.2342810767=1.5496471962
【51】
T(5164898)=33332
(ln5164898)^2=238.9310883814
5164898/238.9310883814=21616.6846892498
33332/21616.6846892498=1.5419570799
【52】
T(5242322)=33751
(ln5242322)^2=239.3912963961
5242322/239.3912963961=21898.5488567052
33751/21898.5488567052=1.5412436788
【53】
T(5557778)=35504
(ln5557778)^2=241.2029203673
5557778/241.2029203673=23041.9183629149
35504/23041.9183629149=1.5408439280
【54】
T(5759618)=36589
(ln5759618)^2=242.3122395734
5759618/242.3122395734=23769.4059950914
36589/23769.4059950914=1.5393316942
【55】
T(5923682)=37494
(ln5923682)^2=243.1874563115
5923682/243.1874563115=24358.5014204529
37494/24358.5014204529=1.5392572537
【56】
T(6386738)=40024
(ln6386738)^2=245.5405702396
6386738/245.5405702396=26010.9276188769
40024/26010.9276188769=1.5387378946
【57】
T(7001282)=43263
(ln7001282)^2=248.4281553918
7001282/248.4281553918=28182.3209167180
43263/28182.3209167180=1.5351113249
【58】
T(7046258)=43510
(ln7046258)^2=248.6300527538
7046258/248.6300527538=28340.3310338247
43510/28340.3310338247=1.5352678819
【59】
T(7457522)=45684
(ln7457522)^2=250.4221981133
7457522/250.4221981133=29779.7961050799
45684/29779.7961050799=1.5340602010
【60】
T(7597202)=46446
(ln7597202)^2=251.0098563889
7597202/251.0098563889=30266.5485303865
46446/30266.5485303865=1.5345654611
【61】
T(7976018)=48486
(ln7976018)^2=252.5540699520
7976018/252.5540699520=31581.4273019473
48486/31581.4273019473=1.5352694334
【62】
T(8217458)=49743
(ln8217458)^2=253.5028068532
8217458/253.5028068532=32415.6489705403
49743/32415.6489705403=1.5345366075
【63】
T(8661122)=52115
(ln8661122)^2=255.1800123417
8661122/255.1800123417=33941.2241598385
52115/33941.2241598385=1.5354484492
【64】
T(8711138)=52366
(ln8711138)^2=255.3640113238
8711138/255.3640113238=34112.6298684051
52366/34112.6298684051=1.5350912610
【65】
T(8912642)=53401
(ln8912642)^2=256.0954097282
8912642/256.0954097282=34802.0372932853
53401/34802.0372932853=1.5344216647
【66】
T(9065282)=54182
(ln9065282)^2=256.6391988329
9065282/256.6391988329=35323.0607063361
54182/35323.0607063361=1.5338987878
【67】
T(9167762)=54721
(ln9167762)^2=256.9994939222
9167762/256.9994939222=35672.2959259029
54721/35672.2959259029=1.5339915354
【68】
T(10008338)=59028
(ln10008338)^2=259.8198754450
10008338/259.8198754450=38520.2940416258
59028/38520.2940416258=1.5323870564

---

作者: 小草    时间: 2026-6-15 08:12
施承忠素数个数π(x)分段系数法

【1】4
ln4=1.3862943611
4/1.3862943611=2.8853900818
2/2.8853900818=0.6931471806
【2】9
ln9=2.1972245773
9/2.1972245773=4.0960765198
4/4.0960765198=0.9765442566
【3】25
ln25=3.2188758248
25/3.2188758248=7.7666866822
9/7.7666866822=1.1587952970
【4】49
ln49=3.8918202981
49/3.8918202981=12.5905093881&#160;
15/12.5905093881=1.1913735606&#160;
【5】121
ln121=4.7957905456
121/4.7957905456=25.2304596812
30/25.2304596812=1.1890389782
【6】
ln169=5.1298987149
169/5.1298987149=32.9441202239
39/32.9441202239=1.1838227804
【7】
ln289=5.6664266881
289/5.6664266881=51.0021598986
61/51.0021598986=1.1960277785
【8】
ln361=5.8888779583
361/5.8888779583=61.3020005774
72/61.3020005774=1.1745130554
【9】
ln529=6.2709884319
529/6.2709884319=84.3567175645
99/84.3567175645=1.1735876271
【10】
ln841=6.7345916600
841/6.7345916600=124.8776529385
146/124.8776529385=1.1691443310
【11】
ln961=6.8679744090
961/6.8679744090=139.9248079231
162/139.9248079231=1.1577646766
【12】
ln1369=7.2218358253
1369/7.2218358253=189.5639880381
219/189.5639880381=1.1552827215
【13】
ln1681=7.4271441334
1681/7.4271441334=226.3319480284
263/226.3319480284=1.1620100578
【14】
ln1849=7.5224002314
1849/7.5224002314=245.7992054560
283/245.7992054560=1.1513462766
【15】
ln2209=7.7002952034
2209/7.7002952034=286.8721187500
329/286.8721187500=1.1468524771
【16】
ln2809=7.9405838271
2809/7.9405838271=353.75232 61720
409/353.7523261720=1.15617614286
【17】
ln3481=8.1550748878
3481/8.1550748878=426.8507705806
487/426.8507705806=1.1409139530
【18】
ln3721=8.2217477283
3721/8.2217477283=452.5801718766
519/452.5801718766=1.1467581486
【19】
ln4489=8.4093852388
4489/8.4093852388=533.8083430033
609/533.8083430033=1.1408589019
【20】
ln5041=8.5253597541
5041/8.5253597541=591.2946955201
675/591.2946955201=1.1415627522
【21】
ln5329=8.5809188823
5329/8.5809188823=621.0290614671
705/621.0290614671=1.1352125750
【22】
ln6241=8.7388957049
6241/8.7388957049=714.1634607792
811/714.1634607792=1.1355943625
【23】
ln6889=8.8376812156
6889/8.8376812156=779.5031108205
886/779.5031108205=1.1366215063
【24】
ln7921=8.9772727395
7921/8.9772727395=882.3392393046
1000/882.3392393046=1.133350933
【25】
ln9409=9.1494219570
9409/9.1494219570=1028.3709773382
1163/1028.3709773382=1.1309148407
【26】
ln10201=9.2302410337
10201/9.2302410337=1105.1715727418
1252/1105.1715727418=1.1328557763
【27】
10609
ln10609=9.2694579765
10609/9.2694579765=1144.5113648388
1294/1144.5113648388=1.1306135000
【28】
11449
ln11449=9.3456576689
11449/9.3456576689=1225.0609219371
1381/1225.0609219371=1.1272908761
【29】
11881
ln11881=9.3826957645
11881/9.3826957645=1266.2672112798
1423/1266.2672112798=1.1237754459
【30】
12769
ln12769=9.4547756374
12769/9.4547756374=1350.5344272253
1523/1350.5344272253=1.1277017226
【31】
16129
ln16129=9.6883741729
16129/9.6883741729=1664.7788072756
1877/1664.7788072756=1.1274771110
【32】
17161
ln17161=9.7503946464
17161/9.7503946464=1760.0313240999
1976/1760.0313240999=1.1227072910
【33】
18769
ln18769=9.8399618517
18769/9.8399618517=1907.4260940105
2141/1907.4260940105=1.1224550229
【34】
19321
ln19321=9.8689478663
19321/9.8689478663=1957.7568208640
2190/1957.7568208640=1.1186271843
【35】
22201
ln22201=10.0078926119
22201/10.0078926119=2218.3491431155
2589/2218.3491431155=1.1670840941
【36】
22801
ln22801=10.0345596736
22801/10.0345596736=2272.2471878848
2547/2272.2471878848=1.1209167795
【37】
24649
ln24649=10.1124916107
24649/10.1124916107=2437.4803904825
2729/2437.4803904825=1.1195987507
【38】
26569
ln26569=10.1875004016
26569/10.1875004016=2607.9998971904
2915/2607.9998971904=1.1177147680
【39】
27889
ln27889=10.2359876248
27889/10.2359876248=2724.6027469230
3043/2724.6027469230=1.1168600646
【40】
29929
ln29929=10.3065831890
29929/10.3065831890=2903.8721612360
3241/2903.8721612360=1.1160959643
【41】
32041
ln32041=10.3747716117
32041/10.3747716117=3088.3571416518
3436/3088.3571416518=1.1125656271
【42】
32761
ln32761=10.3969940625
32761/10.3969940625=3151.0068970956
3512/3151.0068970956=1.1145643646
【43】
36481
ln36481=10.5045468561
36481/10.5045468561=3472.8770788257
3868/3472.8770788257=1.1137739437
【44】
37249
ln37249=10.5253803778
37249/10.5253803778=3538.9694873703
3945/3538.9694873703=1.1147312838
【45】
38809
ln38809=10.5664074575
38809/10.5664074575=3672.8661237130
4089/3672.8661237130=1.1132994948
【46】
39601
ln39601=10.5866096494
39601/10.5866096494=3740.6687609611
4164/3740.6687609611=1.1131699346
【47】
44521
ln44521=10.7037162670
44521/10.7037162670=4159.3965020598
4627/4159.3965020598=1.1124209961
【48】
49729
ln49729=10.8143435429
49729/10.8143435429=4598.4298355908
5106/4598.4298355908=1.11037901687
【49】
51529
ln51529=10.8499000350
51529/10.8499000350=4749.2603465263
5274/4749.2603465263=1.1104887109
【50】
52441
ln52441=10.8674440071
52441/10.8674440071=4825.5137054986
5356/4825.5137054986=1.1099336417
【51】
54289
ln54289=10.9020769071
54289/10.9020769071=4979.6933614222
5522/4979.6933614222=1.1089036210
【52】
57121
ln57121=10.9529271039
57121/10.9529271039=5215.1355941793
5792/5215.1355941793=1.1106135009
【53】
58081
ln58081=10.9695938670
58081/10.9695938670=5294.7265599984
5882/5294.7265599984=1.1109166703
【54】
63001
ln63001=11.0509058783
63001/11.0509058783=5700.9805977726
6320/5700.9805977726=1.10858121539
【55】
66049
ln66049=11.0981521698
66049/11.0981521698=5951.3510888534
6595/5951.3510888534=1.1081517292
【56】
69169
ln69169=11.1443080644
69169/11.1443080644=6206.6661833369
6869/6206.6661833369=1.1067132978
【57】
72361
ln72361=11.1894227592
72361/11.1894227592=6466.9108994478
7161/6466.9108994478=1.1073293125
【58】
73441
ln73441=11.2042376418
73441/11.2042376418=6554.7520811243
7252/6554.7520811243=1.1063728895
【59】
76729
ln76729=11.2480350124
76729/11.2480350124=6821.5470449205
7544/6821.5470449205=1.1059074943
【60】
78961
ln78961=11.2767093387
78961/11.2767093387=7002.1313512992
7743/7002.1313512992=1.1058061627
【61】
80089
ln80089=11.2908937953
80089/11.2908937953=7093.2382725394
7842/7093.2382725394=1.1055599289
【62】
85849
ln85849=11.3603452180
85849/11.3603452180=7556.9006357286
8354/7556.9006357286=1.1054796672
【63】
94249
ln94249=11.4536954952
94249/11.4536954952=8228.6978940114
9089/8228.6978940114=1.1045489963
【64】
96721
ln96721=11.7541075448
96721/11.7541075448=8228.6978940217
9309/8228.6978940217=1.1312846965
【65】
97969
ln97969=11.4924063811
97969/11.4924063811=8524.6724446776
9416/8524.6724446776=1.1045585694
【66】
100489
ln100489=11.5178035478
100489/11.5178035478=8724.6669543339
9631/8724.6669543339=1.1038816783
【67】
109561
ln109561=11.6042367508
109561/11.6042367508=9441.4654192958
10415/9441.4654192958=1.1031126565
【68】
113569
ln113569=11.6401658607
113569/11.6401658607=9756.6479171432
10756/9756.6479171432=1.1024278104
【69】
120409
ln120409=11.6986495599
120409/11.6986495599=10292.5555110849
11335/10292.5555110849=1.1012814056
【70】
121801
ln121801=11.7101438444
121801/11.7101438444=10401.3239818781
11460/10401.3239818781=1.1017828134
【71】
124609
ln124609=11.7329361139
124609/11.7329361139=10620.4447710557
11701/10620.4447710557=1.1017429357
【72】
128881
ln128881=11.7666447770
128881/11.7666447770=10953.0798662267
12064/10953.0798662267=1.1014253660
【73】
134689
ln134689=11.8107236961
134689/11.8107236961=11403.9582557058
12553/11403.9582557058=1.1007581507
【74】
139129
ln139129=11.8431568393
139129/11.8431568393=11747.6279245343
12934/11747.6279245343=1.1009882236
【75】
143641
ln143641=11.8750724102
143641/11.8750724102=12096.0104526706
13314/12096.0104526706=1.1006934933
【76】
146689
ln146689=11.8960699784
146689/11.8960699784=12330.8790437806
13566/12330.8790437806=1.1001648749
【77】
151321
ln151321=11.9271586872
151321/11.9271586872=12687.0953903208
13960/12687.0953903208=1.1003306565
【78】
157609
ln157609=11.9678725614
157609/11.9678725614=13169.3414340270
14490/13169.3414340270=1.1002828101
【79】
160801
ln160801=11.9879228546
160801/11.9879228546-13413.5831495026
14752/13413.5831495026=1.0997807100
【80】
167281
ln167281=12.0274303121
167281/12.0274303121=13908.2909365694
15283/13908.2909365694=1.0988409769
【81】
175561
ln175561=12.0757418398
175561/12.0757418398=14538.3200741651
15953/14538.3200741651=1.0973069735
【82】
177241
ln177241=12.0852656674
177241/12.0852656674=14665.8753624347
16104/14665.8753624347=1.0980592431
【83】
185761
ln185761=12.1322161802
185761/12.1322161802=15311.3822932998
16813/15311.3822932998=1.0980719884
【84】
187489
ln187489=12.1414754560
187489/12.1414754560=15442.0276744329
16964/15442.0276744329=1.0985603936
【85】
192721
ln192721=12.1689988262
192721/12.1689988262=15837.0464778967
17388/15837.0464778967=1.0979319928
【86】
196249
ln196249=12.1871395401
196249/12.1871395401=16102.9583155482
17678/16102.9583155482=1.0978107037
【87】
201601
ln201601=12.2140457755
201601/12.2140457755=16505.6692684408
18108/16505.6692684408=1.0970775983
【88】
208849
ln208849=12.2493667818
208849/12.2493667818=17049.7792841264
18707/17049.7792841264=1.0971989542
【89】
212521
ln212521=12.2667960860
212521/12.2667960860=17324.8987355833
19012/17324.8987355833=1.0973801515
【90】
214369
ln214369=12.2754541082
214369/12.2754541082=17463.2236095283
19157/17463.2236095283=1.0969910498
【91】
218089
ln218089=12.2926585153
218089/12.2926585153=17741.4022954072
19451/17741.4022954072=1.0963620393
【92】
229441
ln229441=12.3434011948
229441/12.3434011948=18588.1505736570
20385/18588.1505736570=1.0966663907
【93】
237169
ln237169=12.3765282462
237169/12.3765282462=19162.8052133940
20997/19162.8052133940=1.0957164030
【94】
241081
ln241081=12.3928882556
241081/12.3928882556=19453.1730640807
21310/19453.1730640807=1.0954511087
【95】
249001
ln249001=12.4252121915
249001/12.4252121915=20039.9796930905
21964/20039.9796930905=1.0960090946
【96】
253009
ln253009=12.4411803402
253009/12.4411803402=20336.4144784941
22282/20336.4144784941=1.0956700368
【97】
259081
ln259081=12.4648960331
259081/12.4648960331=20784.8504561949
22766/20784.8504561949=1.0953169977
【98】
271441
ln271441=12.5115000835
271441/12.5115000835=21695.3201605276
23761/21695.3201605276=1.0952131531
【99】
273529
ln273529=12.5191629281
273529/12.5191629281=21848.8250029919
23926/21848.8250029919=1.0950703297
【100】
292681
ln292681=12.5868385577
292681/12.5868385577=23252.9398592272
25439/23252.9398592272=1.0940122047

---

作者: 小草    时间: 2026-6-20 08:48
x=(2∑(1,n)n)-n
x/2=(∑(1,n)n)-n/2
x/3=2(∑(1,n)n)/3-n/3
x/k=2(∑(1,n)n)/k-n/k
x/p=2(∑(1,n)n)/p-n/p

---

作者: 小草    时间: 2026-6-20 13:22
D(223092870)=2044847
2*3*5*7*11*13*17*19*23=223092870
(ln223092870)^2=369.5275236338
223092870/369.5275236338=603724.6368178084
2044847/603724.6368178084=3.3870524330

D(9699690)=124180
2*3*5*7*11*13*17*19=9699690
(ln9699690)^2=258.8110180401
9699690/258.8110180401=37477.8866581991
124180/37477.8866581991=3.3134205547

D(510510)=9493
2*3*5*7*11*13*17=510510
(ln510510)^2=172.7427994918
510510/172.7427994918=2955.3185516380
9493/2955.3185516380=3.2121748753

D(30030)=905
2*3*5*7*11*13=30030
(ln30030)^2=106.2951135621
30030/106.2951135621=282.5153386045
905/282.5153386045=3.2033658932

D(2310)=114
2*3*5*7*11=2310
(ln2310)^2=59.9850684262
2310/59.9850684262=38.5095834781
114/38.5095834781=2.9603020782

D(210)=19
2*3*5*7=210
(ln210)^2=28.5915589449
210/28.5915589449=7.3448251075
19/7.3448251075=2.5868553331

D(30)=3
2*3*5=30
(ln30)^2=11.5681436290
30/11.5681436290=2.5933287969
3/2.5933287969=1.1568143629

D(6)=1
2*3=6
(ln6)^2=3.2104019956
6/3.2104019956=1.8689248288
1/1.8689248288=0.5350669993

---

作者: 小草    时间: 2026-7-2 07:32
              哥猜数的渐进式

序号【】qk 【】(4qk)^2【】((4qk)^2-(4qk-1)^2)/qk【】∑(1,k)qk
1  【】3 【】36    【】12                【】3        
2n       【】a           【】2n*a 【】上限哥猜数
12*1=12  【】0.3333333333【】4    【】1
12*2=24  【】0.4166666667【】10   【】2
12*3=36  【】0.6111111111【】22   【】3
2n       【】b           【】2n*b 【】下限哥猜数
12       【】1           【】12   【】1
24       【】2.8333333333【】68   【】2
36       【】3.5555555556【】128  【】3
2  【】5 【】100   【】12.8              【】8   
2n          【】a           【】2n*a 【】上限哥猜数
36+12.8=38.8【】0.8762886598【】34   【】4
36+25.6=61.6【】0.7792207792【】48   【】5
36+38.4=74.4【】0.8064516130【】60   【】6
36+51.2=87.2【】0.8944954128【】78   【】7
36+64=100   【】0.8400000000【】84   【】8
2n          【】b           【】2n*b 【】下限哥猜数
38.8        【】3.9175257732【】152  【】4
61.6        【】3.0519480520【】188  【】5
74.4        【】4.4623655914【】332  【】6
87.2        【】4.5642201835【】398  【】7
100         【】3.9800000000【】398  【】7
3  【】11【】484  【】34.9090909091      【】19  
2n=100+34.9090909091*t【】a           【】2n*a 【】上限哥猜数
134.9090909091        【】0.6671159030【】90   【】9      
169.8181818182        【】0.6713062099【】114  【】10
204.7272727273        【】0.5568383659【】114  【】10
239.6363636364        【】0.5007587253【】120  【】12
274.5454545455        【】0.6119205298【】168  【】13
309.4545454546        【】0.5816686251【】180  【】14
344.3636363637        【】0.5227032735【】180  【】14
379.2727272728        【】0.4745925216【】180  【】14
414.1818181819        【】0.4345917471【】180  【】14
449.0909090910        【】0.4008097166【】180  【】14
484                   【】0.4338842975【】210  【】19   
2n                    【】b           【】2n*b 【】下限哥猜数
134.9090909091        【】3.6172506739【】488  【】9
169.8181818182        【】3.7216274090【】632  【】10
204.7272727273        【】3.3801065720【】692  【】11
239.6363636364        【】2.8877086495【】692  【】11
274.5454545455        【】3.6132450331【】992  【】13
309.4545454546        【】3.2056404230【】992  【】13
344.3636363637        【】2.8806758184【】992  【】13
379.2727272728        【】2.9319271333【】1112 【】16
414.1818181819        【】2.6848112379【】1112 【】16
449.0909090910        【】3.1441295547【】1412 【】18
484                   【】2.9173553719【】1412 【】18
4  【】17【】1156     【】39.529411765         【】36
2n=484+39.529411765*t 【】a           【】2n*a 【】上限哥猜数
523.529411765         【】0.4011235955【】210  【】19
563.058823530         【】0.5328040117【】300  【】21
602.588235295         【】0.4978524014【】300  【】21
642.117647060         【】0.4672041041【】300  【】21
681.647058825         【】0.4841215050【】330  【】24
721.176470590         【】0.4575856444【】330  【】24
760.705882355         【】0.4338076090【】330  【】24
800.235294120         【】0.4873566598【】390  【】27
839.764705885         【】0.4644158027【】290  【】27
879.294117650         【】0.4435375970【】390  【】27
918.823529415         【】0.4571062740【】420  【】30
958.352941180         【】0.4382519028【】420  【】30
997.882352945         【】0.5110822919【】510  【】32
1037.411764710        【】0.4916080744【】510  【】32
1076.941176475        【】0.4735634695【】510  【】32
1116.470588240        【】0.4567966280【】510  【】32
1156                  【】0.4411764706【】510  【】32
2n                    【】b           【】2n*b 【】下限哥猜数
523.529411765         【】2.7658426966【】1448 【】20
563.058823530         【】3.0511909737【】1718 【】21
602.588235295         【】2.8510347520【】1718 【】21
642.117647060         【】2.6755221693【】1718 【】21
681.647058825         【】2.5203658957【】1718 【】21
721.176470590         【】2.8398042414【】2048 【】25
760.705882355         【】2.9604082895【】2252 【】26
800.235294120         【】2.8141723023【】2252 【】26
839.764705885         【】3.1818436537【】2672 【】28
879.294117650         【】3.0388011774【】2672 【】28      
918.823529415         【】2.9080665813【】2672 【】28
958.352941180         【】3.0635894918【】2936 【】31
997.882352945         【】2.9422306060【】2936 【】31
1037.411764710        【】2.8301202087【】2936 【】31
1076.941176475        【】2.7652392397【】2978 【】34
1116.470588240        【】2.7694415174【】3092 【】35
1156                  【】2.6747404844【】3092 【】35

---

作者: 小草    时间: 2026-7-2 07:33
              哥猜数的渐进式

序号【】qk 【】(4qk)^2【】((4qk)^2-(4qk-1)^2)/qk【】∑(1,k)qk
1  【】3 【】36    【】12                【】3        
2n       【】a           【】2n*a 【】上限哥猜数
12*1=12  【】0.3333333333【】4    【】1
12*2=24  【】0.4166666667【】10   【】2
12*3=36  【】0.6111111111【】22   【】3
2n       【】b           【】2n*b 【】下限哥猜数
12       【】1           【】12   【】1
24       【】2.8333333333【】68   【】2
36       【】3.5555555556【】128  【】3
2  【】5 【】100   【】12.8              【】8   
2n          【】a           【】2n*a 【】上限哥猜数
36+12.8=38.8【】0.8762886598【】34   【】4
36+25.6=61.6【】0.7792207792【】48   【】5
36+38.4=74.4【】0.8064516130【】60   【】6
36+51.2=87.2【】0.8944954128【】78   【】7
36+64=100   【】0.8400000000【】84   【】8
2n          【】b           【】2n*b 【】下限哥猜数
38.8        【】3.9175257732【】152  【】4
61.6        【】3.0519480520【】188  【】5
74.4        【】4.4623655914【】332  【】6
87.2        【】4.5642201835【】398  【】7
100         【】3.9800000000【】398  【】7
3  【】11【】484  【】34.9090909091      【】19  
2n=100+34.9090909091*t【】a           【】2n*a 【】上限哥猜数
134.9090909091        【】0.6671159030【】90   【】9      
169.8181818182        【】0.6713062099【】114  【】10
204.7272727273        【】0.5568383659【】114  【】10
239.6363636364        【】0.5007587253【】120  【】12
274.5454545455        【】0.6119205298【】168  【】13
309.4545454546        【】0.5816686251【】180  【】14
344.3636363637        【】0.5227032735【】180  【】14
379.2727272728        【】0.4745925216【】180  【】14
414.1818181819        【】0.4345917471【】180  【】14
449.0909090910        【】0.4008097166【】180  【】14
484                   【】0.4338842975【】210  【】19   
2n                    【】b           【】2n*b 【】下限哥猜数
134.9090909091        【】3.6172506739【】488  【】9
169.8181818182        【】3.7216274090【】632  【】10
204.7272727273        【】3.3801065720【】692  【】11
239.6363636364        【】2.8877086495【】692  【】11
274.5454545455        【】3.6132450331【】992  【】13
309.4545454546        【】3.2056404230【】992  【】13
344.3636363637        【】2.8806758184【】992  【】13
379.2727272728        【】2.9319271333【】1112 【】16
414.1818181819        【】2.6848112379【】1112 【】16
449.0909090910        【】3.1441295547【】1412 【】18
484                   【】2.9173553719【】1412 【】18
4  【】17【】1156     【】39.529411765         【】36
2n=484+39.529411765*t 【】a           【】2n*a 【】上限哥猜数
523.529411765         【】0.4011235955【】210  【】19
563.058823530         【】0.5328040117【】300  【】21
602.588235295         【】0.4978524014【】300  【】21
642.117647060         【】0.4672041041【】300  【】21
681.647058825         【】0.4841215050【】330  【】24
721.176470590         【】0.4575856444【】330  【】24
760.705882355         【】0.4338076090【】330  【】24
800.235294120         【】0.4873566598【】390  【】27
839.764705885         【】0.4644158027【】290  【】27
879.294117650         【】0.4435375970【】390  【】27
918.823529415         【】0.4571062740【】420  【】30
958.352941180         【】0.4382519028【】420  【】30
997.882352945         【】0.5110822919【】510  【】32
1037.411764710        【】0.4916080744【】510  【】32
1076.941176475        【】0.4735634695【】510  【】32
1116.470588240        【】0.4567966280【】510  【】32
1156                  【】0.4411764706【】510  【】32
2n                    【】b           【】2n*b 【】下限哥猜数
523.529411765         【】2.7658426966【】1448 【】20
563.058823530         【】3.0511909737【】1718 【】21
602.588235295         【】2.8510347520【】1718 【】21
642.117647060         【】2.6755221693【】1718 【】21
681.647058825         【】2.5203658957【】1718 【】21
721.176470590         【】2.8398042414【】2048 【】25
760.705882355         【】2.9604082895【】2252 【】26
800.235294120         【】2.8141723023【】2252 【】26
839.764705885         【】3.1818436537【】2672 【】28
879.294117650         【】3.0388011774【】2672 【】28      
918.823529415         【】2.9080665813【】2672 【】28
958.352941180         【】3.0635894918【】2936 【】31
997.882352945         【】2.9422306060【】2936 【】31
1037.411764710        【】2.8301202087【】2936 【】31
1076.941176475        【】2.7652392397【】2978 【】34
1116.470588240        【】2.7694415174【】3092 【】35
1156                  【】2.6747404844【】3092 【】35

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