今天2022.09.10教师节，计算一下从20220910开始的连续50个偶数的素对数量

愚工688

重生888@ 发表于 2022-9-21 21:10
我凭肉眼，看这组数据，就能判断以下两个偶数小素数因子多：
2022092142
2022092160

我的计算值：

inf( 2022092100 )≈ 10814828.9 , jd ≈,infS(m) = 3190175.15 , k(m)= 3.39004
inf( 2022092102 )≈  3190175.2 , jd ≈,infS(m) = 3190175.15 , k(m)= 1
inf( 2022092104 )≈  3380503.1 , jd ≈,infS(m) = 3190175.15 , k(m)= 1.05966
inf( 2022092106 )≈  6830787.5 , jd ≈,infS(m) = 3190175.16 , k(m)= 2.1412
inf( 2022092108 )≈  3190175.2 , jd ≈,infS(m) = 3190175.16 , k(m)= 1
inf( 2022092110 )≈  4253566.9 , jd ≈,infS(m) = 3190175.16 , k(m)= 1.33333
inf( 2022092112 )≈  6466507.7 , jd ≈,infS(m) = 3190175.17 , k(m)= 2.02701
inf( 2022092114 )≈  3962027.2 , jd ≈,infS(m) = 3190175.17 , k(m)= 1.24195
inf( 2022092116 )≈  3615900.3 , jd ≈,infS(m) = 3190175.17 , k(m)= 1.13345
inf( 2022092118 )≈  6600362.4 , jd ≈,infS(m) = 3190175.17 , k(m)= 2.06897
inf( 2022092120 )≈  4362632.7 , jd ≈,infS(m) = 3190175.18 , k(m)= 1.36752
inf( 2022092122 )≈  3190175.2 , jd ≈,infS(m) = 3190175.18 , k(m)= 1
inf( 2022092124 )≈  6965352.6 , jd ≈,infS(m) = 3190175.18 , k(m)= 2.18338
inf( 2022092126 )≈  3193779.9 , jd ≈,infS(m) = 3190175.19 , k(m)= 1.00113
inf( 2022092128 )≈  3831157.4 , jd ≈,infS(m) = 3190175.19 , k(m)= 1.20092
inf( 2022092130 )≈  8514945.7 , jd ≈,infS(m) = 3190175.19 , k(m)= 2.66912
inf( 2022092132 )≈  3462552.7 , jd ≈,infS(m) = 3190175.20 , k(m)= 1.08538
inf( 2022092134 )≈  3190319.2 , jd ≈,infS(m) = 3190175.20 , k(m)= 1.00005
inf( 2022092136 )≈  6439979.9 , jd ≈,infS(m) = 3190175.20 , k(m)= 2.01869
inf( 2022092138 )≈  3753147.3 , jd ≈,infS(m) = 3190175.21 , k(m)= 1.17647
inf( 2022092140 )≈  4256696.9 , jd ≈,infS(m) = 3190175.21 , k(m)= 1.33431
inf( 2022092142 )≈  7656420.5 , jd ≈,infS(m) = 3190175.21 , k(m)= 2.4
inf( 2022092144 )≈  3215340.1 , jd ≈,infS(m) = 3190175.22 , k(m)= 1.00789
inf( 2022092146 )≈  3258260.6 , jd ≈,infS(m) = 3190175.22 , k(m)= 1.02134
inf( 2022092148 )≈  6459120.2 , jd ≈,infS(m) = 3190175.22 , k(m)= 2.02469
inf( 2022092150 )≈  4861219.4 , jd ≈,infS(m) = 3190175.23 , k(m)= 1.52381
inf( 2022092152 )≈  3190175.2 , jd ≈,infS(m) = 3190175.23 , k(m)= 1
inf( 2022092154 )≈  6394624.2 , jd ≈,infS(m) = 3190175.23 , k(m)= 2.00447
inf( 2022092156 )≈  3828210.3 , jd ≈,infS(m) = 3190175.23 , k(m)= 1.2
inf( 2022092158 )≈  3214905.3 , jd ≈,infS(m) = 3190175.24 , k(m)= 1.00775
inf( 2022092160 )≈  9604518.0 , jd ≈,infS(m) = 3190175.24 , k(m)= 3.01066
inf( 2022092162 )≈  3217464.2 , jd ≈,infS(m) = 3190175.24 , k(m)= 1.00855
inf( 2022092164 )≈  3308329.9 , jd ≈,infS(m) = 3190175.25 , k(m)= 1.03704
inf( 2022092166 )≈  6829926.8 , jd ≈,infS(m) = 3190175.25 , k(m)= 2.14093
inf( 2022092168 )≈  3192904.2 , jd ≈,infS(m) = 3190175.25 , k(m)= 1.00086
inf( 2022092170 )≈  5131287.2 , jd ≈,infS(m) = 3190175.26 , k(m)= 1.60847
inf( 2022092172 )≈  6488492.1 , jd ≈,infS(m) = 3190175.26 , k(m)= 2.0339
inf( 2022092174 )≈  3196699.1 , jd ≈,infS(m) = 3190175.26 , k(m)= 1.00204
inf( 2022092176 )≈  3709820.6 , jd ≈,infS(m) = 3190175.27 , k(m)= 1.16289
inf( 2022092178 )≈  6381173.9 , jd ≈,infS(m) = 3190175.27 , k(m)= 2.00026
inf( 2022092180 )≈  4560631.7 , jd ≈,infS(m) = 3190175.27 , k(m)= 1.42959
inf( 2022092182 )≈  3544639.2 , jd ≈,infS(m) = 3190175.28 , k(m)= 1.11111
inf( 2022092184 )≈  7688455.9 , jd ≈,infS(m) = 3190175.28 , k(m)= 2.41004
inf( 2022092186 )≈  3263021.9 , jd ≈,infS(m) = 3190175.28 , k(m)= 1.02283
inf( 2022092188 )≈  3190459.5 , jd ≈,infS(m) = 3190175.29 , k(m)= 1.00009
inf( 2022092190 )≈  8520690.4 , jd ≈,infS(m) = 3190175.29 , k(m)= 2.67092
inf( 2022092192 )≈  3196542.9 , jd ≈,infS(m) = 3190175.29 , k(m)= 1.002
inf( 2022092194 )≈  3210721.5 , jd ≈,infS(m) = 3190175.29 , k(m)= 1.00644
inf( 2022092196 )≈  6702825.4 , jd ≈,infS(m) = 3190175.30 , k(m)= 2.10108
inf( 2022092198 )≈  3831536.4 , jd ≈,infS(m) = 3190175.30 , k(m)= 1.20104
time start =09:21:07  ,time end =09:24:47   ,time use = 3分40秒

其中素因子系数 k(m)大的前9位的偶数与素对计算值的计算精度：
G(2022092100) = 10883535；inf( 2022092100 )≈ 10814828.9 , jd ≈0.99369 ,infS(m) = 3190175.15 , k(m)= 3.39004
G(2022092160) = 9667534； inf( 2022092160 )≈  9604518.0 , jd ≈0.99348 ,infS(m) = 3190175.24 , k(m)= 3.01066
G(2022092190) = 8575080； inf( 2022092190 )≈  8520690.4 , jd ≈0.99366 ,infS(m) = 3190175.29 , k(m)= 2.67092
G(2022092130) = 8570859； inf( 2022092130 )≈  8514945.7 , jd ≈0.99348 ,infS(m) = 3190175.19 , k(m)= 2.66912
G(2022092184) = 7737386； inf( 2022092184 )≈  7688455.9 , jd ≈0.99368 ,infS(m) = 3190175.28 , k(m)= 2.41004
G(2022092142) = 7704332； inf( 2022092142 )≈  7656420.5 , jd ≈0.99378 ,infS(m) = 3190175.21 , k(m)= 2.4
G(2022092124) = 7008019； inf( 2022092124 )≈  6965352.6 , jd ≈0.99391 ,infS(m) = 3190175.18 , k(m)= 2.18338
G(2022092106) = 6874442； inf( 2022092106 )≈  6830787.5 , jd ≈0.99365 ,infS(m) = 3190175.16 , k(m)= 2.1412
G(2022092166) = 6876423； inf( 2022092166 )≈  6829926.8 , jd ≈0.99324 ,infS(m) = 3190175.25 , k(m)= 2.14093

愚工688

因式分解：
2022092100 = 2 * 2 * 3 * 3 * 3 * 3 * 5 * 5 * 7 * 19 * 1877
2022092160 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 3 * 5 * 11 * 67 * 1429
2022092190 = 2 * 3 * 3 * 5 * 641 * 35051
2022092130 = 2 * 3 * 5 * 1091 * 61781
2022092184 = 2 * 2 * 2 * 3 * 7 * 241 * 49943
2022092142 =  2 * 3 * 7 *（ 48145051）—— 到此分解程序几乎死机了，余下括号内素数却不显示出来。

就是啊！ 48145051是素数，已经分解完成了，可是我的分解程序不显示 48145051出来，就是死机了，等好久也不出来，只能强退。用另外求素数的程序得出是素数。
48145001 , 48145051 , 48145057 , 48145073 , 48145087 , 48145091 , 48145099 ,
[ 48145000 , 48145100 ]: s(x) =  7 s1 = 0

实验证明我编写的因式分解程序还是存在一些缺陷的。

程序文本：


3   OPEN "shufenj.txt" FOR OUTPUT AS #8
4  DEFDBL A-P
5  INPUT " a ="; a
6  IF a < 6 THEN GOTO 95
10 a1 = a: j1 = 2
12 PRINT #8, a; "=";
14 PRINT a; "=";
20 FOR j = 2 TO a / 2
30 FOR i = 2 TO j ^ (1 / 2)
40 IF INT(j / i) = j / i THEN 70
50 NEXT i
51 IF a1 = j THEN 80
52 IF INT(a1 / j) = a1 / j THEN PRINT j; "*";  ELSE 70
54 IF INT(a1 / j) = a1 / j THEN PRINT #8, j; "*";
58 a1 = a1 / j
60 GOTO 51
70 NEXT j
80  PRINT a1
88 PRINT #8, a1

90 GOTO 5
95 END

重生888@

愚工688 发表于 2022-9-22 11:38
因式分解：
2022092100 = 2 * 2 * 3 * 3 * 3 * 3 * 5 * 5 * 7 * 19 * 1877
2022092160 = 2 * 2 * 2 *  ...

求偶数N最大素数对下限值，是正确的！
G（2022092100）=10814828
D（2022092100）=5/3*（W）=8464842           8464842/4=2116210
D1=2116210*6/5*18/17*4=10755326                D/G=0.994498

重生888@

接上：
G（2022092160）=9667534
D（2022092160）=8464842
D1=8464842*10/9*66/65=9550078
D1/G=0.987850

重生888@

除了愚工计算式，别人的计算式，想达到我这个精度是不可能的，唯有用无穷大比值=1来糊弄人！

重生888@

inf( 2022092122 ) = 1/(1+ .148 )*( 2022092122 /2 -2)*p(m) ≈ 3190175.2 ,k(m)=1; 其它偶数inf(M)/k(m)=3190175.…

麻烦好友再告诉P(m)是多少？谢谢！
如果能容易计算出3190175这个下确界，就很值得称赞！

愚工688

重生888@ 发表于 2022-9-22 21:59
inf( 2022092122 ) = 1/(1+ .148 )*( 2022092122 /2 -2)*p(m) ≈ 3190175.2 ,k(m)=1; 其它偶数inf(M)/k(m)= ...

P(m)是素数连乘式，P(m)=π【(p-2)/p 】×π[(p1-1)/(p1-2)] ；p:√M内的素数，p1：M含有的奇素数因子；

  素对计算式：Xi(M)=t2*c1*M/(logM)^2  ；
  式中：t2=1.358-(log(M))^(.5)*0.05484； c1:只计算√M内素数的类似拉曼扭杨系数。

  G(2022092300) = 4281219  ;Xi(M)≈ 4281088.45   δxi(M)≈? -0.0000306；
  G(2022092302) = 3428270  ;Xi(M)≈ 3427657.47   δxi(M)≈? -0.0001788；
  G(2022092304) = 6642278  ;Xi(M)≈ 6643068.3    δxi(M)≈?  0.0001189；
  G(2022092306) = 3502244  ;Xi(M)≈ 3502708.61   δxi(M)≈?  0.0001328；
  G(2022092308) = 3211891  ;Xi(M)≈ 3210816.27   δxi(M)≈? -0.0003347；
  G(2022092310) = 10300103 ;Xi(M)≈ 10300367.36  δxi(M)≈?  0.0000256；
  G(2022092312) = 3211204  ;Xi(M)≈ 3211221.56   δxi(M)≈?  0.0000061；
  G(2022092314) = 3610075  ;Xi(M)≈ 3611617.84   δxi(M)≈?  0.0004274；
  G(2022092316) = 6525690  ;Xi(M)≈ 6526704.74   δxi(M)≈?  0.0001555；
  G(2022092318) = 3212469  ;Xi(M)≈ 3211963.41   δxi(M)≈? -0.0002416；
  G(2022092320) = 4280770  ;Xi(M)≈ 4281088.49   δxi(M)≈?  0.0000743；
  G(2022092322) = 6421743  ;Xi(M)≈ 6421632.59   δxi(M)≈? -0.0000171；
  G(2022092324) = 3862542  ;Xi(M)≈ 3862219.18   δxi(M)≈? -0.0000836；
  G(2022092326) = 3236661  ;Xi(M)≈ 3237424.68   δxi(M)≈?  0.0002360；
  G(2022092328) = 6993757  ;Xi(M)≈ 6993643.46   δxi(M)≈? -0.0000163；
  time start =08:35:53, time end =08:36:37

无论是素对连乘式的计算值，还是类似哈李公式的素对计算值，它们的计算值相对误差绝对值都是比较小的，并且各个偶数的相对误差的波动性也很小。

时空伴随者

2022-09-23 09:54:14
2022092300 [2, 2, 5, 5, 20220923]
2022092302 [2, 17, 1231, 48313]
2022092304 [2, 2, 2, 2, 3, 31, 1358933]
2022092306 [2, 13, 77772781]
2022092308 [2, 2, 505523077]
2022092310 [2, 3, 5, 7, 7, 463, 2971]
2022092312 [2, 2, 2, 14669, 17231]
2022092314 [2, 11, 83, 1107389]
2022092316 [2, 2, 3, 3, 3, 101, 197, 941]
2022092318 [2, 2801, 360959]
2022092320 [2, 2, 2, 2, 2, 5, 12638077]
2022092322 [2, 3, 337015387]
2022092324 [2, 2, 7, 419, 172357]
2022092326 [2, 137, 1493, 4943]
2022092328 [2, 2, 2, 3, 19, 37, 119849]
2022092330 [2, 5, 202209233]
2022092332 [2, 2, 13, 199, 263, 743]
2022092334 [2, 3, 3, 23, 4884281]
2022092336 [2, 2, 2, 2, 11, 17, 211, 3203]
2022092338 [2, 7, 29, 337, 14779]
2022092340 [2, 2, 3, 5, 151, 307, 727]
2022092342 [2, 1011046171]
2022092344 [2, 2, 2, 379, 757, 881]
2022092346 [2, 3, 4831, 69761]
2022092348 [2, 2, 505523087]
2022092350 [2, 5, 5, 3797, 10651]
2022092352 [2, 2, 2, 2, 2, 2, 3, 3, 7, 501511]
2022092354 [2, 71, 109, 130643]
2022092356 [2, 2, 505523089]
2022092358 [2, 3, 11, 13, 53, 53, 839]
2022092360 [2, 2, 2, 5, 4397, 11497]
2022092362 [2, 1011046181]
2022092364 [2, 2, 3, 233, 723209]
2022092366 [2, 7, 19, 31, 41, 5981]
2022092368 [2, 2, 2, 2, 59, 269, 7963]
2022092370 [2, 3, 3, 3, 5, 17, 440543]
2022092372 [2, 2, 43, 11756351]
2022092374 [2, 47, 79, 272299]
2022092376 [2, 2, 2, 3, 84253849]
2022092378 [2, 1011046189]
2022092380 [2, 2, 5, 7, 11, 23, 57089]
2022092382 [2, 3, 6299, 53503]
2022092384 [2, 2, 2, 2, 2, 13, 4860799]
2022092386 [2, 1011046193]
2022092388 [2, 2, 3, 3, 1789, 31397]
2022092390 [2, 5, 202209239]
2022092392 [2, 2, 2, 227, 647, 1721]
2022092394 [2, 3, 7, 48145057]
2022092396 [2, 2, 29, 17431831]
2022092398 [2, 1103, 916633]
用时 0.0 秒

重生888@

我的公式，在任何偶数段，求出素数对值，都是稳定的：
D（2022092300）=5/6*（W）=4232421       4232421/2=2116210
D（2022092302）=2116210*1.5=3174315
D1=3174315*（17-1）/（17-2）=3385936
两个偶数素数对与真值相比都是0.988.....

愚工688

今天是2022-09-20日，以今天日期的10倍开始的连续偶数的素对数量的计算如下：


      Xi(M)=t2*c1*M/(logM)^2   
式中：t2=1.358-(log(M))^(.5)*0.05484;c1:只计算√M内素数的类似拉曼扭杨系数。
   

  G( 202209240 ) = ?       ;Xi(M)≈ 1088444.56   δxi(M)≈?
  G( 202209242 ) = ?       ;Xi(M)≈ 415305.8     δxi(M)≈?
  G( 202209244 ) = ?       ;Xi(M)≈ 408166.71    δxi(M)≈?
  G( 202209246 ) = ?       ;Xi(M)≈ 825716.6     δxi(M)≈?
  G( 202209248 ) = ?       ;Xi(M)≈ 437621.29    δxi(M)≈?
  G( 202209250 ) = ?       ;Xi(M)≈ 544222.31    δxi(M)≈?
  G( 202209252 ) = ?       ;Xi(M)≈ 979600.16    δxi(M)≈?
  G( 202209254 ) = ?       ;Xi(M)≈ 475258.07    δxi(M)≈?
  G( 202209256 ) = ?       ;Xi(M)≈ 408166.73    δxi(M)≈?
  G( 202209258 ) = ?       ;Xi(M)≈ 816333.48    δxi(M)≈?
  G( 202209260 ) = ?       ;Xi(M)≈ 609261.49    δxi(M)≈?
  G( 202209262 ) = ?       ;Xi(M)≈ 409569.38    δxi(M)≈?
  G( 202209264 ) = ?       ;Xi(M)≈ 820418.35    δxi(M)≈?
  G( 202209266 ) = ?       ;Xi(M)≈ 498101.79    δxi(M)≈?
  G( 202209268 ) = ?       ;Xi(M)≈ 411535.53    δxi(M)≈?
  G( 202209270 ) = ?       ;Xi(M)≈ 1103774.81   δxi(M)≈?
  G( 202209272 ) = ?       ;Xi(M)≈ 412289.62    δxi(M)≈?
  G( 202209274 ) = ?       ;Xi(M)≈ 408251.13    δxi(M)≈?
  G( 202209276 ) = ?       ;Xi(M)≈ 816333.48    δxi(M)≈?
  G( 202209278 ) = ?       ;Xi(M)≈ 416640.66    δxi(M)≈?
  time start =17:10:13, time end =17:10:27

   （明天再验证计算值精度。）