数学中国

标题: [原创]k生素数群的数量公式 [打印本页]

作者: 白新岭 时间: 2010-9-14 20:57
标题: [原创]k生素数群的数量公式
本帖最后由白新岭于 2018-11-5 06:43 编辑

[watermark]当P是素数，而且P+2m1,P+2m2,...P+2m(k-1）也是素数时，称这一组数为k生素数群，这里的m1,m2,m3,....m(k-1)为不同的正整数，且一个比一个要大。谁都知道（P，P+2）为孪生素数对。我们可以把（P,P+2,P+6)或者（P,P+4,P+6)成为3生素数群；4生素数群为（P,P+2,P+6,P+8)，仅此一种（指总间隔最短的4生素数群），也可以称为四胞胎素数群。一般k生素数群的数量与A*∫{1/[LN(n)]^k}d(n)式子联系密切，积分式取前边有限项即可，当阶乘函数值大于或等于LN(n)时截止，后边的项不在要。系数A可以通过分析求的。孪生素数对的系数为2倍的孪生素数常数；3生素数群的系数为：2.85824917688516 ；
5生素数群从素数7就走到正规了,系数为10.1318018169296 ；
7生素数群从素数11就走到正规了,系数为53.9720251184226 ；
4生素数群的系数在基础数学中有。6生的我计算后给出。
有编程能力的网友可以验证它是否正确。[/watermark]
这里所说k生素数群是指最密的k生素数群（前后两个素数的差值最小）。

系数A=P^(K-1)*(p-K)/(P-1)^K的连乘积=（1-k/P)/(1-1/P)^K的连乘积，只是（P-K）及（1-k/P)中的k在2p<=K生素数的总间距时，k值需要分析获得，当2P>K生素数的总间距d时，这时的k值就是k生素数的k值了。

作者: 白新岭 时间: 2010-9-14 22:34
标题: [原创]k生素数群的数量公式
本帖最后由白新岭于 2021-4-16 11:32 编辑

项目→→→→系数→→→→→→→→→→排列结构
Pi2（n)→→1.32032372118072 →→（P,P+2)
Pi3（n)→→2.8582491768851600 →→（P,P+2,P+6)
Pi3（n)→→2.8582491768851600 →→（P,P+4,P+6)
Pi4（n)→→4.1511825513462700 →→（P,P+2,P+6,P+8)
Pi5（n)→→10.1318018169296000 →→（P,P+2,P+6,P+8,P+12)
Pi5（n)→→10.1318018169296000 →→（P,P+4,P+6,P+10,P+12)
Pi6（n)→→17.2986298980835000 →→（P,P+4,P+6,P+10,P+12,P+16)
Pi7（n)→→53.9720251184226000 →→（P,P+2,P+8,P+12,P+14,P+18,P+20)
Pi7（n)→→53.9720251184226000 →→（P,P+2,P+6,P+8,P+12,P+18,P+20)
Pi8（n)→→178.26229268981000 →→（P,P+2,P+6,P+8,P+12,P+18,P+20,P+26)
Pi8（n)→→475.36611383949400 →→（P,P+2,P+6,P+12,P+14,P+20,P+24,P+26)
Pi8（n)→→178.26229268981000 →→（P,P+6,P+8,P+14,P+18,P+20,P+24,P+26)
k生素数的数量公式：主贴已有，关键是k生素数式（的给出），然后求其系数，就可以得到比较精确的公式解了。与真值的比值可以无限制向1靠近，误差率也会无限制向0靠近。今天这不是我要表达的重点，重点是给出k生素数的数量取值范围，即区间：如果用$G_k$(N)表示k生素数的数量，则系数(C)*N*($1\over (ln(N))^k$+$k\over{(ln(N))^{k+1}}$)<$G_k$(N)<系数(C)*N*($1\over (ln(N))^k$+$k\over{(ln(N))^{k+1}}$+$2k(k+1)\over{(ln(N))^{k+2}}$)
当范围值是$10^{k+10}$时，无反例出现
如果用G4-8表示最密4生素数的数量，则其中项和合成数的数量公式为：
$210\over9$∏(1-$16\over{(P-4)^2}$)∏${P_i-4}\over{P_i-8}$∏${P_j-6}\over{P_j-8}$∏${P_k-7}\over{P_k-8}$*$(G4-8)^2\over N$,P取大于7的所有素数，$P_i$整除被合成数；合成数除$P_j$余数为±2或者±6；合成数除$P_k$余数为±4或者±8。
如果用$G_2 (N)$表示孪生素数对的数量，用$G_3 (N)$表示最密3生素数的数量，用$G_4 (N)$表示最密4生素数的数量，用$G_{2L8}(N)$表示相邻二生素数（P，P+8）的数量（在P与（P+8）之间无其它素数）。则：$G_{2L8}(N)$=$G_2 (N)$-2$G_3 (N)$+$G_4 (N)$
存在等差k生素数公差d最小值使它中的素数之和遍历偶数
http://www.mathchina.com/bbs/for ... 5&fromuid=37263
(出处: 数学中国)
上边的链接有关于等差k生素数的中项（或同一位置上的）数和遍历全体偶数的一些相关分析。等差4生素数（P，P+30，P+60，P+90）并不能遍历全体偶数（这是给有心人埋的伏笔）。
存在任意长度的素数差的等比数列且公比为任意正整数及其倒数
http://www.mathchina.com/bbs/for ... 8&fromuid=37263
(出处: 数学中国)
本链接是关于素数差形成等比数列的问题，谈到了，首项值，及什么值可以做公比，一切除0的自然数及其倒数都可以做为公比，当公比是1时，就形成了等差k生素数。
哈代-李特伍尔德给出了哥德巴赫猜想的猜想公式（这是关于二素数之和的分布公式），现在我给出二素数差的公式（关于二素数差是同一个值的分布情况），由于二素数差的本身特性，决定它的计算精度优越于哈代-李特伍尔德给出的有关哥德巴赫猜想的公式（只是数值的接近真实值的程度上，理论上大相径庭，因为哈代-李特伍尔德给的公式是用高深莫测的圆法获得，而我的仅仅是是用数论的初步知识，结合二元运算和群论给出的，方法不在这里叙述，也不公布）。
用$G_2 (2m)$表示二素差值等于2m的数量则：2$C_2$∏${P_i-1}\over {P_i-2}$ ${N-2m}\over(ln(N-2m))^2$,$P_i$整除2m
相邻k生素数数量公式及包含的其它k生素数
http://www.mathchina.com/bbs/for ... 9&fromuid=37263
(出处: 数学中国)
这是有关相邻k生素数数量的分析与探讨。
等差4生素数中项的合成分布
http://www.mathchina.com/bbs/for ... 7&fromuid=37263
(出处: 数学中国)
这是一个关于等差4生素数的中项和分布问题专区。
最密2生素数的中项和中（即孪生素数对的中项和，或者二生素数（P,P+4）的中项和中），合成方法与余数类目关系恒等：
$(P-2)^2$=1*(P-2)+2*(P-3)+(P-3）*（P-4)，P≥5.

3生素数有两种形式，一种是（P,P+2,P+6),另一种是（P,P+4,P+6)，这里的三生素数是第一种形式，中项即P+3.其公式D3中（N）=17.2986185466273*∏${P_i-4}\over{P_i-6}$∏${P_j-5}\over{P_j-6}$*$N\over(ln(N))^6$,$P_i$≥7,N≡-2，0，4mod$P_i$；$P_j$≥7,N≡-6，2，6mod$P_j$；当N≡4MOD5时，还需要乘2.
一个孪生素数对中项合成数（6n）的一种公式：$G_2$(6n)=6∏(1-$4\over(P-2)^2$)∏${P_i-2}\over{P_i-4}$∏${P_j-3}\over{P_j-4}$$(孪生素数对数量)^2\over{6n}$，$P_i$整除6n，6n除$P_j$的余数为±2.
Hardy-Littlewood为搜索做准备。
对于线性不定方程的正整数解的问题:$X_1$+$X_2$+$X_3$+$X_4$+$X_5$+$X_6$+......+$X_m$=N,
我们可以用高中学过的排列组合学来解决。用插入挡板法，对于排列好的一组物体（可以是任何的实物，比方用乒乓球），共计N个物体，现在我们拿来m-1个挡板，这N个物体之间有N-1个空隙，我们把这m-1块挡板放到N-1个空隙中去，就把这N个物体分成了m块区域，有前后顺序的m块区域，安前后顺序分别对应着$X_i$,正好对应着每个未知数，所以这种放挡板的方法数就是线性不定方程正整数的解组数。即为：$C_{N-1}^{m-1}$.
我的签名中除(m-1)!也是来源于此。
【成功】需要高人指点，贵人相助，小人监督，个人奋斗。

作者: 白新岭 时间: 2010-9-14 22:40
标题: [原创]k生素数群的数量公式
Table of PI_X(10^n)( 2 <= X <= 7, 8 < n < 17)
__________________________________________________________________________________________________
| x |  PI2(x)  t2(s) | PI3(x) t3(s) |PI4(x) t4(s) |PI5(x) t5(s)| PI6(x) t6(s)| PI7(X)  t(7)
---------------------------------------------------------------------------------------------------
| 10^09 |3424506    0.75|379508    0.55|28388 0.22 |3633    0.19|317    0.09| 54
|    |          0.25|379748    0.17|       0.08 |3588          |       0.03| 49
----------------------------------------------------------------------------------------------------
| 10^10 |27412679 7.24|2713347    4.63|180529  1.64 |20203    1.28|1613    0.55| 234
|    |          2.37|2712226    1.56|       0.58 |20211    0.53|       0.17| 239 0.17
---------------------------------------------------------------------------------------------------
| 10^11 |224376048 112|20093124 64.7|1209318 19.3 |122457 12.95|8626 4.34|1183
|    |          26.3|20081601 17.9|       6.15 |122855    3.91|       1.50|1152 1.22
----------------------------------------------------------------------------------------------------
| 10^12 |1870585220  1005|152850135 580|8398278 186. |776237 117.2|50408 40.51|6056
|    |          255|152839134 156|       53.5 |775986    34.1|       12.4|5913  10.2
----------------------------------------------------------------------------------------------------
| 10^13 |15834664872    |1189795268    |60069713 2324|5108291       |303828 440|33395
|    |          4369|1189826966  2304|+877    685|5109269    381|       132|33066 102
----------------------------------------------------------------------------------------------------
| 10^14 |135780321665 |9443942337    |441296836 |34709176    |1911246    |193078
|    |          35694|9443899421 20344|       6440|34701400 3750|       1304|192731 988
----------------------------------------------------------------------------------------------------
| 10^15 |1177209242304 |76222348070  (x)|3314576487 |242554539    |12431996    |1167688 +24
|    |             |             |+8790 96564|242526656 50564|+133 16116|1166385 +26 10563
----------------------------------------------------------------------------------------------------
| 10^16 |10304195697298  |             |25379433651  |             |83217782    |
|    |       3000h |             |          |             |    216236|
----------------------------------------------------------------------------------------------------
| 10^17 |             |             |          |             |482142192 (x)|
|    |             |             |          |             |+1170 3556211|
----------------------------------------------------------------------------------------------------
prime 4-tuples(10 ^ 16) = 25379433651,       time use 340h
prime 6-tuples(10 ^ 16) = 82942101 + 1170,    time use 55.01h
prime 6-tuples(10 ^ 15) = 12431996 + 133,    time use 16116.41s
prime 4-tuples(10 ^ 14) = 441295937+ 899,    time use 6439.90s
prime 4-tuples(10 ^ 15) = 3314576487,          time use 96563.25s
prime 2-tuples(10 ^ 14) = 135780262685 + 58980, time use 35693.32s
prime 8-tuples(10 ^ 15) = 116493,             time use 8427.10s // one of the patterns
这是数学研发论坛上一位网友提供的数据

作者: 白新岭 时间: 2010-9-16 16:34
标题: [原创]k生素数群的数量公式
10^n││5生素数数量
8││681
9││3585
10││20372
11││122828
12││776669
13││5107218
14││34706119
15││242545119
16││1736514735
17││12697644704
18││94586697962
19││7.16292E+11
20││5.50479E+12
21││4.28683E+13
22││3.37851E+14
23││2.69172E+15
24││2.16591E+16
25││1.7587E+17
26││1.44003E+18
27││1.18821E+19
28││9.87449E+19
29││8.26057E+20
30││6.95314E+21
31││5.88639E+22
32││5.01017E+23
33││4.28592E+24
34││3.68377E+25
35││3.18036E+26
36││2.7573E+27
37││2.40001E+28
38││2.09688E+29
39││1.83855E+30
40││1.61749E+31
41││1.42758E+32
42││1.26381E+33
43││1.12208E+34
44││9.98998E+34
45││8.91771E+35
46││7.98064E+36
47││7.1593E+37
48││6.43734E+38
49││5.80101E+39
50││5.2387E+40
51││4.74055E+41
52││4.29818E+42
53││3.90444E+43
54││3.5532E+44
55││3.2392E+45
56││2.95793E+46
57││2.70546E+47
58││2.47841E+48
59││2.27385E+49
60││2.08923E+50
61││1.9223E+51
62││1.77113E+52
63││1.634E+53
64││1.50941E+54
65││1.39606E+55
66││1.29277E+56
以上是5生素数的近似组数（其中一种，5生素数有两种排列顺序，在2楼已经写出）

作者: 白新岭 时间: 2010-9-16 17:01
标题: [原创]k生素数群的数量公式
10^n││5生素数数量││6生素数数量││7生素数数量
8││681││70││13
9││3585││319││52
10││20372││1611││234
11││122828││8753││1145
12││776669││50400││5995
13││5107218││304356││33222
14││34706119││1912615││192970
15││242545119││12433000││1166417
16││1736514735││83213875││7296237
17││12697644704││571290926││47021237
18││94586697962││4010801182││311077956
19││7.16292E+11││28722154081││2106339586
20││5.50479E+12││2.0936E+11││14560885311
21││4.28683E+13││1.55053E+12││1.02549E+11
22││3.37851E+14││1.16497E+13││7.34476E+11
23││2.69172E+15││8.86781E+13││5.34138E+12
24││2.16591E+16││6.83113E+14││3.93891E+13
25││1.7587E+17││5.31996E+15││2.94196E+14
26││1.44003E+18││4.18486E+16││2.22325E+15
27││1.18821E+19││3.32256E+17││1.69838E+16
28││9.87449E+19││2.66064E+18││1.31047E+17
29││8.26057E+20││2.14759E+19││1.02059E+18
30││6.95314E+21││1.74635E+20││8.01737E+18
31││5.88639E+22││1.42992E+21││6.34912E+19
32││5.01017E+23││1.1784E+22││5.06605E+20
33││4.28592E+24││9.77027E+22││4.07094E+21
34││3.68377E+25││8.14681E+23││3.29309E+22
35││3.18036E+26││6.82956E+24││2.68055E+23
36││2.7573E+27││5.75423E+25││2.19483E+24
37││2.40001E+28││4.87137E+26││1.80715E+25
38││2.09688E+29││4.14258E+27││1.49579E+26
39││1.83855E+30││3.53788E+28││1.24425E+27
40││1.61749E+31││3.03371E+29││1.03992E+28
41││1.42758E+32││2.6114E+30││8.73049E+28
42││1.26381E+33││2.25612E+31││7.36092E+29
43││1.12208E+34││1.95598E+32││6.23148E+30
44││9.98998E+34││1.70141E+33││5.29582E+31
45││8.91771E+35││1.48466E+34││4.51733E+32
46││7.98064E+36││1.29946E+35││3.86693E+33
47││7.1593E+37││1.14066E+36││3.32138E+34
48││6.43734E+38││1.00405E+37││2.86204E+35
49││5.80101E+39││8.86148E+37││2.47389E+36
50││5.2387E+40││7.84089E+38││2.14475E+37
51││4.74055E+41││6.95484E+39││1.86472E+38
52││4.29818E+42││6.18344E+40││1.62571E+39
53││3.90444E+43││5.51004E+41││1.42107E+40
54││3.5532E+44││4.92067E+42││1.24535E+41
55││3.2392E+45││4.40355E+43││1.09403E+42
56││2.95793E+46││3.94874E+44││9.63366E+42
57││2.70546E+47││3.5478E+45││8.50235E+43
58││2.47841E+48││3.19357E+46││7.52035E+44
59││2.27385E+49││2.87992E+47││6.66585E+45
60││2.08923E+50││2.60163E+48││5.92054E+46
61││1.9223E+51││2.35421E+49││5.26897E+47
62││1.77113E+52││2.13381E+50││4.69807E+48
63││1.634E+53││1.93712E+51││4.19678E+49
64││1.50941E+54││1.76126E+52││3.7557E+50
65││1.39606E+55││1.60374E+53││3.36682E+51
66││1.29277E+56││1.46242E+54││3.02328E+52

作者: 白新岭 时间: 2010-9-24 07:51
标题: [原创]k生素数群的数量公式
项目→→→→系数→→→→→→→→→→排列结构
Pi2（n)→→1.32032372118072 →→（P,P+2)
Pi3（n)→→2.8582491768851600 →→（P,P+2,P+6)
Pi3（n)→→2.8582491768851600 →→（P,P+4,P+6)
Pi4（n)→→4.1511825513462700 →→（P,P+2,P+6,P+8)
Pi5（n)→→10.1318018169296000 →→（P,P+2,P+6,P+8,P+12)
Pi5（n)→→10.1318018169296000 →→（P,P+4,P+6,P+10,P+12)
Pi6（n)→→17.2986298980835000 →→（P,P+4,P+6,P+10,P+12,P+16)
Pi7（n)→→53.9720251184226000 →→（P,P+2,P+8,P+12,P+14,P+18,P+20)
Pi7（n)→→53.9720251184226000 →→（P,P+2,P+6,P+8,P+12,P+18,P+20)
Pi8（n)→→178.26229268981000 →→（P,P+2,P+6,P+8,P+12,P+18,P+20,P+26)
Pi8（n)→→475.36611383949400 →→（P,P+2,P+6,P+12,P+14,P+20,P+24,P+26)
Pi8（n)→→178.26229268981000 →→（P,P+6,P+8,P+14,P+18,P+20,P+24,P+26)
Pi9（n)→→630.06589997229100 →→（P,P+2,P+6,P+8,P+12,P+18,P+20,P+26,P+30)
Pi9（n)→→1260.13179994458000 →→（P,P+2,P+6,P+12,P+14,P+20,P+24,P+26,P+30)
Pi9（n)→→1260.13179994458000 →→（P,P+4,P+6,P+10,P+16,P+18,P+24,P+28,P+30)
Pi9（n)→→630.06589997229100 →→（P,P+4,P+10,P+12,P+18,P+22,P+24,P+28,P+30)
Pi10（n)→→1704.74613953383000 →→（P,P+2,P+6,P+12,P+14,P+20,P+24,P+26,P+30,P+32)
Pi10（n)→→1704.74613953383000 →→（P,P+2,P+6,P+8,P+12,P+18,P+20,P+26,P+30,P+32)
Pi11（n)→→3062.09074084973000 →→（P,P+4,P+6,P+10,P+16,P+18,P+24,P+28,P+30,P+34,P+36)
Pi11（n)→→3062.09074084973000 →→（P,P+2,P+6,P+8,P+12,P+18,P+20,P+26,P+30,P+32,P+36)
Pi12（n)→→9931.36007094338000 →→（P,P+2,P+6,P+8,P+12,P+18,P+20,P+26,P+30,P+32,P+36,P+42)
Pi12（n)→→9931.36007094338000 →→（P,P+6,P+10,P+12,P+16,P+22,P+24,P+30,P+34,P+36,P+40,P+42)

作者: 白新岭 时间: 2010-9-24 07:52
标题: [原创]k生素数群的数量公式
10^n││2生素数数量││3生素数数量││4生素数数量
8││440365││55482││4722
9││3425306││379794││28384
10││27411416││2715284││181063
11││224368877││20089649││1209944
12││1870559991││152830589││8394569
13││15834599375││1189763338││60075450
14││135780274095 ││9443892325││441290899
15││1177208571645 ││76217795487││3314551625
16││10304193252876 ││6.24025E+11││25379451643
17││90948839425186 ││5.17369E+12││1.97622E+11
18││808675956302870 ││4.33714E+13││1.56177E+12
19││7.23752E+15││3.67176E+14││1.25056E+13
20││6.51543E+16││3.13588E+15││1.01319E+14
21││5.8963E+17││2.69947E+16││8.29588E+14
22││5.36144E+18││2.34045E+17││6.85773E+15
23││4.89622E+19││2.0424E+18││5.71827E+16
24││4.48905E+20││1.79291E+19││4.80603E+17
25││4.13065E+21││1.58246E+20││4.06873E+18
26││3.81354E+22││1.40372E+21││3.46759E+19
27││3.5316E+23││1.25091E+22││2.97351E+20
28││3.27981E+24││1.11952E+23││2.56441E+21
29││3.05403E+25││1.0059E+24││2.22332E+22
30││2.85079E+26││9.07153E+24││1.93711E+23
31││2.66719E+27││8.20924E+25││1.69552E+24
32││2.50077E+28││7.45288E+26││1.49046E+25
33││2.34946E+29││6.78668E+27││1.31548E+26
34││2.21148E+30││6.19758E+28││1.16545E+27
35││2.08531E+31││5.67475E+29││1.03622E+28
36││1.96964E+32││5.20912E+30││9.24412E+28
37││1.86334E+33││4.79308E+31││8.2729E+29
38││1.76541E+34││4.42019E+32││7.42596E+30
39││1.67501E+35││4.08501E+33││6.68469E+31
40││1.59138E+36││3.78288E+34││6.03367E+32
41││1.51386E+37││3.50983E+35││5.46001E+33
42││1.44187E+38││3.26244E+36││4.95295E+34
43││1.37489E+39││3.03777E+37││4.50341E+35
44││1.31248E+40││2.83326E+38││4.10374E+36
45││1.25422E+41││2.64671E+39││3.74745E+37
46││1.19976E+42││2.47619E+40││3.429E+38
47││1.14877E+43││2.32E+41││3.14367E+39
48││1.10096E+44││2.17668E+42││2.88742E+40
49││1.05608E+45││2.04493E+43││2.65675E+41
50││1.01389E+46││1.9236E+44││2.44867E+42
51││9.74171E+46││1.81169E+45││2.26056E+43
52││9.36746E+47││1.70829E+46││2.09018E+44
53││9.01436E+48││1.61261E+47││1.93556E+45
54││8.68086E+49││1.52394E+48││1.79497E+46
55││8.36554E+50││1.44166E+49││1.66692E+47
56││8.06709E+51││1.3652E+50││1.55009E+48
57││7.78433E+52││1.29405E+51││1.44331E+49
58││7.51618E+53││1.22776E+52││1.34558E+50
59││7.26165E+54││1.16592E+53││1.25598E+51
60││7.01984E+55││1.10817E+54││1.17371E+52
61││6.78991E+56││1.05417E+55││1.09807E+53
62││6.57109E+57││1.00362E+56││1.02843E+54
63││6.36268E+58││9.56252E+56││9.64226E+54
64││6.16404E+59││9.1182E+57││9.04953E+55
65││5.97455E+60││8.70098E+58││8.50166E+56
66││5.79367E+61││8.30883E+59││7.99462E+57

作者: 白新岭 时间: 2010-9-24 07:53
标题: [原创]k生素数群的数量公式
10^n││8生素数数量││8生素数数量││9生素数数量││9生素数数量
8││3││7││1││1
9││9││25││2││3
10││36││97││6││12
11││159││425││24││48
12││758││2020││103││206
13││3849││10264││479││957
14││20653││55075││2371││4742
15││116037││309431││12376││24752
16││678171││1808457││67558││135116
17││4101786││10938095││383389││766777
18││25566765││68178041││2251055││4502110
19││163662705││436433879││13621011││27242023
20││1072864137││2860971031││84661816││169323632
21││7184652904││19159074411││539043103││1078086205
22││49049400344││1.30798E+11││3507502810││7015005620
23││3.40765E+11││9.08708E+11││23277483146││46554966291
24││2.40548E+12││6.4146E+12││1.57282E+11││3.14565E+11
25││1.72301E+13││4.59468E+13││1.08036E+12││2.16072E+12
26││1.25083E+14││3.33555E+14││7.53399E+12││1.5068E+13
27││9.19361E+14││2.45163E+15││5.32765E+13││1.06553E+14
28││6.83511E+15││1.8227E+16││3.81636E+14││7.63271E+14
29││5.13594E+16││1.36958E+17││2.76668E+15││5.53337E+15
30││3.89752E+17││1.03934E+18││2.02818E+16││4.05636E+16
31││2.98513E+18││7.96034E+18││1.50233E+17││3.00466E+17
32││2.30613E+19││6.14968E+19││1.12368E+18││2.24736E+18
33││1.79604E+20││4.78943E+20││8.4815E+18││1.6963E+19
34││1.40943E+21││3.75849E+21││6.45676E+19││1.29135E+20
35││1.11397E+22││2.9706E+22││4.95507E+20││9.91013E+20
36││8.864E+22││2.36373E+23││3.83156E+21││7.66313E+21
37││7.09816E+23││1.89284E+24││2.98408E+22││5.96817E+22
38││5.71838E+24││1.5249E+25││2.33984E+23││4.67967E+23
39││4.63312E+25││1.2355E+26││1.84648E+24││3.69296E+24
40││3.77417E+26││1.00644E+27││1.46603E+25││2.93207E+25
41││3.09027E+27││8.24073E+27││1.17072E+26││2.34143E+26
42││2.54268E+28││6.78049E+28││9.40039E+26││1.88008E+27
43││2.10187E+29││5.60499E+29││7.58772E+27││1.51754E+28
44││1.7452E+30││4.65386E+30││6.15521E+28││1.23104E+29
45││1.45519E+31││3.8805E+31││5.01697E+29││1.00339E+30
46││1.21829E+32││3.24876E+32││4.10786E+30││8.21571E+30
47││1.0239E+33││2.7304E+33││3.37814E+31││6.75629E+31
48││8.6372E+33││2.30325E+34││2.78965E+32││5.57929E+32
49││7.31187E+34││1.94983E+35││2.31288E+33││4.62576E+33
50││6.21099E+35││1.65626E+36││1.92495E+34││3.8499E+34
51││5.29311E+36││1.4115E+37││1.60798E+35││3.21597E+35
52││4.52505E+37││1.20668E+38││1.34796E+36││2.69592E+36
53││3.88012E+38││1.0347E+39││1.13382E+37││2.26764E+37
54││3.33678E+39││8.89808E+39││9.56823E+37││1.91365E+38
55││2.87755E+40││7.67347E+40││8.09998E+38││1.62E+39
56││2.48822E+41││6.63525E+41││6.87783E+39││1.37557E+40
57││2.15715E+42││5.75241E+42││5.85718E+40││1.17144E+41
58││1.87483E+43││4.99954E+43││5.00207E+41││1.00041E+42
59││1.6334E+44││4.35573E+44││4.28344E+42││8.56688E+42
60││1.42639E+45││3.80371E+45││3.67771E+43││7.35542E+43
61││1.24843E+46││3.32915E+46││3.16567E+44││6.33134E+44
62││1.09507E+47││2.92018E+47││2.73163E+45││5.46326E+45
63││9.62574E+47││2.56686E+48││2.36271E+46││4.72543E+46
64││8.47845E+48││2.26092E+49││2.04833E+47││4.09667E+47
65││7.48273E+49││1.99539E+50││1.77975E+48││3.5595E+48
66││6.61665E+50││1.76444E+51││1.54973E+49││3.09946E+49

作者: 白新岭 时间: 2010-9-24 07:55
标题: [原创]k生素数群的数量公式
10^n││10生素数数量││11生素数数量││12生素数数量
8││0││0││0
9││0││0││0
10││1││0││0
11││3││0││0
12││11││1││0
13││46││3││0
14││209││12││1
15││1013││55││5
16││5161││262││24
17││27470││1309││113
18││151897││6813││553
19││868657││36816││2821
20││5118603││205636││14932
21││30982408││1183149││81652
22││192131139││6991776││459763
23││1217923593││42331059││2658378
24││7876536132││262009150││15746509
25││51880709114││1654792675││95354503
26││3.47524E+11││10646963304││589255184
27││2.36431E+12││69683997723││3710056020
28││1.63175E+13││4.63348E+11││23766265766
29││1.14127E+14││3.12645E+12││1.54704E+11
30││8.08172E+14││2.13856E+13││1.02215E+12
31││5.78944E+15││1.48155E+14││6.84796E+12
32││4.19238E+16││1.03868E+15││4.64785E+13
33││3.06677E+17││7.36347E+15││3.19321E+14
34││2.2648E+18││5.2751E+16││2.21905E+15
35││1.68757E+19││3.8164E+17││1.55874E+16
36││1.2681E+20││2.7868E+18││1.10606E+17
37││9.60513E+20││2.05288E+19││7.92389E+17
38││7.33027E+21││1.52481E+20││5.72829E+18
39││5.6342E+22││1.1415E+21││4.17667E+19
40││4.35994E+23││8.60935E+21││3.07017E+20
41││3.39561E+24││6.53931E+22││2.27429E+21
42││2.66076E+25││5.00049E+23││1.69713E+22
43││2.09711E+26││3.84833E+24││1.27531E+23
44││1.66204E+27││2.97976E+25││9.64738E+23
45││1.32423E+28││2.3207E+26││7.34451E+24
46││1.06042E+29││1.8175E+27││5.62539E+25
47││8.53281E+29││1.43099E+28││4.33376E+26
48││6.8979E+30││1.13244E+29││3.3573E+27
49││5.60103E+31││9.00555E+29││2.61474E+28
50││4.56737E+32││7.19513E+30││2.04685E+29
51││3.73971E+33││5.77456E+31││1.61017E+30
52││3.07407E+34││4.6545E+32││1.27263E+31
53││2.53646E+35││3.7673E+33││1.01042E+32
54││2.10047E+36││3.06141E+34││8.05737E+32
55││1.74552E+37││2.49737E+35││6.45218E+33
56││1.45544E+38││2.04481E+36││5.18771E+34
57││1.21751E+39││1.68025E+37││4.18733E+35
58││1.02168E+40││1.38545E+38││3.3926E+36
59││8.59939E+40││1.14619E+39││2.7587E+37
60││7.25923E+41││9.51296E+39││2.25113E+38
61││6.14525E+42││7.92E+40││1.84319E+39
62││5.21646E+43││6.61363E+41││1.51413E+40
63││4.43976E+44││5.53882E+42││1.24776E+41
64││3.78839E+45││4.65177E+43││1.03143E+42
65││3.24062E+46││3.91745E+44││8.55137E+42
66││2.77871E+47││3.30779E+45││7.11027E+43

作者: 白新岭 时间: 2010-10-6 19:19
标题: [原创]k生素数群的数量公式
本帖最后由白新岭于 2016-7-18 09:15 编辑

这些数据随着n的增大，前边的有效数字是非常准确的，及相对误差越来越小，会无限制的接近0，但永远也不会是0.
很多人对拉曼扭杨系数都感兴趣，都知道那是用特异功能感应到的系数，却不寻找其原因，不追根问底，所以就没有新的发现，找不到更具有深刻含义的系数。
你可以找到偶数在孪生素数对集合中的分拆公式和系数，还可以继续深挖。

作者: 白新岭 时间: 2010-10-24 15:40
标题: [原创]k生素数群的数量公式
试着给出30n的偶数在4生素数群中值的分拆公式。4生素数群指（P,P+2,P+6,P+8)这样的素数群，这一组数同时都是素数，每组中的素数间隔距离恒定。中值是指P+4,它是合数，一定有因子5，但P,及P+2,P+6，P+8都是素数。

作者: 白新岭 时间: 2010-11-17 07:58
标题: [原创]k生素数群的数量公式
上边各楼分别列出了2-12生素数在10^66次方以前的数量，有编程能力的网友可以验证。

作者: 白新岭 时间: 2010-11-29 20:48
标题: [原创]k生素数群的数量公式
有兴趣的网友可以继续研究k生素数群的中值的2维加法合成，即k生素数群的前后两个素数的中项值相加的分布情况，也可以给出渐进公式。

作者: 白新岭 时间: 2011-4-20 08:04
标题: [原创]k生素数群的数量公式
k生素数群的数量渐进公式已经找到。只是系数不能全部给出。

作者: APB先生 时间: 2011-4-20 20:52
标题: [原创]k生素数群的数量公式
助君成功！

作者: 白新岭 时间: 2011-5-4 06:28
标题: [原创]k生素数群的数量公式
素数与歌猜，孪生素数对与12n类数的猜想及渐进公式值

作者: 白新岭 时间: 2011-8-19 07:58
标题: [原创]k生素数群的数量公式
今天浏览此帖时已沉到10页，为了方便感兴趣的网友阅读特顶起。

作者: 白新岭 时间: 2011-11-30 10:41
标题: [原创]k生素数群的数量公式
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→48→→→→0→→→→0→→→→48
2→→→→2→→→→46→→→→6→→→→6→→→→42
6→→→→4→→→→42→→→→12→→→→6→→→→36
8→→→→2→→→→40→→→→16→→→→4→→→→32
12→→→→4→→→→36→→→→18→→→→2→→→→30
18→→→→6→→→→30→→→→22→→→→4→→→→26
20→→→→2→→→→28→→→→28→→→→6→→→→20
26→→→→6→→→→22→→→→30→→→→2→→→→18
30→→→→4→→→→18→→→→36→→→→6→→→→12
32→→→→2→→→→16→→→→40→→→→4→→→→8
36→→→→4→→→→12→→→→42→→→→2→→→→6
42→→→→6→→→→6→→→→46→→→→4→→→→2
48→→→→6→→→→0→→→→48→→→→2→→→→0
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→48→→→→0→→→→0→→→→48
4→→→→4→→→→44→→→→2→→→→2→→→→46
6→→→→2→→→→42→→→→8→→→→6→→→→40
10→→→→4→→→→38→→→→14→→→→6→→→→34
16→→→→6→→→→32→→→→18→→→→4→→→→30
18→→→→2→→→→30→→→→20→→→→2→→→→28
24→→→→6→→→→24→→→→24→→→→4→→→→24
28→→→→4→→→→20→→→→30→→→→6→→→→18
30→→→→2→→→→18→→→→32→→→→2→→→→16
34→→→→4→→→→14→→→→38→→→→6→→→→10
40→→→→6→→→→8→→→→42→→→→4→→→→6
46→→→→6→→→→2→→→→44→→→→2→→→→4
48→→→→2→→→→0→→→→48→→→→4→→→→0
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→48→→→→0→→→→0→→→→48
4→→→→4→→→→44→→→→2→→→→2→→→→46
6→→→→2→→→→42→→→→12→→→→10→→→→36
10→→→→4→→→→38→→→→14→→→→2→→→→34
16→→→→6→→→→32→→→→18→→→→4→→→→30
18→→→→2→→→→30→→→→20→→→→2→→→→28
24→→→→6→→→→24→→→→24→→→→4→→→→24
28→→→→4→→→→20→→→→30→→→→6→→→→18
30→→→→2→→→→18→→→→32→→→→2→→→→16
34→→→→4→→→→14→→→→38→→→→6→→→→10
36→→→→2→→→→12→→→→42→→→→4→→→→6
46→→→→10→→→→2→→→→44→→→→2→→→→4
48→→→→2→→→→0→→→→48→→→→4→→→→0
以前发表了前12生的排列形式及最短间距和10的66次方内的数量，及系数，这是13生素数的6种不同的排列形式，和最短间距。这样多的排列形式出乎我的意料。

作者: 白新岭 时间: 2011-11-30 11:37
标题: [原创]k生素数群的数量公式
14生素数的最短间距和排列顺序（即结构式）
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→50→→→→0→→→→0→→→→50
2→→→→2→→→→48→→→→2→→→→2→→→→48
8→→→→6→→→→42→→→→6→→→→4→→→→44
14→→→→6→→→→36→→→→8→→→→2→→→→42
18→→→→4→→→→32→→→→12→→→→4→→→→38
20→→→→2→→→→30→→→→18→→→→6→→→→32
24→→→→4→→→→26→→→→20→→→→2→→→→30
30→→→→6→→→→20→→→→26→→→→6→→→→24
32→→→→2→→→→18→→→→30→→→→4→→→→20
38→→→→6→→→→12→→→→32→→→→2→→→→18
42→→→→4→→→→8→→→→36→→→→4→→→→14
44→→→→2→→→→6→→→→42→→→→6→→→→8
48→→→→4→→→→2→→→→48→→→→6→→→→2
50→→→→2→→→→0→→→→50→→→→2→→→→0

作者: 白新岭 时间: 2011-11-30 13:42
标题: [原创]k生素数群的数量公式
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→56→→→→0→→→→0→→→→56
2→→→→2→→→→54→→→→6→→→→6→→→→50
6→→→→4→→→→50→→→→8→→→→2→→→→48
8→→→→2→→→→48→→→→14→→→→6→→→→42
12→→→→4→→→→44→→→→20→→→→6→→→→36
18→→→→6→→→→38→→→→24→→→→4→→→→32
20→→→→2→→→→36→→→→26→→→→2→→→→30
26→→→→6→→→→30→→→→30→→→→4→→→→26
30→→→→4→→→→26→→→→36→→→→6→→→→20
32→→→→2→→→→24→→→→38→→→→2→→→→18
36→→→→4→→→→20→→→→44→→→→6→→→→12
42→→→→6→→→→14→→→→48→→→→4→→→→8
48→→→→6→→→→8→→→→50→→→→2→→→→6
50→→→→2→→→→6→→→→54→→→→4→→→→2
56→→→→6→→→→0→→→→56→→→→2→→→→0
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→56→→→→0→→→→0→→→→56
2→→→→2→→→→54→→→→2→→→→2→→→→54
6→→→→4→→→→50→→→→6→→→→4→→→→50
12→→→→6→→→→44→→→→12→→→→6→→→→44
14→→→→2→→→→42→→→→14→→→→2→→→→42
20→→→→6→→→→36→→→→20→→→→6→→→→36
24→→→→4→→→→32→→→→26→→→→6→→→→30
26→→→→2→→→→30→→→→30→→→→4→→→→26
30→→→→4→→→→26→→→→32→→→→2→→→→24
36→→→→6→→→→20→→→→36→→→→4→→→→20
42→→→→6→→→→14→→→→42→→→→6→→→→14
44→→→→2→→→→12→→→→44→→→→2→→→→12
50→→→→6→→→→6→→→→50→→→→6→→→→6
54→→→→4→→→→2→→→→54→→→→4→→→→2
56→→→→2→→→→0→→→→56→→→→2→→→→0
以上是15生素数的最短间距和排列顺序（即结构式）

作者: 白新岭 时间: 2011-11-30 13:45
标题: [原创]k生素数群的数量公式
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→60→→→→0→→→→0→→→→60
4→→→→4→→→→56→→→→2→→→→2→→→→58
6→→→→2→→→→54→→→→6→→→→4→→→→54
10→→→→4→→→→50→→→→12→→→→6→→→→48
16→→→→6→→→→44→→→→14→→→→2→→→→46
18→→→→2→→→→42→→→→20→→→→6→→→→40
24→→→→6→→→→36→→→→26→→→→6→→→→34
28→→→→4→→→→32→→→→30→→→→4→→→→30
30→→→→2→→→→30→→→→32→→→→2→→→→28
34→→→→4→→→→26→→→→36→→→→4→→→→24
40→→→→6→→→→20→→→→42→→→→6→→→→18
46→→→→6→→→→14→→→→44→→→→2→→→→16
48→→→→2→→→→12→→→→50→→→→6→→→→10
54→→→→6→→→→6→→→→54→→→→4→→→→6
58→→→→4→→→→2→→→→56→→→→2→→→→4
60→→→→2→→→→0→→→→60→→→→4→→→→0
以上是16生素数的最短间距和排列顺序（即结构式）

作者: 白新岭 时间: 2011-11-30 14:03
标题: [原创]k生素数群的数量公式
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
13→→→→0→→→→66→→→→2231→→→→0→→→→66
17→→→→4→→→→62→→→→2237→→→→6→→→→60
19→→→→2→→→→60→→→→2239→→→→2→→→→58
23→→→→4→→→→56→→→→2243→→→→4→→→→54
29→→→→6→→→→50→→→→2249→→→→6→→→→48
31→→→→2→→→→48→→→→2251→→→→2→→→→46
37→→→→6→→→→42→→→→2257→→→→6→→→→40
41→→→→4→→→→38→→→→2263→→→→6→→→→34
43→→→→2→→→→36→→→→2267→→→→4→→→→30
47→→→→4→→→→32→→→→2269→→→→2→→→→28
53→→→→6→→→→26→→→→2273→→→→4→→→→24
59→→→→6→→→→20→→→→2279→→→→6→→→→18
61→→→→2→→→→18→→→→2281→→→→2→→→→16
67→→→→6→→→→12→→→→2287→→→→6→→→→10
71→→→→4→→→→8→→→→2291→→→→4→→→→6
73→→→→2→→→→6→→→→2293→→→→2→→→→4
79→→→→6→→→→0→→→→2297→→→→4→→→→0
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
17→→→→0→→→→66→→→→2227→→→→0→→→→66
19→→→→2→→→→64→→→→2231→→→→4→→→→62
23→→→→4→→→→60→→→→2237→→→→6→→→→56
29→→→→6→→→→54→→→→2239→→→→2→→→→54
31→→→→2→→→→52→→→→2243→→→→4→→→→50
37→→→→6→→→→46→→→→2249→→→→6→→→→44
41→→→→4→→→→42→→→→2251→→→→2→→→→42
43→→→→2→→→→40→→→→2257→→→→6→→→→36
47→→→→4→→→→36→→→→2263→→→→6→→→→30
53→→→→6→→→→30→→→→2267→→→→4→→→→26
59→→→→6→→→→24→→→→2269→→→→2→→→→24
61→→→→2→→→→22→→→→2273→→→→4→→→→20
67→→→→6→→→→16→→→→2279→→→→6→→→→14
71→→→→4→→→→12→→→→2281→→→→2→→→→12
73→→→→2→→→→10→→→→2287→→→→6→→→→6
79→→→→6→→→→4→→→→2291→→→→4→→→→2
83→→→→4→→→→0→→→→2293→→→→2→→→→0
以上是17生素数的最短间距和排列顺序（即结构式）

作者: 白新岭 时间: 2011-12-1 21:04
标题: [原创]k生素数群的数量公式
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→70→→→→0→→→→0→→→→70
4→→→→4→→→→66→→→→4→→→→4→→→→66
6→→→→2→→→→64→→→→10→→→→6→→→→60
10→→→→4→→→→60→→→→12→→→→2→→→→58
16→→→→6→→→→54→→→→16→→→→4→→→→54
18→→→→2→→→→52→→→→22→→→→6→→→→48
24→→→→6→→→→46→→→→24→→→→2→→→→46
28→→→→4→→→→42→→→→30→→→→6→→→→40
30→→→→2→→→→40→→→→36→→→→6→→→→34
34→→→→4→→→→36→→→→40→→→→4→→→→30
40→→→→6→→→→30→→→→42→→→→2→→→→28
46→→→→6→→→→24→→→→46→→→→4→→→→24
48→→→→2→→→→22→→→→52→→→→6→→→→18
54→→→→6→→→→16→→→→54→→→→2→→→→16
58→→→→4→→→→12→→→→60→→→→6→→→→10
60→→→→2→→→→10→→→→64→→→→4→→→→6
66→→→→6→→→→4→→→→66→→→→2→→→→4
70→→→→4→→→→0→→→→70→→→→4→→→→0
这是18生素数的最短间距及排列顺序和相邻素数的间隔排列顺序。

作者: ysr 时间: 2011-12-2 11:30
标题: [原创]k生素数群的数量公式
能搞到渐进公式很不错,系数不会是常数吧,素数是越来越稀的,希望公式是多项式级的,不要太复杂,否则不实用,上面数据看不太懂,其中的0是p+n中n的值吗?是间隔为0吗?

作者: 白新岭 时间: 2011-12-4 20:09
标题: [原创]k生素数群的数量公式
系数当然是一个常数，变数就没有意义了。主项是一个式子的积分。取前有限项即可，并不复杂。0是p+n中的n值，表示第一项p

作者: 白新岭 时间: 2011-12-4 20:13
标题: [原创]k生素数群的数量公式
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→76→→→→0→→→→0→→→→76
4→→→→4→→→→72→→→→6→→→→6→→→→70
6→→→→2→→→→70→→→→10→→→→4→→→→66
10→→→→4→→→→66→→→→16→→→→6→→→→60
16→→→→6→→→→60→→→→18→→→→2→→→→58
18→→→→2→→→→58→→→→22→→→→4→→→→54
24→→→→6→→→→52→→→→28→→→→6→→→→48
28→→→→4→→→→48→→→→30→→→→2→→→→46
30→→→→2→→→→46→→→→36→→→→6→→→→40
34→→→→4→→→→42→→→→42→→→→6→→→→34
40→→→→6→→→→36→→→→46→→→→4→→→→30
46→→→→6→→→→30→→→→48→→→→2→→→→28
48→→→→2→→→→28→→→→52→→→→4→→→→24
54→→→→6→→→→22→→→→58→→→→6→→→→18
58→→→→4→→→→18→→→→60→→→→2→→→→16
60→→→→2→→→→16→→→→66→→→→6→→→→10
66→→→→6→→→→10→→→→70→→→→4→→→→6
70→→→→4→→→→6→→→→72→→→→2→→→→4
76→→→→6→→→→0→→→→76→→→→4→→→→0
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→76→→→→0→→→→0→→→→76
4→→→→4→→→→72→→→→4→→→→4→→→→72
6→→→→2→→→→70→→→→6→→→→2→→→→70
10→→→→4→→→→66→→→→10→→→→4→→→→66
16→→→→6→→→→60→→→→12→→→→2→→→→64
22→→→→6→→→→54→→→→16→→→→4→→→→60
24→→→→2→→→→52→→→→24→→→→8→→→→52
30→→→→6→→→→46→→→→30→→→→6→→→→46
34→→→→4→→→→42→→→→34→→→→4→→→→42
36→→→→2→→→→40→→→→40→→→→6→→→→36
42→→→→6→→→→34→→→→42→→→→2→→→→34
46→→→→4→→→→30→→→→46→→→→4→→→→30
52→→→→6→→→→24→→→→52→→→→6→→→→24
60→→→→8→→→→16→→→→54→→→→2→→→→22
64→→→→4→→→→12→→→→60→→→→6→→→→16
66→→→→2→→→→10→→→→66→→→→6→→→→10
70→→→→4→→→→6→→→→70→→→→4→→→→6
72→→→→2→→→→4→→→→72→→→→2→→→→4
76→→→→4→→→→0→→→→76→→→→4→→→→0
这是19生素数的4种不同的排列顺序及间距。

作者: 白新岭 时间: 2011-12-4 20:29
标题: [原创]k生素数群的数量公式
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→→→→→80→→→→0→→→→→→→→80
2→→→→2→→→→78→→→→2→→→→2→→→→78
8→→→→6→→→→72→→→→6→→→→4→→→→74
12→→→→4→→→→68→→→→8→→→→2→→→→72
14→→→→2→→→→66→→→→12→→→→4→→→→68
18→→→→4→→→→62→→→→20→→→→8→→→→60
24→→→→6→→→→56→→→→26→→→→6→→→→54
30→→→→6→→→→50→→→→30→→→→4→→→→50
32→→→→2→→→→48→→→→36→→→→6→→→→44
38→→→→6→→→→42→→→→38→→→→2→→→→42
42→→→→4→→→→38→→→→42→→→→4→→→→38
44→→→→2→→→→36→→→→48→→→→6→→→→32
50→→→→6→→→→30→→→→50→→→→2→→→→30
54→→→→4→→→→26→→→→56→→→→6→→→→24
60→→→→6→→→→20→→→→62→→→→6→→→→18
68→→→→8→→→→12→→→→66→→→→4→→→→14
72→→→→4→→→→8→→→→68→→→→2→→→→12
74→→→→2→→→→6→→→→72→→→→4→→→→8
78→→→→4→→→→2→→→→78→→→→6→→→→2
80→→→→2→→→→0→→→→80→→→→2→→→→0
这是20生素数的2种排列顺序及间隔

作者: 白新岭 时间: 2011-12-4 20:48
标题: [原创]k生素数群的数量公式
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→84→→→→0→→→→0→→→→84
2→→→→2→→→→82→→→→4→→→→4→→→→80
8→→→→6→→→→76→→→→6→→→→2→→→→78
12→→→→4→→→→72→→→→10→→→→4→→→→74
14→→→→2→→→→70→→→→12→→→→2→→→→72
18→→→→4→→→→66→→→→16→→→→4→→→→68
24→→→→6→→→→60→→→→24→→→→8→→→→60
30→→→→6→→→→54→→→→30→→→→6→→→→54
32→→→→2→→→→52→→→→34→→→→4→→→→50
38→→→→6→→→→46→→→→40→→→→6→→→→44
42→→→→4→→→→42→→→→42→→→→2→→→→42
44→→→→2→→→→40→→→→46→→→→4→→→→38
50→→→→6→→→→34→→→→52→→→→6→→→→32
54→→→→4→→→→30→→→→54→→→→2→→→→30
60→→→→6→→→→24→→→→60→→→→6→→→→24
68→→→→8→→→→16→→→→66→→→→6→→→→18
72→→→→4→→→→12→→→→70→→→→4→→→→14
74→→→→2→→→→10→→→→72→→→→2→→→→12
78→→→→4→→→→6→→→→76→→→→4→→→→8
80→→→→2→→→→4→→→→82→→→→6→→→→2
84→→→→4→→→→0→→→→84→→→→2→→→→0
这是21生素数的2种排列顺序及间隔

作者: 白新岭 时间: 2011-12-6 21:15
标题: [原创]k生素数群的数量公式
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→90→→→→0→→→→0→→→→90
6→→→→6→→→→84→→→→4→→→→4→→→→86
8→→→→2→→→→82→→→→6→→→→2→→→→84
14→→→→6→→→→76→→→→10→→→→4→→→→80
18→→→→4→→→→72→→→→12→→→→2→→→→78
20→→→→2→→→→70→→→→16→→→→4→→→→74
24→→→→4→→→→66→→→→24→→→→8→→→→66
30→→→→6→→→→60→→→→30→→→→6→→→→60
36→→→→6→→→→54→→→→34→→→→4→→→→56
38→→→→2→→→→52→→→→40→→→→6→→→→50
44→→→→6→→→→46→→→→42→→→→2→→→→48
48→→→→4→→→→42→→→→46→→→→4→→→→44
50→→→→2→→→→40→→→→52→→→→6→→→→38
56→→→→6→→→→34→→→→54→→→→2→→→→36
60→→→→4→→→→30→→→→60→→→→6→→→→30
66→→→→6→→→→24→→→→66→→→→6→→→→24
74→→→→8→→→→16→→→→70→→→→4→→→→20
78→→→→4→→→→12→→→→72→→→→2→→→→18
80→→→→2→→→→10→→→→76→→→→4→→→→14
84→→→→4→→→→6→→→→82→→→→6→→→→8
86→→→→2→→→→4→→→→84→→→→2→→→→6
90→→→→4→→→→0→→→→90→→→→6→→→→0
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→→→→→90→→→→0→→→→→→→→90
4→→→→4→→→→86→→→→2→→→→2→→→→88
10→→→→6→→→→80→→→→6→→→→4→→→→84
12→→→→2→→→→78→→→→8→→→→2→→→→82
18→→→→6→→→→72→→→→12→→→→4→→→→78
22→→→→4→→→→68→→→→20→→→→8→→→→70
24→→→→2→→→→66→→→→26→→→→6→→→→64
28→→→→4→→→→62→→→→30→→→→4→→→→60
34→→→→6→→→→56→→→→36→→→→6→→→→54
40→→→→6→→→→50→→→→38→→→→2→→→→52
42→→→→2→→→→48→→→→42→→→→4→→→→48
48→→→→6→→→→42→→→→48→→→→6→→→→42
52→→→→4→→→→38→→→→50→→→→2→→→→40
54→→→→2→→→→36→→→→56→→→→6→→→→34
60→→→→6→→→→30→→→→62→→→→6→→→→28
64→→→→4→→→→26→→→→66→→→→4→→→→24
70→→→→6→→→→20→→→→68→→→→2→→→→22
78→→→→8→→→→12→→→→72→→→→4→→→→18
82→→→→4→→→→8→→→→78→→→→6→→→→12
84→→→→2→→→→6→→→→80→→→→2→→→→10
88→→→→4→→→→2→→→→86→→→→6→→→→4
90→→→→2→→→→0→→→→90→→→→4→→→→0
这是22生素数的4种排列顺序及间隔

作者: 白新岭 时间: 2011-12-6 22:25
标题: [原创]k生素数群的数量公式
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→100→→→→0→→→→0→→→→100
4→→→→4→→→→96→→→→4→→→→4→→→→96
6→→→→2→→→→94→→→→6→→→→2→→→→94
10→→→→4→→→→90→→→→12→→→→6→→→→88
16→→→→6→→→→84→→→→16→→→→4→→→→84
18→→→→2→→→→82→→→→24→→→→8→→→→76
24→→→→6→→→→76→→→→30→→→→6→→→→70
28→→→→4→→→→72→→→→34→→→→4→→→→66
30→→→→2→→→→70→→→→40→→→→6→→→→60
34→→→→4→→→→66→→→→42→→→→2→→→→58
40→→→→6→→→→60→→→→46→→→→4→→→→54
46→→→→6→→→→54→→→→52→→→→6→→→→48
48→→→→2→→→→52→→→→54→→→→2→→→→46
54→→→→6→→→→46→→→→60→→→→6→→→→40
58→→→→4→→→→42→→→→66→→→→6→→→→34
60→→→→2→→→→40→→→→70→→→→4→→→→30
66→→→→6→→→→34→→→→72→→→→2→→→→28
70→→→→4→→→→30→→→→76→→→→4→→→→24
76→→→→6→→→→24→→→→82→→→→6→→→→18
84→→→→8→→→→16→→→→84→→→→2→→→→16
88→→→→4→→→→12→→→→90→→→→6→→→→10
94→→→→6→→→→6→→→→94→→→→4→→→→6
96→→→→2→→→→4→→→→96→→→→2→→→→4
100→→→→4→→→→0→→→→100→→→→4→→→→0
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→100→→→→0→→→→0→→→→100
4→→→→4→→→→96→→→→4→→→→4→→→→96
6→→→→2→→→→94→→→→6→→→→2→→→→94
10→→→→4→→→→90→→→→10→→→→4→→→→90
16→→→→6→→→→84→→→→12→→→→2→→→→88
18→→→→2→→→→82→→→→16→→→→4→→→→84
24→→→→6→→→→76→→→→24→→→→8→→→→76
28→→→→4→→→→72→→→→30→→→→6→→→→70
30→→→→2→→→→70→→→→34→→→→4→→→→66
34→→→→4→→→→66→→→→40→→→→6→→→→60
40→→→→6→→→→60→→→→42→→→→2→→→→58
48→→→→8→→→→52→→→→46→→→→4→→→→54
54→→→→6→→→→46→→→→52→→→→6→→→→48
58→→→→4→→→→42→→→→60→→→→8→→→→40
60→→→→2→→→→40→→→→66→→→→6→→→→34
66→→→→6→→→→34→→→→70→→→→4→→→→30
70→→→→4→→→→30→→→→72→→→→2→→→→28
76→→→→6→→→→24→→→→76→→→→4→→→→24
84→→→→8→→→→16→→→→82→→→→6→→→→18
88→→→→4→→→→12→→→→84→→→→2→→→→16
90→→→→2→→→→10→→→→90→→→→6→→→→10
94→→→→4→→→→6→→→→94→→→→4→→→→6
96→→→→2→→→→4→→→→96→→→→2→→→→4
100→→→→4→→→→0→→→→100→→→→4→→→→0
以上为24生素数的4种排列顺序及间距，正好为100.

作者: 白新岭 时间: 2011-12-6 22:31
标题: [原创]k生素数群的数量公式
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→94→→→→0→→→→0→→→→94
4→→→→4→→→→90→→→→4→→→→4→→→→90
10→→→→6→→→→84→→→→6→→→→2→→→→88
12→→→→2→→→→82→→→→10→→→→4→→→→84
18→→→→6→→→→76→→→→12→→→→2→→→→82
22→→→→4→→→→72→→→→16→→→→4→→→→78
24→→→→2→→→→70→→→→24→→→→8→→→→70
28→→→→4→→→→66→→→→30→→→→6→→→→64
34→→→→6→→→→60→→→→34→→→→4→→→→60
40→→→→6→→→→54→→→→40→→→→6→→→→54
42→→→→2→→→→52→→→→42→→→→2→→→→52
48→→→→6→→→→46→→→→46→→→→4→→→→48
52→→→→4→→→→42→→→→52→→→→6→→→→42
54→→→→2→→→→40→→→→54→→→→2→→→→40
60→→→→6→→→→34→→→→60→→→→6→→→→34
64→→→→4→→→→30→→→→66→→→→6→→→→28
70→→→→6→→→→24→→→→70→→→→4→→→→24
78→→→→8→→→→16→→→→72→→→→2→→→→22
82→→→→4→→→→12→→→→76→→→→4→→→→18
84→→→→2→→→→10→→→→82→→→→6→→→→12
88→→→→4→→→→6→→→→84→→→→2→→→→10
90→→→→2→→→→4→→→→90→→→→6→→→→4
94→→→→4→→→→0→→→→94→→→→4→→→→0
这是23生素数的2种排列顺序及间隔

作者: 白新岭 时间: 2011-12-7 21:05
标题: [原创]k生素数群的数量公式
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→110→→→→0→→→→0→→→→110
2→→→→2→→→→108→→→→2→→→→2→→→→108
8→→→→6→→→→102→→→→8→→→→6→→→→102
12→→→→4→→→→98→→→→12→→→→4→→→→98
14→→→→2→→→→96→→→→26→→→→14→→→→84
18→→→→4→→→→92→→→→30→→→→4→→→→80
24→→→→6→→→→86→→→→32→→→→2→→→→78
30→→→→6→→→→80→→→→36→→→→4→→→→74
32→→→→2→→→→78→→→→38→→→→2→→→→72
38→→→→6→→→→72→→→→42→→→→4→→→→68
42→→→→4→→→→68→→→→50→→→→8→→→→60
44→→→→2→→→→66→→→→56→→→→6→→→→54
50→→→→6→→→→60→→→→60→→→→4→→→→50
54→→→→4→→→→56→→→→66→→→→6→→→→44
60→→→→6→→→→50→→→→68→→→→2→→→→42
68→→→→8→→→→42→→→→72→→→→4→→→→38
72→→→→4→→→→38→→→→78→→→→6→→→→32
74→→→→2→→→→36→→→→80→→→→2→→→→30
78→→→→4→→→→32→→→→86→→→→6→→→→24
80→→→→2→→→→30→→→→92→→→→6→→→→18
84→→→→4→→→→26→→→→96→→→→4→→→→14
98→→→→14→→→→12→→→→98→→→→2→→→→12
102→→→→4→→→→8→→→→102→→→→4→→→→8
108→→→→6→→→→2→→→→108→→→→6→→→→2
110→→→→2→→→→0→→→→110→→→→2→→→→0
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→110→→→→0→→→→0→→→→110
2→→→→2→→→→108→→→→2→→→→2→→→→108
6→→→→4→→→→104→→→→14→→→→12→→→→96
8→→→→2→→→→102→→→→18→→→→4→→→→92
12→→→→4→→→→98→→→→20→→→→2→→→→90
20→→→→8→→→→90→→→→24→→→→4→→→→86
26→→→→6→→→→84→→→→30→→→→6→→→→80
30→→→→4→→→→80→→→→32→→→→2→→→→78
36→→→→6→→→→74→→→→38→→→→6→→→→72
38→→→→2→→→→72→→→→42→→→→4→→→→68
42→→→→4→→→→68→→→→44→→→→2→→→→66
50→→→→8→→→→60→→→→48→→→→4→→→→62
56→→→→6→→→→54→→→→54→→→→6→→→→56
62→→→→6→→→→48→→→→60→→→→6→→→→50
66→→→→4→→→→44→→→→68→→→→8→→→→42
68→→→→2→→→→42→→→→72→→→→4→→→→38
72→→→→4→→→→38→→→→74→→→→2→→→→36
78→→→→6→→→→32→→→→80→→→→6→→→→30
80→→→→2→→→→30→→→→84→→→→4→→→→26
86→→→→6→→→→24→→→→90→→→→6→→→→20
90→→→→4→→→→20→→→→98→→→→8→→→→12
92→→→→2→→→→18→→→→102→→→→4→→→→8
96→→→→4→→→→14→→→→104→→→→2→→→→6
108→→→→12→→→→2→→→→108→→→→4→→→→2
110→→→→2→→→→0→→→→110→→→→2→→→→0
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→110→→→→0→→→→0→→→→110
2→→→→2→→→→108→→→→2→→→→2→→→→108
6→→→→4→→→→104→→→→12→→→→10→→→→98
8→→→→2→→→→102→→→→14→→→→2→→→→96
12→→→→4→→→→98→→→→18→→→→4→→→→92
20→→→→8→→→→90→→→→20→→→→2→→→→90
26→→→→6→→→→84→→→→24→→→→4→→→→86
30→→→→4→→→→80→→→→30→→→→6→→→→80
36→→→→6→→→→74→→→→32→→→→2→→→→78
38→→→→2→→→→72→→→→38→→→→6→→→→72
42→→→→4→→→→68→→→→42→→→→4→→→→68
48→→→→6→→→→62→→→→44→→→→2→→→→66
56→→→→8→→→→54→→→→54→→→→10→→→→56
66→→→→10→→→→44→→→→62→→→→8→→→→48
68→→→→2→→→→42→→→→68→→→→6→→→→42
72→→→→4→→→→38→→→→72→→→→4→→→→38
78→→→→6→→→→32→→→→74→→→→2→→→→36
80→→→→2→→→→30→→→→80→→→→6→→→→30
86→→→→6→→→→24→→→→84→→→→4→→→→26
90→→→→4→→→→20→→→→90→→→→6→→→→20
92→→→→2→→→→18→→→→98→→→→8→→→→12
96→→→→4→→→→14→→→→102→→→→4→→→→8
98→→→→2→→→→12→→→→104→→→→2→→→→6
108→→→→10→→→→2→→→→108→→→→4→→→→2
110→→→→2→→→→0→→→→110→→→→2→→→→0
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→110→→→→0→→→→0→→→→110
2→→→→2→→→→108→→→→6→→→→6→→→→104
6→→→→4→→→→104→→→→8→→→→2→→→→102
12→→→→6→→→→98→→→→14→→→→6→→→→96
14→→→→2→→→→96→→→→20→→→→6→→→→90
20→→→→6→→→→90→→→→24→→→→4→→→→86
24→→→→4→→→→86→→→→30→→→→6→→→→80
26→→→→2→→→→84→→→→36→→→→6→→→→74
30→→→→4→→→→80→→→→38→→→→2→→→→72
32→→→→2→→→→78→→→→44→→→→6→→→→66
42→→→→10→→→→68→→→→50→→→→6→→→→60
44→→→→2→→→→66→→→→54→→→→4→→→→56
54→→→→10→→→→56→→→→56→→→→2→→→→54
56→→→→2→→→→54→→→→66→→→→10→→→→44
60→→→→4→→→→50→→→→68→→→→2→→→→42
66→→→→6→→→→44→→→→78→→→→10→→→→32
72→→→→6→→→→38→→→→80→→→→2→→→→30
74→→→→2→→→→36→→→→84→→→→4→→→→26
80→→→→6→→→→30→→→→86→→→→2→→→→24
86→→→→6→→→→24→→→→90→→→→4→→→→20
90→→→→4→→→→20→→→→96→→→→6→→→→14
96→→→→6→→→→14→→→→98→→→→2→→→→12
102→→→→6→→→→8→→→→104→→→→6→→→→6
104→→→→2→→→→6→→→→108→→→→4→→→→2
110→→→→6→→→→0→→→→110→→→→2→→→→0
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→110→→→→0→→→→0→→→→110
2→→→→2→→→→108→→→→2→→→→2→→→→108
12→→→→10→→→→98→→→→6→→→→4→→→→104
14→→→→2→→→→96→→→→8→→→→2→→→→102
18→→→→4→→→→92→→→→12→→→→4→→→→98
20→→→→2→→→→90→→→→20→→→→8→→→→90
24→→→→4→→→→86→→→→26→→→→6→→→→84
30→→→→6→→→→80→→→→30→→→→4→→→→80
32→→→→2→→→→78→→→→36→→→→6→→→→74
38→→→→6→→→→72→→→→38→→→→2→→→→72
42→→→→4→→→→68→→→→42→→→→4→→→→68
44→→→→2→→→→66→→→→50→→→→8→→→→60
54→→→→10→→→→56→→→→56→→→→6→→→→54
60→→→→6→→→→50→→→→66→→→→10→→→→44
68→→→→8→→→→42→→→→68→→→→2→→→→42
72→→→→4→→→→38→→→→72→→→→4→→→→38
74→→→→2→→→→36→→→→78→→→→6→→→→32
80→→→→6→→→→30→→→→80→→→→2→→→→30
84→→→→4→→→→26→→→→86→→→→6→→→→24
90→→→→6→→→→20→→→→90→→→→4→→→→20
98→→→→8→→→→12→→→→92→→→→2→→→→18
102→→→→4→→→→8→→→→96→→→→4→→→→14
104→→→→2→→→→6→→→→98→→→→2→→→→12
108→→→→4→→→→2→→→→108→→→→10→→→→2
110→→→→2→→→→0→→→→110→→→→2→→→→0
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→110→→→→0→→→→0→→→→110
8→→→→8→→→→102→→→→2→→→→2→→→→108
12→→→→4→→→→98→→→→6→→→→4→→→→104
14→→→→2→→→→96→→→→8→→→→2→→→→102
18→→→→4→→→→92→→→→12→→→→4→→→→98
20→→→→2→→→→90→→→→18→→→→6→→→→92
24→→→→4→→→→86→→→→20→→→→2→→→→90
32→→→→8→→→→78→→→→26→→→→6→→→→84
38→→→→6→→→→72→→→→30→→→→4→→→→80
42→→→→4→→→→68→→→→32→→→→2→→→→78
48→→→→6→→→→62→→→→36→→→→4→→→→74
54→→→→6→→→→56→→→→42→→→→6→→→→68
60→→→→6→→→→50→→→→50→→→→8→→→→60
68→→→→8→→→→42→→→→56→→→→6→→→→54
74→→→→6→→→→36→→→→62→→→→6→→→→48
78→→→→4→→→→32→→→→68→→→→6→→→→42
80→→→→2→→→→30→→→→72→→→→4→→→→38
84→→→→4→→→→26→→→→78→→→→6→→→→32
90→→→→6→→→→20→→→→86→→→→8→→→→24
92→→→→2→→→→18→→→→90→→→→4→→→→20
98→→→→6→→→→12→→→→92→→→→2→→→→18
102→→→→4→→→→8→→→→96→→→→4→→→→14
104→→→→2→→→→6→→→→98→→→→2→→→→12
108→→→→4→→→→2→→→→102→→→→4→→→→8
110→→→→2→→→→0→→→→110→→→→8→→→→0
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→110→→→→0→→→→0→→→→110
2→→→→2→→→→108→→→→2→→→→2→→→→108
12→→→→10→→→→98→→→→6→→→→4→→→→104
18→→→→6→→→→92→→→→8→→→→2→→→→102
20→→→→2→→→→90→→→→12→→→→4→→→→98
24→→→→4→→→→86→→→→20→→→→8→→→→90
30→→→→6→→→→80→→→→26→→→→6→→→→84
32→→→→2→→→→78→→→→30→→→→4→→→→80
38→→→→6→→→→72→→→→36→→→→6→→→→74
42→→→→4→→→→68→→→→38→→→→2→→→→72
44→→→→2→→→→66→→→→42→→→→4→→→→68
54→→→→10→→→→56→→→→48→→→→6→→→→62
60→→→→6→→→→50→→→→50→→→→2→→→→60
62→→→→2→→→→48→→→→56→→→→6→→→→54
68→→→→6→→→→42→→→→66→→→→10→→→→44
72→→→→4→→→→38→→→→68→→→→2→→→→42
74→→→→2→→→→36→→→→72→→→→4→→→→38
80→→→→6→→→→30→→→→78→→→→6→→→→32
84→→→→4→→→→26→→→→80→→→→2→→→→30
90→→→→6→→→→20→→→→86→→→→6→→→→24
98→→→→8→→→→12→→→→90→→→→4→→→→20
102→→→→4→→→→8→→→→92→→→→2→→→→18
104→→→→2→→→→6→→→→98→→→→6→→→→12
108→→→→4→→→→2→→→→108→→→→10→→→→2
110→→→→2→→→→0→→→→110→→→→2→→→→0
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→110→→→→0→→→→0→→→→110
2→→→→2→→→→108→→→→2→→→→2→→→→108
14→→→→12→→→→96→→→→6→→→→4→→→→104
18→→→→4→→→→92→→→→8→→→→2→→→→102
20→→→→2→→→→90→→→→12→→→→4→→→→98
24→→→→4→→→→86→→→→20→→→→8→→→→90
30→→→→6→→→→80→→→→26→→→→6→→→→84
32→→→→2→→→→78→→→→30→→→→4→→→→80
38→→→→6→→→→72→→→→36→→→→6→→→→74
42→→→→4→→→→68→→→→38→→→→2→→→→72
44→→→→2→→→→66→→→→42→→→→4→→→→68
48→→→→4→→→→62→→→→48→→→→6→→→→62
54→→→→6→→→→56→→→→56→→→→8→→→→54
62→→→→8→→→→48→→→→62→→→→6→→→→48
68→→→→6→→→→42→→→→66→→→→4→→→→44
72→→→→4→→→→38→→→→68→→→→2→→→→42
74→→→→2→→→→36→→→→72→→→→4→→→→38
80→→→→6→→→→30→→→→78→→→→6→→→→32
84→→→→4→→→→26→→→→80→→→→2→→→→30
90→→→→6→→→→20→→→→86→→→→6→→→→24
98→→→→8→→→→12→→→→90→→→→4→→→→20
102→→→→4→→→→8→→→→92→→→→2→→→→18
104→→→→2→→→→6→→→→96→→→→4→→→→14
108→→→→4→→→→2→→→→108→→→→12→→→→2
110→→→→2→→→→0→→→→110→→→→2→→→→0
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→110→→→→0→→→→0→→→→110
8→→→→8→→→→102→→→→2→→→→2→→→→108
12→→→→4→→→→98→→→→6→→→→4→→→→104
14→→→→2→→→→96→→→→8→→→→2→→→→102
20→→→→6→→→→90→→→→12→→→→4→→→→98
24→→→→4→→→→86→→→→18→→→→6→→→→92
32→→→→8→→→→78→→→→20→→→→2→→→→90
38→→→→6→→→→72→→→→26→→→→6→→→→84
42→→→→4→→→→68→→→→30→→→→4→→→→80
48→→→→6→→→→62→→→→32→→→→2→→→→78
54→→→→6→→→→56→→→→36→→→→4→→→→74
60→→→→6→→→→50→→→→42→→→→6→→→→68
62→→→→2→→→→48→→→→48→→→→6→→→→62
68→→→→6→→→→42→→→→50→→→→2→→→→60
74→→→→6→→→→36→→→→56→→→→6→→→→54
78→→→→4→→→→32→→→→62→→→→6→→→→48
80→→→→2→→→→30→→→→68→→→→6→→→→42
84→→→→4→→→→26→→→→72→→→→4→→→→38
90→→→→6→→→→20→→→→78→→→→6→→→→32
92→→→→2→→→→18→→→→86→→→→8→→→→24
98→→→→6→→→→12→→→→90→→→→4→→→→20
102→→→→4→→→→8→→→→96→→→→6→→→→14
104→→→→2→→→→6→→→→98→→→→2→→→→12
108→→→→4→→→→2→→→→102→→→→4→→→→8
110→→→→2→→→→0→→→→110→→→→8→→→→0
以上为25生素数的18种排列顺序及间距，正好为110.

作者: 白新岭 时间: 2011-12-8 10:09
标题: [原创]k生素数群的数量公式
[这个贴子最后由白新岭在 2011/12/08 11:16am 第 1 次编辑]

p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→114→→→→0→→→→0→→→→114
2→→→→2→→→→112→→→→4→→→→4→→→→110
14→→→→12→→→→100→→→→6→→→→2→→→→108
18→→→→4→→→→96→→→→10→→→→4→→→→104
20→→→→2→→→→94→→→→12→→→→2→→→→102
24→→→→4→→→→90→→→→16→→→→4→→→→98
30→→→→6→→→→84→→→→24→→→→8→→→→90
32→→→→2→→→→82→→→→30→→→→6→→→→84
38→→→→6→→→→76→→→→34→→→→4→→→→80
42→→→→4→→→→72→→→→40→→→→6→→→→74
44→→→→2→→→→70→→→→42→→→→2→→→→72
48→→→→4→→→→66→→→→46→→→→4→→→→68
54→→→→6→→→→60→→→→52→→→→6→→→→62
62→→→→8→→→→52→→→→60→→→→8→→→→54
68→→→→6→→→→46→→→→66→→→→6→→→→48
72→→→→4→→→→42→→→→70→→→→4→→→→44
74→→→→2→→→→40→→→→72→→→→2→→→→42
80→→→→6→→→→34→→→→76→→→→4→→→→38
84→→→→4→→→→30→→→→82→→→→6→→→→32
90→→→→6→→→→24→→→→84→→→→2→→→→30
98→→→→8→→→→16→→→→90→→→→6→→→→24
102→→→→4→→→→12→→→→94→→→→4→→→→20
104→→→→2→→→→10→→→→96→→→→2→→→→18
108→→→→4→→→→6→→→→100→→→→4→→→→14
110→→→→2→→→→4→→→→112→→→→12→→→→2
114→→→→4→→→→0→→→→114→→→→2→→→→0
以上为26生素数的2种排列顺序及间距.

作者: 白新岭 时间: 2011-12-8 11:25
标题: [原创]k生素数群的数量公式
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→120→→→→0→→→→0→→→→120
4→→→→4→→→→116→→→→2→→→→2→→→→118
10→→→→6→→→→110→→→→8→→→→6→→→→112
12→→→→2→→→→108→→→→12→→→→4→→→→108
18→→→→6→→→→102→→→→26→→→→14→→→→94
22→→→→4→→→→98→→→→30→→→→4→→→→90
24→→→→2→→→→96→→→→32→→→→2→→→→88
28→→→→4→→→→92→→→→36→→→→4→→→→84
34→→→→6→→→→86→→→→38→→→→2→→→→82
40→→→→6→→→→80→→→→42→→→→4→→→→78
42→→→→2→→→→78→→→→50→→→→8→→→→70
48→→→→6→→→→72→→→→56→→→→6→→→→64
52→→→→4→→→→68→→→→60→→→→4→→→→60
54→→→→2→→→→66→→→→66→→→→6→→→→54
60→→→→6→→→→60→→→→68→→→→2→→→→52
64→→→→4→→→→56→→→→72→→→→4→→→→48
70→→→→6→→→→50→→→→78→→→→6→→→→42
78→→→→8→→→→42→→→→80→→→→2→→→→40
82→→→→4→→→→38→→→→86→→→→6→→→→34
84→→→→2→→→→36→→→→92→→→→6→→→→28
88→→→→4→→→→32→→→→96→→→→4→→→→24
90→→→→2→→→→30→→→→98→→→→2→→→→22
94→→→→4→→→→26→→→→102→→→→4→→→→18
108→→→→14→→→→12→→→→108→→→→6→→→→12
112→→→→4→→→→8→→→→110→→→→2→→→→10
118→→→→6→→→→2→→→→116→→→→6→→→→4
120→→→→2→→→→0→→→→120→→→→4→→→→0
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→120→→→→0→→→→0→→→→120
4→→→→4→→→→116→→→→2→→→→2→→→→118
10→→→→6→→→→110→→→→6→→→→4→→→→114
18→→→→8→→→→102→→→→8→→→→2→→→→112
22→→→→4→→→→98→→→→12→→→→4→→→→108
24→→→→2→→→→96→→→→18→→→→6→→→→102
30→→→→6→→→→90→→→→20→→→→2→→→→100
34→→→→4→→→→86→→→→26→→→→6→→→→94
42→→→→8→→→→78→→→→30→→→→4→→→→90
48→→→→6→→→→72→→→→32→→→→2→→→→88
52→→→→4→→→→68→→→→36→→→→4→→→→84
58→→→→6→→→→62→→→→42→→→→6→→→→78
64→→→→6→→→→56→→→→48→→→→6→→→→72
70→→→→6→→→→50→→→→50→→→→2→→→→70
72→→→→2→→→→48→→→→56→→→→6→→→→64
78→→→→6→→→→42→→→→62→→→→6→→→→58
84→→→→6→→→→36→→→→68→→→→6→→→→52
88→→→→4→→→→32→→→→72→→→→4→→→→48
90→→→→2→→→→30→→→→78→→→→6→→→→42
94→→→→4→→→→26→→→→86→→→→8→→→→34
100→→→→6→→→→20→→→→90→→→→4→→→→30
102→→→→2→→→→18→→→→96→→→→6→→→→24
108→→→→6→→→→12→→→→98→→→→2→→→→22
112→→→→4→→→→8→→→→102→→→→4→→→→18
114→→→→2→→→→6→→→→110→→→→8→→→→10
118→→→→4→→→→2→→→→116→→→→6→→→→4
120→→→→2→→→→0→→→→120→→→→4→→→→0
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→120→→→→0→→→→0→→→→120
4→→→→4→→→→116→→→→2→→→→2→→→→118
6→→→→2→→→→114→→→→6→→→→4→→→→114
10→→→→4→→→→110→→→→14→→→→8→→→→106
16→→→→6→→→→104→→→→20→→→→6→→→→100
18→→→→2→→→→102→→→→26→→→→6→→→→94
24→→→→6→→→→96→→→→32→→→→6→→→→88
28→→→→4→→→→92→→→→36→→→→4→→→→84
30→→→→2→→→→90→→→→42→→→→6→→→→78
34→→→→4→→→→86→→→→44→→→→2→→→→76
36→→→→2→→→→84→→→→50→→→→6→→→→70
46→→→→10→→→→74→→→→54→→→→4→→→→66
48→→→→2→→→→72→→→→60→→→→6→→→→60
58→→→→10→→→→62→→→→62→→→→2→→→→58
60→→→→2→→→→60→→→→72→→→→10→→→→48
66→→→→6→→→→54→→→→74→→→→2→→→→46
70→→→→4→→→→50→→→→84→→→→10→→→→36
76→→→→6→→→→44→→→→86→→→→2→→→→34
78→→→→2→→→→42→→→→90→→→→4→→→→30
84→→→→6→→→→36→→→→92→→→→2→→→→28
88→→→→4→→→→32→→→→96→→→→4→→→→24
94→→→→6→→→→26→→→→102→→→→6→→→→18
100→→→→6→→→→20→→→→104→→→→2→→→→16
106→→→→6→→→→14→→→→110→→→→6→→→→10
114→→→→8→→→→6→→→→114→→→→4→→→→6
118→→→→4→→→→2→→→→116→→→→2→→→→4
120→→→→2→→→→0→→→→120→→→→4→→→→0
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→120→→→→0→→→→0→→→→120
4→→→→4→→→→116→→→→2→→→→2→→→→118
6→→→→2→→→→114→→→→6→→→→4→→→→114
10→→→→4→→→→110→→→→12→→→→6→→→→108
16→→→→6→→→→104→→→→14→→→→2→→→→106
18→→→→2→→→→102→→→→20→→→→6→→→→100
28→→→→10→→→→92→→→→26→→→→6→→→→94
30→→→→2→→→→90→→→→32→→→→6→→→→88
34→→→→4→→→→86→→→→36→→→→4→→→→84
36→→→→2→→→→84→→→→42→→→→6→→→→78
48→→→→12→→→→72→→→→44→→→→2→→→→76
58→→→→10→→→→62→→→→50→→→→6→→→→70
60→→→→2→→→→60→→→→54→→→→4→→→→66
64→→→→4→→→→56→→→→56→→→→2→→→→64
66→→→→2→→→→54→→→→60→→→→4→→→→60
70→→→→4→→→→50→→→→62→→→→2→→→→58
76→→→→6→→→→44→→→→72→→→→10→→→→48
78→→→→2→→→→42→→→→84→→→→12→→→→36
84→→→→6→→→→36→→→→86→→→→2→→→→34
88→→→→4→→→→32→→→→90→→→→4→→→→30
94→→→→6→→→→26→→→→92→→→→2→→→→28
100→→→→6→→→→20→→→→102→→→→10→→→→18
106→→→→6→→→→14→→→→104→→→→2→→→→16
108→→→→2→→→→12→→→→110→→→→6→→→→10
114→→→→6→→→→6→→→→114→→→→4→→→→6
118→→→→4→→→→2→→→→116→→→→2→→→→4
120→→→→2→→→→0→→→→120→→→→4→→→→0
以上为27生素数的8种排列顺序及间距

作者: 白新岭 时间: 2011-12-8 20:49
标题: [原创]k生素数群的数量公式
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→126→→→→0→→→→0→→→→126
6→→→→6→→→→120→→→→2→→→→2→→→→124
10→→→→4→→→→116→→→→6→→→→4→→→→120
12→→→→2→→→→114→→→→14→→→→8→→→→112
16→→→→4→→→→110→→→→20→→→→6→→→→106
22→→→→6→→→→104→→→→26→→→→6→→→→100
24→→→→2→→→→102→→→→32→→→→6→→→→94
30→→→→6→→→→96→→→→36→→→→4→→→→90
34→→→→4→→→→92→→→→42→→→→6→→→→84
36→→→→2→→→→90→→→→44→→→→2→→→→82
40→→→→4→→→→86→→→→50→→→→6→→→→76
42→→→→2→→→→84→→→→54→→→→4→→→→72
52→→→→10→→→→74→→→→60→→→→6→→→→66
54→→→→2→→→→72→→→→62→→→→2→→→→64
64→→→→10→→→→62→→→→72→→→→10→→→→54
66→→→→2→→→→60→→→→74→→→→2→→→→52
72→→→→6→→→→54→→→→84→→→→10→→→→42
76→→→→4→→→→50→→→→86→→→→2→→→→40
82→→→→6→→→→44→→→→90→→→→4→→→→36
84→→→→2→→→→42→→→→92→→→→2→→→→34
90→→→→6→→→→36→→→→96→→→→4→→→→30
94→→→→4→→→→32→→→→102→→→→6→→→→24
100→→→→6→→→→26→→→→104→→→→2→→→→22
106→→→→6→→→→20→→→→110→→→→6→→→→16
112→→→→6→→→→14→→→→114→→→→4→→→→12
120→→→→8→→→→6→→→→116→→→→2→→→→10
124→→→→4→→→→2→→→→120→→→→4→→→→6
126→→→→2→→→→0→→→→126→→→→6→→→→0
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→126→→→→0→→→→0→→→→126
4→→→→4→→→→122→→→→6→→→→6→→→→120
6→→→→2→→→→120→→→→8→→→→2→→→→118
10→→→→4→→→→116→→→→12→→→→4→→→→114
16→→→→6→→→→110→→→→20→→→→8→→→→106
18→→→→2→→→→108→→→→26→→→→6→→→→100
24→→→→6→→→→102→→→→32→→→→6→→→→94
28→→→→4→→→→98→→→→38→→→→6→→→→88
30→→→→2→→→→96→→→→42→→→→4→→→→84
34→→→→4→→→→92→→→→48→→→→6→→→→78
36→→→→2→→→→90→→→→50→→→→2→→→→76
46→→→→10→→→→80→→→→56→→→→6→→→→70
48→→→→2→→→→78→→→→60→→→→4→→→→66
58→→→→10→→→→68→→→→66→→→→6→→→→60
60→→→→2→→→→66→→→→68→→→→2→→→→58
66→→→→6→→→→60→→→→78→→→→10→→→→48
70→→→→4→→→→56→→→→80→→→→2→→→→46
76→→→→6→→→→50→→→→90→→→→10→→→→36
78→→→→2→→→→48→→→→92→→→→2→→→→34
84→→→→6→→→→42→→→→96→→→→4→→→→30
88→→→→4→→→→38→→→→98→→→→2→→→→28
94→→→→6→→→→32→→→→102→→→→4→→→→24
100→→→→6→→→→26→→→→108→→→→6→→→→18
106→→→→6→→→→20→→→→110→→→→2→→→→16
114→→→→8→→→→12→→→→116→→→→6→→→→10
118→→→→4→→→→8→→→→120→→→→4→→→→6
120→→→→2→→→→6→→→→122→→→→2→→→→4
126→→→→6→→→→0→→→→126→→→→4→→→→0
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→126→→→→0→→→→0→→→→126
4→→→→4→→→→122→→→→6→→→→6→→→→120
6→→→→2→→→→120→→→→8→→→→2→→→→118
10→→→→4→→→→116→→→→12→→→→4→→→→114
16→→→→6→→→→110→→→→18→→→→6→→→→108
18→→→→2→→→→108→→→→20→→→→2→→→→106
28→→→→10→→→→98→→→→26→→→→6→→→→100
30→→→→2→→→→96→→→→32→→→→6→→→→94
34→→→→4→→→→92→→→→38→→→→6→→→→88
36→→→→2→→→→90→→→→42→→→→4→→→→84
48→→→→12→→→→78→→→→48→→→→6→→→→78
58→→→→10→→→→68→→→→50→→→→2→→→→76
60→→→→2→→→→66→→→→56→→→→6→→→→70
64→→→→4→→→→62→→→→60→→→→4→→→→66
66→→→→2→→→→60→→→→62→→→→2→→→→64
70→→→→4→→→→56→→→→66→→→→4→→→→60
76→→→→6→→→→50→→→→68→→→→2→→→→58
78→→→→2→→→→48→→→→78→→→→10→→→→48
84→→→→6→→→→42→→→→90→→→→12→→→→36
88→→→→4→→→→38→→→→92→→→→2→→→→34
94→→→→6→→→→32→→→→96→→→→4→→→→30
100→→→→6→→→→26→→→→98→→→→2→→→→28
106→→→→6→→→→20→→→→108→→→→10→→→→18
108→→→→2→→→→18→→→→110→→→→2→→→→16
114→→→→6→→→→12→→→→116→→→→6→→→→10
118→→→→4→→→→8→→→→120→→→→4→→→→6
120→→→→2→→→→6→→→→122→→→→2→→→→4
126→→→→6→→→→0→→→→126→→→→4→→→→0
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→126→→→→0→→→→0→→→→126
2→→→→2→→→→124→→→→4→→→→4→→→→122
6→→→→4→→→→120→→→→10→→→→6→→→→116
12→→→→6→→→→114→→→→12→→→→2→→→→114
14→→→→2→→→→112→→→→16→→→→4→→→→110
24→→→→10→→→→102→→→→22→→→→6→→→→104
26→→→→2→→→→100→→→→24→→→→2→→→→102
30→→→→4→→→→96→→→→30→→→→6→→→→96
32→→→→2→→→→94→→→→36→→→→6→→→→90
44→→→→12→→→→82→→→→42→→→→6→→→→84
54→→→→10→→→→72→→→→46→→→→4→→→→80
56→→→→2→→→→70→→→→52→→→→6→→→→74
60→→→→4→→→→66→→→→54→→→→2→→→→72
62→→→→2→→→→64→→→→60→→→→6→→→→66
66→→→→4→→→→60→→→→64→→→→4→→→→62
72→→→→6→→→→54→→→→66→→→→2→→→→60
74→→→→2→→→→52→→→→70→→→→4→→→→56
80→→→→6→→→→46→→→→72→→→→2→→→→54
84→→→→4→→→→42→→→→82→→→→10→→→→44
90→→→→6→→→→36→→→→94→→→→12→→→→32
96→→→→6→→→→30→→→→96→→→→2→→→→30
102→→→→6→→→→24→→→→100→→→→4→→→→26
104→→→→2→→→→22→→→→102→→→→2→→→→24
110→→→→6→→→→16→→→→112→→→→10→→→→14
114→→→→4→→→→12→→→→114→→→→2→→→→12
116→→→→2→→→→10→→→→120→→→→6→→→→6
122→→→→6→→→→4→→→→124→→→→4→→→→2
126→→→→4→→→→0→→→→126→→→→2→→→→0
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→126→→→→0→→→→0→→→→126
2→→→→2→→→→124→→→→4→→→→4→→→→122
6→→→→4→→→→120→→→→6→→→→2→→→→120
8→→→→2→→→→118→→→→16→→→→10→→→→110
12→→→→4→→→→114→→→→18→→→→2→→→→108
20→→→→8→→→→106→→→→28→→→→10→→→→98
26→→→→6→→→→100→→→→30→→→→2→→→→96
30→→→→4→→→→96→→→→34→→→→4→→→→92
36→→→→6→→→→90→→→→36→→→→2→→→→90
38→→→→2→→→→88→→→→40→→→→4→→→→86
42→→→→4→→→→84→→→→46→→→→6→→→→80
48→→→→6→→→→78→→→→48→→→→2→→→→78
56→→→→8→→→→70→→→→54→→→→6→→→→72
66→→→→10→→→→60→→→→58→→→→4→→→→68
68→→→→2→→→→58→→→→60→→→→2→→→→66
72→→→→4→→→→54→→→→70→→→→10→→→→56
78→→→→6→→→→48→→→→78→→→→8→→→→48
80→→→→2→→→→46→→→→84→→→→6→→→→42
86→→→→6→→→→40→→→→88→→→→4→→→→38
90→→→→4→→→→36→→→→90→→→→2→→→→36
92→→→→2→→→→34→→→→96→→→→6→→→→30
96→→→→4→→→→30→→→→100→→→→4→→→→26
98→→→→2→→→→28→→→→106→→→→6→→→→20
108→→→→10→→→→18→→→→114→→→→8→→→→12
110→→→→2→→→→16→→→→118→→→→4→→→→8
120→→→→10→→→→6→→→→120→→→→2→→→→6
122→→→→2→→→→4→→→→124→→→→4→→→→2
126→→→→4→→→→0→→→→126→→→→2→→→→0
以上为28生素数的10种排列顺序及间距

作者: 白新岭 时间: 2012-1-5 07:34
标题: [原创]k生素数群的数量公式
最近在天山草先生的k家村之后，又出现了n阶m生素数。
这是k生素数的减法合成问题与加法合成相对应，2元的比较好研究，好分析；多元的就是多维的，可在低元，低维，低阶的基础上向外扩展，就像多元方程组有多到少解决问题的反运用，这时要把多元，多维，高阶的从低元，低维，低阶一步一步的向上扩，直到增到为止。这里有个问题需要解决和处理，要把k生素数看成一个整体，这样问题才能简化，才有可能解决问题。

作者: 白新岭 时间: 2012-1-5 07:37
标题: [原创]k生素数群的数量公式
上楼是自己早晨浏览n阶m生素数时偶然想到的。2012年1月5日早晨7.36分前。

作者: 白新岭 时间: 2012-2-27 11:47
标题: [原创]k生素数群的数量公式
好久不来了，从新看一看，或许有收获。

作者: 白新岭 时间: 2012-7-21 08:51
标题: [原创]k生素数群的数量公式
温故而知新，可以为师矣。顶起

作者: 白新岭 时间: 2013-2-4 09:05
标题: [原创]k生素数群的数量公式
一年多了，没有时间，没有精力研究k生素数了，有喜爱素数的朋友可以继续去研究，去挖掘里边的奥秘，功夫没有白费的，会有回报。

作者: 尚九天 时间: 2013-2-4 09:31
标题: [原创]k生素数群的数量公式

下面引用由白新岭在 2013/02/04 09:05am 发表的内容：
一年多了，没有时间，没有精力研究k生素数了，有喜爱素数的朋友可以继续去研究，去挖掘里边的奥秘，功夫没有白费的，会有回报。

老友相会，当干一杯！

作者: 重生888 时间: 2013-2-9 07:40
标题: [原创]k生素数群的数量公式

下面引用由尚九天在 2013/02/04 09:31am 发表的内容：
老友相会，当干一杯！

老友天天见，只是不说话！祝各位老友新春快乐！

作者: 尚九天 时间: 2013-2-9 07:46
标题: [原创]k生素数群的数量公式

下面引用由重生888在 2013/02/09 07:40am 发表的内容：
老友天天见，只是不说话！祝各位老友新春快乐！

新春多幸福，见面就发财！

作者: 志明 时间: 2013-2-9 23:30
标题: [原创]k生素数群的数量公式
祝各位网友新年快乐！家庭幸福！

作者: 尚九天 时间: 2013-2-10 06:17
标题: [原创]k生素数群的数量公式

下面引用由志明在 2013/02/09 11:30pm 发表的内容：
祝各位网友新年快乐！家庭幸福！

志明先生：春节好！

作者: 白新岭 时间: 2013-2-10 13:07
标题: [原创]k生素数群的数量公式
老朋友们，蛇年好，祝各位朋友新年快乐，身体健康，财源广进，事业有成。

作者: 白新岭 时间: 2013-12-10 08:15
标题: [原创]k生素数群的数量公式
一晃一年就有过去，时间过得真快，提前预祝各位朋友元旦愉快，身体健康。

作者: 白新岭 时间: 2016-7-18 15:35
由数学研发论坛提供的4胞胎素数个数在10^14内为：441295937+899；10^15内为:3314576487;10^16内为:25379433651. 自己用k生素数公式求出的4胞胎素数个数在10^14内为：441290899；10^15内为:3314551625;10^16内为:25379451643. 它们的绝对误差及相对误差分别为：10^14时，绝对误差5937个，相对误差5937/441296836=0.00001345；10^15时，绝对误差24862个，相对误差24862/3314576487=0.0000075；10^16时，绝对误差-17992/25379451643=-0.0000007089.从相对误差看，每增加一个量级，相对误差就会降低一个量级，这说明，用公式求得的k生素数的个数是有保证的，它随着数量级的增加，逐步在缩小，而不是在扩大。

作者: 白新岭 时间: 2016-7-18 17:45
我以前只对最密k生素数群进行了研究和推广，获得2-12的k生素数群的数量公式，并计算系数，得到了结果，也与有编程能力的网友提供的数量进行了比较，知道公式获得的结果比较接近真实值。现在天山草有提到k家村问题，如果我有时间的话，我会去找k家村的代数式，和其排列规律，然后运用以前k生素数群的公式来推到出k家村数量公式。

作者: 白新岭 时间: 2016-7-21 17:26
k生素数群的k生素数式数量的增加为pi-4倍（必须pi大于4时，小于时置数1）

作者: 白新岭 时间: 2018-9-28 17:56
最近看到素数差的素数对数量问题。例如差值为6的，为8的，为2k的（k为自然数）。
在范围比较大的区域内（相对于间距而言），2^k的数量基本一致，如在1000亿内，间距为2的，为4的，为8的，为16的，为32的，为64的，为128的，为256的等等。还有2^K*3^J的也基本一致，例如（用L表示间距2字，后边的数字表示间距）L6，L12，L18，L24，L36，L48，L54，L72，L96，等等，细心的读者，一定会发现L30，L42，L60，L66，L78，L84，L90被去掉了，因为他们的数量与L6的不同，这里只有构成因子相同的，其数量才基本一致；开始举的例子全是因子2构成的，接下来是因子2，3构成的数。不同因子构成的素数间距其数量不同，相同因子构成的素数间距其素数对数量基本一致，前提是范围值必须比间距要大的多。

作者: 大傻8888888 时间: 2018-9-28 22:42
   我在“[猜想] 这些表达式均有极限，谁能给出极限的一般表达式？”这个帖子50楼里说“∏(1-k/p)和k生素数个数也应该有函数关系”。
   今天我推出一个关于三生素数个数的公式如下：
E(N)=N/6*∏(1-3/p)/[2e^(-γ)]^3 ( 其中3﹤p≤√N )
   三生素数有两种，如7,11,13，间隔是4,2.另一种是11,13,17，间隔是2,4.上面公式应该是其中一种的个数。望有数据和计算能力的网友加以验证。

作者: 白新岭 时间: 2018-11-5 16:02
K生素数素数式 →→ 总间距
最密2生 0,2 →→ 2
次最密2生 0,4 →→ 4
最密3生 0,2,4 →→ 6
最密3生 0,4,2 →→ 6
最密4生 0,2,4,2 →→ 8
次最密4生 0,4,2,4 →→ 10
最密5生 0,2,4,2,4 →→ 12
最密5生 0,4,2,4,2 →→ 12
次最密5生 0,2,4,6,2 →→ 14
次最密5生 0,2,6,4,2 →→ 14
最密6生 0,4,2,4,2,4 →→ 16
次最密6生 0,2,4,2,4,6 →→ 18
次最密6生 0,6,4,2,4,2 →→ 18
次最密6生 0,2,6,4,2,4 →→ 18
次最密6生 0,4,2,4,6,2 →→ 18
最密7生 0,2,6,4,2,4,2 →→ 20
最密7生 0,2,4,2,4,6,2 →→ 20
次最密7生 0,4,2,4,2,4,8 →→ 24
次最密7生 0,8,4,2,4,2,4 →→ 24
次最密7生 0,2,6,4,2,4,6 →→ 24
次最密7生 0,6,4,2,4,6,2 →→ 24
次最密7生 0,4,2,4,6,2,6 →→ 24
次最密7生 0,6,2,6,4,2,4 →→ 24
次最密7生 0,2,6,4,2,6,4 →→ 24
次最密7生 0,4,6,2,4,6,2 →→ 24
次最密7生 0,2,10,2,4,2,4 →→ 24
次最密7生 0,4,2,4,2,10,2 →→ 24
次最密7生 0,2,4,6,2,6,4 →→ 24
次最密7生 0,4,6,2,6,4,2 →→ 24
次最密7生 0,2,6,6,4,2,4 →→ 24
次最密7生 0,4,2,4,6,6,2 →→ 24
最密8生 0,2,4,2,4,6,2,6 →→ 26
最密8生 0,6,2,6,4,2,4,2 →→ 26
最密8生 0,2,4,6,2,6,4,2 →→ 26
次最密8生 0,4,6,2,6,4,2,4 →→ 28
次最密8生 0,4,2,4,6,2,6,4 →→ 28
最密9生 0,2,4,2,4,6,2,6,4 →→ 30
最密9生 0,2,4,6,2,6,4,2,4 →→ 30
最密9生 0,4,2,4,6,2,6,4,2 →→ 30
最密9生 0,4,6,2,6,4,2,4,2 →→ 30
最密10生 0,2,4,2,4,6,2,6,4,2 →→ 32
最密10生 0,2,4,6,2,6,4,2,4,2 →→ 32
次最密10生 0,4,2,4,6,2,6,4,2,4 →→ 34
最密11生 0,2,4,2,4,6,2,6,4,2,4 →→ 36
最密11生 0,4,2,4,6,2,6,4,2,4,2 →→ 36
次最密11生 0,4,2,4,6,2,6,4,2,4,6 →→ 40
次最密11生 0,6,4,2,4,6,2,6,4,2,4 →→ 40
最密12生 0,2,4,2,4,6,2,6,4,2,4,6 →→ 42
最密12生 0,6,4,2,4,6,2,6,4,2,4,2 →→ 42
次最密12生 0,2,6,4,2,4,6,6,2,6,4,2 →→ 44
次最密12生 0,2,4,6,2,6,6,4,2,4,6,2 →→ 44
次最密12生 0,2,4,6,2,6,4,2,4,6,6,2 →→ 44
次最密12生 0,2,6,6,4,2,4,6,2,6,4,2 →→ 44
次最密12生 0,2,4,6,2,6,4,2,4,2,10,2 →→ 44
次最密12生 0,2,10,2,4,2,4,6,2,6,4,2 →→ 44
次最密12生 0,4,2,4,6,2,6,4,2,4,2,10 →→ 46
次最密12生 0,10,2,4,2,4,6,2,6,4,2,4 →→ 46
次最密12生 0,4,2,4,6,2,6,4,2,4,6,6 →→ 46
次最密12生 0,6,6,4,2,4,6,2,6,4,2,4 →→ 46
次最密12生 0,4,2,4,6,6,2,6,4,2,6,4 →→ 46
次最密12生 0,4,6,2,4,6,2,6,6,4,2,4 →→ 46
次最密12生 0,4,2,6,4,6,8,4,2,4,2,4 →→ 46
次最密12生 0,4,2,4,2,4,8,6,4,6,2,4 →→ 46
次最密12生 0,4,2,4,2,10,2,10,2,4,2,4 →→ 46
最密13生 0,2,4,2,4,6,2,6,4,2,4,6,6 →→ 48
最密13生 0,6,6,4,2,4,6,2,6,4,2,4,2 →→ 48
最密13生 0,2,6,6,4,2,4,6,2,6,4,2,4 →→ 48
最密13生 0,4,2,4,6,2,6,4,2,4,6,6,2 →→ 48
最密13生 0,2,10,2,4,2,4,6,2,6,4,2,4 →→ 48
最密13生 0,4,2,4,6.2,6,4,2,4,2,10,2 →→ 48
最密14生 0,2,4,2,4,6,2,6,4,2,4,6,6,2 →→ 50
最密14生 0,2,6,6,4,2,4,6,2,6,4,2,4,2 →→ 50
次最密14生 0,2,10,2,4,2,4,6,2,6,4,2,4,6 →→ 54
次最密14生 0,6,4,2,4,6,2,6,4,2,4,2,10,2 →→ 54
次最密14生 0,4,2,4,6,2,6,4,2,4,6,6,2,6 →→ 54
次最密14生 0,6,2,6,6,4,2,4,6,2,6,4,2,4 →→ 54
次最密14生 0,2,6,4,2,4,6,6,2,6,4,2,6,4 →→ 54
次最密14生 0,4,6,2,4,6,2,6,6,4,2,4,6,2 →→ 54
次最密14生 0,2,6,4,2,6,4,6,8,4,2,4,2,4 →→ 54
次最密14生 0,4,2,4,2,4,8,6,4,6,2,4,6,2 →→ 54
次最密14生 0,2,6,4,2,4,2,10,2,10,2,4,2,4 →→ 54
次最密14生 0,4,2,4,2,10,2,10,2,4,2,4,6,2 →→ 54
次最密14生 0,2,4,6,2,6,6,4,2,4,6,2,6,4 →→ 54
次最密14生 0,4,6,2,6,4,2,4,6,6,2,6,4,2 →→ 54
次最密14生 0,2,4,6,2,6,4,2,4,6,6,2,6,4 →→ 54
次最密14生 0,4,6,2,6,6,4,2,4,6,2,6,4,2 →→ 54
最密15生 0,2,4,6,2,6,6,4,2,4,6,2,6,4,2 →→ 56
最密15生 0,2,4,6,2,6,4,2,4,6,6,2,6,4,2 →→ 56
最密15生 0,2,4,2,4,6,2,6,4,2,4,6,6,2,6 →→ 56
最密15生 0,6,2,6,6,4,2,4,6,2,6,4,2,4,2 →→ 56
次最密15生 0,4,2,4,6,2,6,4,2,4,6,6,2,6,4 →→ 58
次最密15生 0,4,6,2,6,6,4,2,4,6,2,6,4,2,4 →→ 58
最密16生 0,4,2,4,6,2,6,4,2,4,6,6,2,6,4,2 →→ 60
最密16生 0,2,4,6,2,6,6,4,2,4,6,2,6,4,2,4 →→ 60
最密17生 0,4,2,4,6,2,6,4,2,4,6,6,2,6,4,2,6 →→ 66
最密17生 0,6,2,4,6,2,6,6,4,2,4,6,2,6,4,2,4 →→ 66
最密17生 0,2,4,6,2,6,4,2,4,6,6,2,6,4,2,6,4 →→ 66
最密17生 0,4,6,2,4,6,2,6,6,4,2,4,6,2,6,4,2 →→ 66
最密18生 0,4,2,4,6,2,6,4,2,4,6,6,2,6,4,2,6,4 →→ 70
最密18生 0,4,6,2,4,6,2,6,6,4,2,4,6,2,6,4,2,4 →→ 70
最密19生 0,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2,4 →→ 76
最密19生 0,4,2,4,2,4,8,6,4,6,2,4,6,2,6,6,4,2,4 →→ 76
最密19生 0,4,2,4,6,2,6,4,2,4,6,6,2,6,4,2,6,4,6 →→ 76
最密19生 0,6,4,6,2,4,6,2,6,6,4,2,4,6,2,6,4,2,4 →→ 76
最密20生 0,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2 →→ 80
最密20生 0,2,4,2,4,8,6,4,6,2,4,6,2,6,6,4,2,4,6,2 →→ 80
最密21生 0,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2,4 →→ 84
最密21生 0,4,2,4,2,4,8,6,4,6,2,4,6,2,6,6,4,2,4,6,2 →→ 84
最密22生 0,4,6,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2 →→ 90
最密22生 0,2,4,2,4,8,6,4,6,2,4,6,2,6,6,4,2,4,6,2,6,4 →→ 90
最密22生 0,6,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2,4 →→ 90
最密22生 0,4,2,4,2,4,8,6,4,6,2,4,6,2,6,6,4,2,4,6,2,6 →→ 90
最密23生 0,4,2,4,2,4,8,6,4,6,2,4,6,2,6,6,4,2,4,6,2,6,4 →→ 94
最密23生 0,4,6,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2,4 →→ 94
最密24生 0,4,2,4,2,4,8,6,4,6,2,4,6,8,6,4,2,4,6,2,6,4,2,4 →→ 100
最密24生 0,4,2,4,6,2,6,4,2,4,6,8,6,4,2,6,4,6,8,4,2,4,2,4 →→ 100
最密24生 0,4,2,4,6,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,6,2,4 →→ 100
最密24生 0,4,2,6,4,8,6,4,6,2,4,6,2,6,6,4,2,4,6,2,6,4,2,4 →→ 100
最密25生 →→ 108
最密26生 →→ 114
最密27生 →→ 120
最密28生 →→ 126
最密29生 →→ 130
最密30生 →→ 136
最密31生 →→ 140
最密32生 →→ 146
最密33生 →→ 152
最密34生 →→ 156
最密35生 →→ 158
最密36生 →→ 162
最密37生 →→ 168
最密38生 →→ 176
最密39生 →→ 180
最密40生 →→ 182
最密41生 →→ 186
最密42生 →→ 188
最密43生 →→ 198
最密44生 →→ 200
最密45生 →→ 210
最密46生 →→ 212
最密47生 →→ 216
最密48生 →→ 218
最密49生 →→ 230
最密50生 →→ 240
最密51生 →→ 242
最密52生 →→ 246
最密53生 →→ 252
最密54生 →→ 258
最密55生 →→ 266
最密56生 →→ 270
最密57生 →→ 272
最密58生 →→ 276
最密59生 →→ 282
最密60生 →→ 288
最密61生 →→ 300
上面写出了k生素数相邻两个素数的间距及总间距和排列顺序。

作者: 白新岭 时间: 2018-11-5 16:24
在一楼说了系数A中k的取值问题，例如当k=16时，排列顺序为0,2,4,6,2,6,6,4,2,4,6,2,6,4,2,4
的，总间距是60，60/2=30，30以内的素数有2，3，5，7，11，13，17，19，23，29，那么它们对应的k的取值是几呢？分别是1，2，4，6，10，12，13，14，15，15，剩余1，1，1，1，1，1，4，5，8，14. 以后的素数对应的k值才是16，这里的k取值是逐渐变大到k的最大取值的，也有例外的情况，指k的取值可能先大点，后边又变小，再变大；也就是说在2P<=d（总间距），k的取值还是比较复杂的，只有2P>d时，才都取定值k。

作者: 白新岭 时间: 2018-11-5 17:01
当k=24时，排列顺序0,4,2,4,6,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,6,2,4，总间距d=100，100/2=50, 50内的素数有2，3，5，7，11，13，17，19，23，29，31，37，41，43，47，对应k的取值分别为1，2，4，6，10，12，16，16，18，21，22，23，22，23，22，（以后都是24），到17时是16，到19时还是16， 37时是23，当41时变为了22，43又对应23了，47时对应22，53以后的素数对应的k值才是24，由此看来，k的取值在2p小于等于d时，其变化是复杂的，必须具体分析才能知道k的实际取值，不一定在p<k时，其取值就是P-1.

作者: 白新岭 时间: 2018-11-10 13:52
k生素数群的数量与总间距和排列顺序及k值得大小和范围有密切关系，对于总间距相同，相邻素数间距排列顺序互逆的两种k生素数群的数量大致是相同，在10万内，3生素数群0，2，6的及0，6，2的它们的数量都是224组；在10万内，3生素数群0，2，4的为259组，0，4，2的为248组；再就是，0，2，6的3生素数群的数量与3生素数群0，2，4的数量减去4生素数群（0，2，4，2）的数量差不多，4生素数群10万内有39组，有259-39=220组，实际为224组。原先我认为3生素数（0，2，6）的除本身每一素数周期产生增量外，还有4生素数新裂解得到的，其实是4生素数它所占有的，即4生素数去掉中间的某一个素数，它就变成了某一种3生素数。

作者: 白新岭 时间: 2018-11-11 15:57
10^n → 2生素数数量 → 实际孪生素数 → 公式/实际
8 → 440365 → 440312 → 1.000120369
9 → 3425306 → 3424506 → 1.00023361
10 → 27411416 → 27412679 → 0.999953926
11 → 224368877 → 224376048 → 0.99996804
12 → 1870559991 → 1870585220 → 0.999986513
13 → 15834599375 → 15834664872 → 0.999995864
14 → 135780274095 → 135780321665 → 0.99999965
15 → 1177208571645 → 1177209242304 → 0.99999943
16 → 10304193252876 → 10304195697298 → 0.999999763
17 → 90948839425186 → 90948839353159 → 1.000000001
18 → 808675956302870 → 808675888577435 → 1.000000084
实际孪生素数的数量是从dlpangong的帖子中获得的。

作者: yanghh19981102 时间: 2018-11-11 16:26
k生素数群的数量与总间距和排列顺序及k值得大小和范围有密切关系，对于总间距相同，相邻素数间距排列顺序互逆的两种k生素数群的数量大致是相同，符合一种函数规律

作者: 白新岭 时间: 2018-11-11 16:39
10^n → 3生素数数量 → 实际3生素数 → 3生公式/实际
9 → 379794 → 379508 → 1.000753607
10 → 2715284 → 2713347 → 1.000713878
11 → 20089649 → 20093124 → 0.999827055
12 → 152830589 → 152850135 → 0.999872123
13 → 1189763338 → 1189795268 → 0.999973163
14 → 9443892325 → 9443942337 → 0.999994704
15 → 76217795487 → 76222348070 → 0.999940272

作者: 白新岭 时间: 2018-11-11 17:09
10^n → 4生素数数量 → 实际4生素数 → 4生公式/实际
9 → 28384 → 28388 → 0.999859095
10 → 181063 → 180529 → 1.002957974
11 → 1209944 → 1209318 → 1.000517647
12 → 8394569 → 8398278 → 0.999558362
13 → 60075450 → 60069713 → 1.000095506
14 → 441290899 → 441296836 → 0.999986546
15 → 3314551625 → 3314576487 → 0.999992499
16 → 25379451643 → 25379433651 → 1.000000709

作者: 白新岭 时间: 2018-11-12 12:28
10^n → 5生素数数量 → 实际5生素数 → 5生公式/实际
9 → 3585 → 3633 → 0.986787779
10 → 20372 → 20203 → 1.008365094
11 → 122828 → 122457 → 1.003029635
12 → 776669 → 776237 → 1.000556531
13 → 5107218 → 5108291 → 0.999789949
14 → 34706119 → 34709176 → 0.999911925
15 → 242545119 → 242554539 → 0.999961163

作者: 白新岭 时间: 2018-11-12 12:34
从以上比较数据看，公式计算的k生素数的数量与实际数量还是比较吻合的。所以系数A的取值是正确的。

作者: 白新岭 时间: 2018-11-12 12:58
10^n → 6生素数数量 → 实际6生素数 → 6生公式/实际
9 → 319 → 317 → 1.006309148
10 → 1611 → 1613 → 0.998760074
11 → 8753 → 8626 → 1.014722931
12 → 50400 → 50408 → 0.999841295
13 → 304356 → 303828 → 1.001737825
14 → 1912615 → 1911246 → 1.000716287
15 → 12433000 → 12431996 → 1.000080759
16 → 83213875 → 83217782 → 0.999953051

作者: 白新岭 时间: 2018-11-12 13:37
10^n → 7生素数数量 → 实际7生素数 → 7生公式/实际
9 → 52 → 54 → 0.962962963
10 → 234 → 234 → 1
11 → 1145 → 1183 → 0.967878276
12 → 5995 → 6056 → 0.989927345
13 → 33222 → 33395 → 0.994819584
14 → 192970 → 193078 → 0.999440641
15 → 1166417 → 1167688 → 0.998911524

作者: 白新岭 时间: 2018-11-12 14:04
10^n → 7生素数数量 → 实际7生素数 → 7生公式/实际
9 → 52 → 49 → 1.06122449
10 → 234 → 239 → 0.979079498
11 → 1145 → 1152 → 0.993923611
12 → 5995 → 5913 → 1.013867749
13 → 33222 → 33066 → 1.004717837
14 → 192970 → 192731 → 1.00124007
15 → 1166417 → 1166385 → 1.000027435
这里的7生素数的实际数量是另一种，与上楼的总间距相同，相邻素数间距的排列顺序互逆，除10^10时比上楼的7生素数多5个以外，其余范围都比上一楼的7生素数的实际数量少。但从理论上讲，两种总间距相同，排列顺序互逆的k生素数其数量大致是相同的。

作者: 白新岭 时间: 2018-11-12 14:35
以上各楼的实际数据是本帖3#的数据，提供了2=<K=<7,范围是10^9到10^16的，有的还提供另一种K生素数的数量。在这里感谢一下数学研发论坛的那位网友，现在我找不到那个帖子的出处了，因为主题是什么我不知道了，网名也不知道了。

作者: 白新岭 时间: 2018-11-13 13:55
∫（lnx）^n dx=x（lnx）^n-n∫lnx）^(n-1), n属于整数，当n=0时，积分=x+c；当n=1时，积分=xlnx-x+c，当n>1时，通过降阶的积分公式可得到结果；当n<0时，就成了扩散形式，无法用有限项的函数式表达出来。不过我们求k生素数时，只取前有限项个函数式就可以了，当-（n-j）>lnX时就不要了。j表示增加的项。

作者: 白新岭 时间: 2018-11-13 17:00
N值→→→→4(8)素数个数→孪生素数对数目→2.38128115124→误差→误差率CP
10000000→898→→→→→58755→→→→822→→→→→76→0.084632517t
20000000→1467→→→→→107246→→→→1369→→→→→98→0.0668029991
30000000→1951→→→→→152790→→→→1853→→→→→98→0.050230651cBW:&
40000000→2403→→→→→196566→→→→2300→→→→→103→0.042863088l;\`5/q
50000000→2846→→→→→239094→→→→2722→→→→→124→0.043569923{
60000000→3257→→→→→280666→→→→3126→→→→→131→0.0402210625h
70000000→3646→→→→→321468→→→→3515→→→→→131→0.035929786~#
80000000→4033→→→→→361627→→→→3892→→→→→141→0.034961567Hm9CBn
90000000→4401→→→→→401236→→→→4259→→→→→142→0.0322653948V_I
100000000→4767→→→→→440366→→→→4617→→→→→150→0.031466331nL[QTQ
110000000→5115→→→→→479074→→→→4968→→→→→147→0.028739003X<
120000000→5441→→→→→517402→→→→5312→→→→→129→0.0237088770*L
130000000→5797→→→→→555388→→→→5650→→→→→147→0.025357944Wz(
140000000→6112→→→→→593062→→→→5982→→→→→130→0.021269634y$N0Xt
150000000→6450→→→→→630450→→→→6309→→→→→141→0.021860465Gvh,uS
160000000→6792→→→→→667574→→→→6632→→→→→160→0.023557126~0l
170000000→7113→→→→→704453→→→→6951→→→→→162→0.0227752]OX'
180000000→7446→→→→→741104→→→→7266→→→→→180→0.0241740531]4
190000000→7794→→→→→777541→→→→7577→→→→→217→0.027841936Sgq
200000000→8096→→→→→813777→→→→7884→→→→→212→0.026185771Tv2n
210000000→8400→→→→→849824→→→→8189→→→→→211→0.025119048HEt
220000000→8699→→→→→885692→→→→8490→→→→→209→0.02402575Md&q
230000000→8978→→→→→921391→→→→8789→→→→→189→0.021051459 M
240000000→9270→→→→→956928→→→→9085→→→→→185→0.01995685 h3Dh
250000000→9565→→→→→992313→→→→9379→→→→→186→0.019445896dyYRqA
260000000→9836→→→→→1027551→→→→9670→→→→→166→0.016876779FOTa
270000000→10135→→→→→1062650→→→→9959→→→→→176→0.017365565T
280000000→10431→→→→→1097615→→→→10245→→→→→186→0.017831464W,"Mt
290000000→10701→→→→→1132452→→→→10530→→→→→171→0.015979815}
300000000→10972→→→→→1167166→→→→10813→→→→→159→0.014491433Q
310000000→11280→→→→→1201762→→→→11093→→→→→187→0.016578014=j
320000000→11589→→→→→1236243→→→→11372→→→→→217→0.018724653:gJ1
330000000→11862→→→→→1270615→→→→11649→→→→→213→0.0179565C6zb
340000000→12126→→→→→1304880→→→→11925→→→→→201→0.016575952;#nw+$
350000000→12370→→→→→1339043→→→→12199→→→→→171→0.013823767lS
360000000→12632→→→→→1373107→→→→12471→→→→→161→0.012745408yg%s}
370000000→12900→→→→→1407075→→→→12742→→→→→158→0.0122480628
380000000→13164→→→→→1440950→→→→13011→→→→→153→0.011622607Zj|^Cw
390000000→13438→→→→→1474735→→→→13279→→→→→159→0.011832118l#]9A
400000000→13712→→→→→1508433→→→→13545→→→→→167→0.012179113[a3Lz
410000000→13957→→→→→1542045→→→→13810→→→→→147→0.010532349q
420000000→14247→→→→→1575575→→→→14074→→→→→173→0.012142907VWu0;
430000000→14516→→→→→1609025→→→→14337→→→→→179→0.012331221Z^|(x
440000000→14770→→→→→1642396→→→→14598→→→→→172→0.011645227j
450000000→15030→→→→→1675691→→→→14858→→→→→172→0.011443779|
460000000→15289→→→→→1708912→→→→15117→→→→→172→0.0112499181
470000000→15559→→→→→1742061→→→→15375→→→→→184→0.011825953b3:<2&
480000000→15823→→→→→1775139→→→→15632→→→→→191→0.012071036B|wI,j
490000000→16093→→→→→1808148→→→→15888→→→→→205→0.012738458u,?Pb2
500000000→16330→→→→→1841090→→→→16143→→→→→187→0.011451317A1
510000000→16579→→→→→1873967→→→→16396→→→→→183→0.01103806Sk6!kK
520000000→16816→→→→→1906779→→→→16649→→→→→167→0.009931018u}r$b
530000000→17069→→→→→1939528→→→→16901→→→→→168→0.009842404m8Z8?

作者: 白新岭 时间: 2018-11-13 17:03
最密4生素数群的组数公式=2.38128115124*{2C2∫dt/[LN(t)]^2}^2/n,积分范围是[2,n], C2=0.66016181....即孪生素数常数

作者: 白新岭 时间: 2018-11-13 17:11
本帖最后由白新岭于 2018-11-13 09:20 编辑

本帖3#数据来自数学研发论坛的---算法交流--孪生素数的计算（楼主是tprime）8#。
在数学研发论坛搜索”孪生素数“就可以搜索到那个帖子。

作者: 白新岭 时间: 2018-11-16 16:46
2018年11月16日：对于合成数的数量问题，它等于系数*范围内符合条件
的元素个数的平方/范围值，系数=周期*占有率（比例）。
2生的与素数和的方法是一致的，那么3生素数，4生素数以及到k生素数
呢？它们当然与3个素数之和，4个素数之和以及k个素数之和不同。现在
我们研究4生素数，那么为什么不先研究3生素数呢？因为我们无法构建
其模型，4生素数就可以构建其模型，我们可以把2生素数看成一个整体，
然后，象素数减法一样，去获得系数。
我们如果用中间数代替孪生素数对，那么当筛选时，去掉余数是±1的，
在2至7的孪生素数对的代数式中有15组代数式，2时是1，到3时还是1，
到5时是3=（5-2），到7时是15=（5-2）*（7-2），这时为3组合成数为6
即占比例为：（7-4）/((5-2)*(7-2))^2,到11时是135=（5-2）*（7-2）*
（11-2），这时所占比例（7-4）*（11-4）/((5-2)*(7-2)*(11-2))^2,
从合成结果看，每个素数Pj能把合成总量扩大（Pj-2）^2倍，而差为6的
数量仅增加Pj-4倍，所以根据系数=周期*比例等式，可得出4生素数数量
"=2*3*∏(Pj*（Pj-4）/(Pj-2）^2)*孪生素数对数量^2/N,Pj>3为素数，
而孪生素数对等于=2*∏(Pj*（Pj-2）/(Pj-1）^2)*N/(ln（N))^2,把此
式代入替换掉孪生素数对数量的平方，化简后得到=（2*3）^3*∏
(Pj^3*（Pj-4）/(Pj-1）^4)*N/(ln（N))^4,Pj>3为素数.这我们就看到
了k生素数的数量公式中的系数是∏Pj^(K-1)*∏(Pj-k）/(Pj-1）^K,
只是（Pj-k）中的K的取值需要分析获得，当2Pj>k生素数总间距时，k
的取值就是实际k生素数中的k值了。这是理解k生素数的系数的一个实例
当然k不是2^a时，我们也无法构建模型来获得系数，即便是k=2^a我们
也找不到第二个实例，因为没有最密的对称结构，我看了一下，
最密8生素数0,2,4,6,2,6,4,2还是可以将就的因为它们是两组互逆的4生
素数，但是我们无法从2生素数获得4生素数，因为每一组4生素数不是对
称的，一个间距是2，另一个间距是6，其数量不一致，虽然4生的一致，
任何互逆两种k生素数在理论上其数量是一致的。所以找不到第二个实例
系数有三项构成Pj^(K-1)的连乘积，（Pj-k）的连乘积，（Pj-1）^K的
连乘积,分子分母关于Pj同阶，即它们的方幂相同。
通过对2至7素数式的差值分布分析和2至11素数式的差值分布分析得到，
差距为6的是数量最少的。

作者: 白新岭 时间: 2019-1-31 19:45
最密25生素数式 0,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2,4,14,4,6,2（用的是相邻素数间隔的排列表示的），总间距为110，也就是说在110的跨度内可以有25个素数。它的素数式到19时有6组。
下面是一组实际的解。
29
31
37
41
43
47
53
59
61
67
71
73
79
83
89
97
101
103
107
109
113
127
131
137
139
这是最小的一组，想找到下一组或许有点难。

作者: 白新岭 时间: 2019-2-1 21:45
最密25生 0,2,4,2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8 →→ 110 2
最密25生 0,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2,4,2 →→ 110 2
最密25生 0,2,4,2,4,6,2,6,4,2,4,6,8,6,6,6,4,6,8,4,2,4,2,4,8 →→ 110 1
最密25生 0,8,4,2,4,2,4,8,6,4,6,6,6,8,6,4,2,4,6,2,6,4,2,4,2 →→ 110 1
最密25生 0,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2,4,14,4,6,2 →→ 110 6
最密25生 0,2,6,4,14,4,2,4,2,4,8,6,4,6,2,4,6,2,6,6,4,2,4,6,2 →→ 110 6
最密25生 0,2,4,6,2,6,4,2,4,2,10,2,10,2,4,6,6,2,6,6,4,6,6,2,6 →→ 110 1
最密25生 0,6,2,6,6,4,6,6,2,6,6,4,2,10,2,10,2,4,2,4,6,2,6,4,2 →→ 110 1
最密25生 0,2,4,2,4,8,6,4,6,2,4,8,6,6,4,2,4,6,2,6,4,2,4,12,2 →→ 110 1
最密25生 0,2,12,4,2,4,6,2,6,4,2,4,6,6,8,4,2,6,4,6,8,4,2,4,2 →→ 110 1
最密25生 0,2,4,2,4,8,6,4,6,2,4,8,6,10,2,4,6,2,6,4,2,4,2,10,2 →→ 110 1
最密25生 0,2,10,2,4,2,4，6,2,6,4,2,10,6,8,4,2,6,4,6,8,4,2,4,2 →→ 110 1
最密25生 0,2,10,6,2,4,6,2,6,4,2,10,6,2,6,4,2,6,4,6,8,4,2,4,2 →→ 110 1
最密25生 0,2,4,2,4,8,6,4,6,2,4,6,2,6,10,2,4,6,2,6,4,2,6,10,2 →→ 110 1
最密25生 0,2,4,2,4,8,6,4,6,2,4,6,8,6,4,2,4,6,2,6,4,2,4,12,2 →→ 110 1
最密25生 0,2,12,4,2,4,6,2,6,4,2,4,6,8,6,4,2,6,4,6,8,4,2,4,2 →→ 110 1
最密25生 0,2,10,2,4,2,4，6,2,6,4,2,10,8,6,4,2,6,4,6,8,4,2,4,2 →→ 110 1
最密25生 0,2,4,2,4,8,6,4,6,2,4,6,8,10,2,4,6,2,6,4,2,4,2,10,2 →→ 110 1
今天找到了所有最密25生素数的相邻素数间距的排列顺序，总间距110，到素数19的素数式个数是最后一列对应数值。共计18种

作者: 白新岭 时间: 2019-2-2 17:37
在寻找25生素数式时，因为但从观察很难区分它们，所以对总间距相同，相邻间距不同或相同时，采取了一次间距与2次间距累加的和作为区分，一次间距是从第一个相邻间距累加到最后一个相邻间距，它们最后的值都是110，通过对应位置的值比较，可以确定是不是同一类k生素数式，这样的比较还是有点被动；我又采取了2次累加，即把它们每个值从新累加一遍，这样得到值，就不一样了，最后得到互逆的一对k生素数式的和值都一致，而每个和值，不同的k生素数式值都不一样，也有巧合的情况，不同的k生素数式的值却一样，但是极少出现这种情况。它们的平均累计值为1375.每一对互逆的k生素数式的序号和一致，这说明每一对互逆k生素数式都是关于中心对称的。

作者: 白新岭 时间: 2019-2-3 10:15
以前不知道发过没有发过类似的帖子。一直以来我都是以最密k生素数作为研究对象的，它们在k生素数中的规律还是比较简单的，而次最密k生素数大部分是比较复杂的，如间距为8的三生素数，它也有两种形式，（0，2，6），（0，6，2），它们的数量但从素数式上看不出与最密的3生素数的区别，而实际上的数量比最密的要少，正好是最密三生素数与最密4生素数的差。也就是说次最密的3生素数如果中间还有其他的素数时，从素数式上无法排除，因为它只判断它自己的占位是素数就可以了，当中间还有一个素数时它是排除不掉的（这里的k生素数都是指连续的几个素数，且相邻间隔排列顺序相同，总间距一致，两个素数之间不能有其他素数。

作者: 白新岭 时间: 2019-2-3 11:16
对25生素数式在2-19中的筛选可知，在2-17中应出现20组，实际出现了24组110跨度的25生素数式，这里可定有暂时性的，即通不过素数19的检验，我用间距2次累加值获得了这4组假25生素数式，它们出现的相对位置为3，9，16，22，经验证到19时就夭折了。

作者: 白新岭 时间: 2019-2-3 12:09
最密26生 0,2,12,4,2,4,6,2,6,4,2,4,6,8,6,4,2,6,4,6,8,4,2,4,2,4
最密26生 0,4,2,4,2,4,8,6,4,6,2,4,6,8,6,4,2,4,6,2,6,4,2,4,12,2
这是最密26生素数式的相邻素数间距的排列顺序，总间距114，只有这两种形式的最密26生素数。

作者: 白新岭 时间: 2019-2-3 13:37
当素数的2倍大于总间距时，在k生素数的数量公式中的系数一定是取∏P^(K-1)*(P-K)/(P-1)^K=∏(1-K/P)/(1-1/P)^K, 2P>素数组的总间距。小于时，需分析填列。

作者: 白新岭 时间: 2019-2-3 13:53
从这里可以看出，如果n*∏（1-k/P)能够表示k生素数的个数，则(∏（1-1/P)^-1)^K与（ln（n））^K是一个数量级，也就是说∏（1-1/P)^-1与ln（n）可建立比例关系，根据欧拉公式，∏（1-1/P)^-1与∑（1/n）能建立等式关系。这就可顺理成章的把用素数定理代替素数个数的公式与直接用连乘积的形式表示k生素数的形式建立起关系。

作者: 白新岭 时间: 2019-2-3 15:15
最密27生 0,4,6,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2,4,14,4,6,2 →→ 120 2
最密27生 0,2,6,4,14,4,2,4,2,4,8,6,4,6,2,4,6,2,6,6,4,2,4,6,2,6,4 →→ 120 2
最密27生 0,2,4,2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4 →→ 120 2
最密27生 0,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2,4,2 →→ 120 2
最密27生 4,2,4,6,2,6,4,2,4,2,10,2,10,2,6,4,6,2,6,4,6,6,6,8,4,2 →→ 120 2
最密27生 2,4,8,6,6,6,4,6,2,6,4,6,2,10,2,10,2,4,2,4,6,2,6,4,2,4 →→ 120 2
最密27生 2,4,6,2,6,6,6,4,6,2,6,4,2,4,2,10,12,2,4,2,10,2,6,4,2,4 →→ 120 1
最密27生 4,2,4,6,2,10,2,4,2,12,10,2,4,2,4,6,2,6,4,6,6,6,2,6,4,2 →→ 120 1
这是最密27生素数式用相邻素数间隔排序表示的8种形式，再没有其它的最密27生素数了，最后一列是到素数19时，它们所对应的素数式个数。相邻间隔的2次累加和的平均值为1620.
2次累计和位置 2次累计和位置
1484 4 1756 11
1484 10 1756 5
1532 2 1708 13
1532 7 1708 8
1556 1 1684 14
1556 9 1684 6
1606 3 1634 12
2次累加和一致的是同一种27生素数，平行的是一对互逆的27生素数，即颠倒顺序后排列一致。
如果我们用excel软件，可以用连接符把k生素数的相邻间隔的表示形式得到。

作者: 白新岭 时间: 2019-2-4 12:10
最密28生 4,2,4,6,2,6,4,2,4,2,10,2,10,2,6,4,6,2,6,4,6,6,6,8,4,2,6 →→ 126 2
最密28生 6,2,4,8,6,6,6,4,6,2,6,4,6,2,10,2,10,2,4,2,4,6,2,6,4,2,4 →→ 126 2
最密28生 6,4,2,4,6,2,6,4,2,4,2,10,2,10,2,6,4,6,2,6,4,6,6,6,8,4,2 →→ 126 2
最密28生 2,4,8,6,6,6,4,6,2,6,4,6,2,10,2,10,2,4,2,4,6,2,6,4,2,4,6 →→ 126 2
最密28生 2,4,2,4,8,6,4,6,2,4,6,8,10,2,4,6,2,6,4,2,4,2,10,2,10,2,4 →→ 126 1
最密28生 4,2,10,2,10,2,4,2,4,6,2,6,4,2,10,8,6,4,2,6,4,6,8,4,2,4,2 →→ 126 1
最密28生 4,6,2,4,6,2,6,6,6,4,6,2,6,4,2,4,2,10,12,2,4,2,10,2,6,4,2 →→ 126 1
最密28生 2,4,6,2,10,2,4,2,12,10,2,4,2,4,6,2,6,4,6,6,6,2,6,4,2,6,4 →→ 126 1
最密28生 4,2,4,6,2,10,2,4,2,12,10,2,4,2,4,6,2,6,4,6,6,6,2,6,4,2,6 →→ 126 1
最密28生 6,2,4,6,2,6,6,6,4,6,2,6,4,2,4,2,10,12,2,4,2,10,2,6,4,2,4 →→ 126 1
这是最密28生素数用相邻素数的间隔表示的形式。只有这10种，每个素数式如果开始没有0就是发贴的时候给丢了，它表示素数本身。最后一列数字是到素数19时出现的组数。

作者: 白新岭 时间: 2019-2-4 12:17
最密29生 4,6,2,4,6,2,6,6,6,4,6,2,6,4,2,4,2,10,12,2,4,2,10,2,6,4,2,4 →→ 130 1
最密29生 4,2,4,6,2,10,2,4,2,12,10,2,4,2,4,6,2,6,4,6,6,6,2,6,4,2,6,4 →→ 130 1
最密30生 6,4,6,2,4,6,2,6,6,6,4,6,2,6,4,2,4,2,10,12,2,4,2,10,2,6,4,2,4 →→ 136 1
最密30生 4,2,4,6,2,10,2,4,2,12,10,2,4,2,4,6,2,6,4,6,6,6,2,6,4,2,6,4,6 →→ 136 1
这是最密29生素数与最密30生素数的相邻间隔的排列顺序，各有两种，再没有其它的。后边一列是到素数19时出现的组数，到素数几就是从素数2开始到某素数的连乘积范围时。

作者: 白新岭 时间: 2019-2-6 16:01
最密31生 2,4,2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2 →→ 140 2
最密31生 2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2,4,2 →→ 140 2
最密32生 2,4,2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2,6 →→ 146 2
最密32生 6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2,4,2 →→ 146 2
最密32生 2,4,6,2,6,6,4,2,4,6,2,10,2,4,12,2,12,4,2,4,8,6,4,2,4,6,6,2,6,4,2 →→ 146 2
最密32生 2,4,6,2,6,6,4,2,4,6,8,4,2,4,12,2,12,4,2,10,2,6,4,2,4,6,6,2,6,4,2 →→ 146 2
这是最密31生素数与最密32生素数的相邻素数间隔的排列顺序，31生素数只有两种，32生素数只有4种。最后一列是到素数19时出现的素数式个数（范围是9699690，即2*3*5*7*11*13*17*19）

作者: 白新岭 时间: 2019-2-6 16:11
最密33生 2,4,2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2,6,6 →→ 152 2
最密33生 6,6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2,4,2 →→ 152 2
最密33生 2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2,4,14,4,6,2,10,2,6,6,4,6,6,2 →→ 152 4
最密33生 2,6,6,4,6,6,2,10,2,6,4,14,4,2,4,2,4,8,6,4,6,2,4,6,2,6,6,4,2,4,6,2 →→ 152 4
最密33生 2,4,6,2,6,4,2,4,2,10,2,10,2,6,4,6,2,6,4,6,6,6,8,4,2,6,10,8,4,2,4,2 →→ 152 2
最密33生 2,4,2,4,8,10,6,2,4,8,6,6,6,4,6,2,6,4,6,2,10,2,10,2,4,2,4,6,2,6,4,2 →→ 152 2
最密33生 2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2,6,6,4,2 →→ 152 2
最密33生 2,4,6,6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2 →→ 152 2
最密33生 2,4,2,4,8,6,4,6,2,4,6,2,6,6,6,4,6,2,6,4,6,12,2,12,4,2,4,6,2,6,4,2 →→ 152 3
最密33生 2,4,6,2,6,4,2,4,12,2,12,6,4,6,2,6,4,6,6,6,2,6,4,2,6,4,6,8,4,2,4,2 →→ 152 3
最密33生 2,4,6,2,6,6,4,2,4,6,8,4,2,4,12,2,12,4,2,10,2,6,4,2,4,6,6,2,6,4,2,6 →→ 152 2
最密33生 6,2,4,6,2,6,6,4,2,4,6,2,10,2,4,12,2,12,4,2,4,8,6,4,2,4,6,6,2,6,4,2 →→ 152 2
最密33生 2,4,6,2,6,4,6,2,10,2,10,2,6,4,6,2,6,4,6,6,6,2,6,6,6,4,6,8,4,2,4,2 →→ 152 4
最密33生 2,4,2,4,8,6,4,6,6,6,2,6,6,6,4,6,2,6,4,6,2,10,2,10,2,6,4,6,2,6,4,2 →→ 152 4
这是所有形式的33生素数，有14种，最后一列是到19时出现的33生素数式的个数。下面有一组实例：
29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181 从素数29到素数181连续33个素数，总间距152，它是最小的一组，如果想找到另一组怕是非常非常难。间隔排列 0，2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2,4,14,4,6,2,10,2,6,6,4,6,6,2为第三种的形式。

作者: 白新岭 时间: 2019-2-6 17:06
最密34生 2,4,2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2,6,6,4 →→ 156 2
最密34生 4,6,6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2,4,2 →→ 156 2
最密34生 4,2,4,6,2,6,4,2,4,2,10,2,10,2,6,4,6,2,6,4,6,6,6,8,4,2,6,10,8,4,2,4,2 →→ 156 2
最密34生 2,4,2,4,8,10,6,2,4,8,6,6,6,4,6,2,6,4,6,2,10,2,10,2,4,2,4,6,2,6,4,2,4 →→ 156 2
最密34生 4,2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2,6,6,4,2 →→ 156 2
最密34生 2,4,6,6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2,4 →→ 156 2
最密34生 2,4,6,2,6,4,2,4,2,10,2,10,2,6,4,6,2,6,4,6,6,6,8,4,2,6,10,8,4,2,4,2,4 →→ 156 2
最密34生 4,2,4,2,4,8,10,6,2,4,8,6,6,6,4,6,2,6,4,6,2,10,2,10,2,4,2,4,6,2,6,4,2 →→ 156 2
最密34生 4,2,4,2,4,8,6,4,6,2,4,6,2,6,6,6,4,6,2,6,4,6,12,2,12,4,2,4,6,2,6,4,2 →→ 156 3
最密34生 2,4,6,2,6,4,2,4,12,2,12,6,4,6,2,6,4,6,6,6,2,6,4,2,6,4,6,8,4,2,4,2,4 →→ 156 3
最密34生 2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2,6,6,4,2,4 →→ 156 2
最密34生 4,2,4,6,6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2 →→ 156 2
最密34生 2,4,2,4,8,6,4,6,2,4,6,2,6,6,6,4,6,2,6,4,6,12,2,12,4,2,4,6,2,6,4,2,4 →→ 156 3
最密34生 4,2,4,6,2,6,4,2,4,12,2,12,6,4,6,2,6,4,6,6,6,2,6,4,2,6,4,6,8,4,2,4,2 →→ 156 3
最密34生 4,2,4,6,2,6,4,6,2,10,2,10,2,6,4,6,2,6,4,6,6,6,2,6,6,6,4,6,8,4,2,4,2 →→ 156 4
最密34生 2,4,2,4,8,6,4,6,6,6,2,6,6,6,4,6,2,6,4,6,2,10,2,10,2,6,4,6,2,6,4,2,4 →→ 156 4
最密34生 4,2,4,2,4,8,6,4,6,6,6,2,6,6,6,4,6,2,6,4,6,2,10,2,10,2,6,4,6,2,6,4,2 →→ 156 4
最密34生 2,4,6,2,6,4,6,2,10,2,10,2,6,4,6,2,6,4,6,6,6,2,6,6,6,4,6,8,4,2,4,2,4 →→ 156 4
最密34生 2,4,6,2,6,6,4,2,4,6,8,4,2,4,12,2,12,4,2,10,2,6,4,2,4,6,6,2,6,4,2,6,4 →→ 156 2
最密34生 4,6,2,4,6,2,6,6,4,2,4,6,2,10,2,4,12,2,12,4,2,4,8,6,4,2,4,6,6,2,6,4,2 →→ 156 2
这是最密34生素数式的相邻素数间隔的排列顺序，它有20种，截止目前为止，它是最多的（从种数上说）
在34生素数式中2次累加和为2590与2714中都是对应着两种素数式，非一种，但从
相邻间隔的2次累加和中不能区分这两种34生素数，但是一次累加的中间值的余数，
得到的结果是在素数19时一种34生素数只有3组，非5组，这就提示了还有其他形式
的34生素数，虽然这种情况很少，但是不能排除，总会有有的时候，以前已经出
现过这种情况，这是第二次了。2次相邻间距累加和均值2652，最后一对它们的差值
为4，这应该是排列顺序与间隔基本相同的一对互逆34生素数。

作者: 白新岭 时间: 2019-2-6 17:42
最密35生 2,4,2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2,6,6,4,2 →→ 158 2
最密35生 2,4,6,6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2,4,2 →→ 158 2
最密36生 2,4,2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2,6,6,4,2,4 →→ 162 2
最密36生 4,2,4,6,6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2,4,2 →→ 162 2
这是最密35生素数与最密36生素数，都是各有2种形式。

作者: 白新岭 时间: 2019-2-6 18:05
最密37生 2,4,2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2,6,6,4,2,4,6 →→ 168 1
最密37生 6,4,2,4,6,6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2,4,2 →→ 168 1
这是最密37生素数的相邻素数间隔的排列形式，只有这一对互逆的37生素数。

作者: 白新岭 时间: 2019-2-7 16:30
最密38生 2,4,2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2,6,6,4,2,4,6,8 →→ 176 1
最密38生 8,6,4,2,4,6,6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2,4,2 →→ 176 1
最密38生 6,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2,4,14,4,6,2,10,2,6,6,4,6,6,2,10,2,4,2 →→ 176 1
最密38生 2,4,2,10,2,6,6,4,6,6,2,10,2,6,4,14,4,2,4,2,4,8,6,4,6,2,4,6,2,6,6,4,2,4,6,2,6 →→ 176 1
最密38生 2,4,2,4,8,6,4,2,4,6,6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6 →→ 176 1
这是最密38生素数的相邻间距的6种排列形式，除此以外再没有其它的最密38生素数了。
这里有一组实例：
38生实例 38生邻距
23 0
29 6
31 2
37 6
41 4
43 2
47 4
53 6
59 6
61 2
67 6
71 4
73 2
79 6
83 4
89 6
97 8
101 4
103 2
107 4
109 2
113 4
127 14
131 4
137 6
139 2
149 10
151 2
157 6
163 6
167 4
173 6
179 6
181 2
191 10
193 2
197 4
199 2

作者: 白新岭 时间: 2019-2-7 16:31
没有总间距为180的39生素数，到19时全部夭折了。

作者: 白新岭 时间: 2019-2-7 18:32
最密39生 2,4,2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2,6,6,4,2,4,6,8,6 →→ 182 1
最密39生 6,8,6,4,2,4,6,6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2,4,2 →→ 182 1
最密39生 2,4,2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2,6,6,4,2,4,14,4,2 →→ 182 1
最密39生 2,4,14,4,2,4,6,6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2,4,2 →→ 182 1
最密39生 2,4,2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,6,8,6,4,8,4,6,2,6,6,4,2,4,6,8,4,2 →→ 182 1
最密39生 2,4,8,6,4,2,4,6,6,2,6,4,8,4,6,8,6,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2,4,2 →→ 182 1
最密39生 2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2,6,6,4,2,4,6,8,6,4,2 →→ 182 1
最密39生 2,4,6,8,6,4,2,4,6,6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2 →→ 182 1
最密39生 2,4,2,4,8,6,4,2,4,6,6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,6 →→ 182 1
最密39生 6,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2,6,6,4,2,4,6,8,4,2,4,2 →→ 182 1
最密39生 2,4,2,4,6,2,6,4,2,10,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2,6,6,4,2,4,6,8,4,2 →→ 182 1
最密39生 2,4,8,6,4,2,4,6,6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,10,2,4,6,2,6,4,2,4,2 →→ 182 1
最密39生 2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2,6,6,4,2,4,14,4,2,4,2 →→ 182 1
最密39生 2,4,2,4,14,4,2,4,6,6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2 →→ 182 1
最密39生 2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2,6,10,2,4,6,8,4,2,4,2 →→ 182 1
最密39生 2,4,2,4,8,6,4,2,10,6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2 →→ 182 1
最密39生 2,4,6,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2,6,6,4,2,4,6,8,4,2 →→ 182 1
最密39生 2,4,8,6,4,2,4,6,6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,6,4,2 →→ 182 1
最密39生 2,4,2,4,8,6,4,6,2,4,6,2,6,6,4,2,4,6,2,10,2,16,2,16,2,4,6,2,6,4,2,4,6,6,2,6,4,2 →→ 182 1
最密39生 2,4,6,2,6,6,4,2,4,6,2,6,4,2,16,2,16,2,10,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2 →→ 182 1
最密39生 2,4,6,2,6,6,4,2,4,6,8,4,2,4,12,2,12,4,2,10,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,6,4,2 →→ 182 1
最密39生 2,4,6,8,6,4,6,2,4,6,2,6,6,4,2,4,6,2,10,2,4,12,2,12,4,2,4,8,6,4,2,4,6,6,2,6,4,2 →→ 182 1
最密39生 2,4,2,4,8,6,4,6,2,4,6,2,6,10,2,4,6,2,6,4,2,16,2,16,2,4,6,2,6,4,2,4,6,6,2,6,4,2 →→ 182 1
最密39生 2,4,6,2,6,6,4,2,4,6,2,6,4,2,16,2,16,2,4,6,2,6,4,2,10,6,2,6,4,2,6,4,6,8,4,2,4,2 →→ 182 1
最密39生 2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,6,8,6,4,8,4,6,2,6,6,4,2,4,6,8,4,2,4,2 →→ 182 1
最密39生 2,4,2,4,8,6,4,2,4,6,6,2,6,4,8,4,6,8,6,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2 →→ 182 1
这是最密的39生素数的相邻间距的排列形式，有26种，突破了以前的记录（最多20种）
在39生素数中和值是3466与3632的各是两种39生素数，非一种。到此已经是第三种
这样的情况了。所以，在2次邻距累加和中即便是值一样，也不敢保证就是同一种k
生素数，虽然大多数情况下是同一种。

作者: 白新岭 时间: 2019-2-14 14:29
10^n 素数个数 1.760431509 1.760431509 差值
13 3.46066E+11 21083166428 19647217418 1435949010
14 3.20494E+12 1.80825E+11 1.69407E+11 11418261931
15 2.98446E+13 1.56801E+12 1.47572E+12 92289169100
16 2.79238E+14 1.37268E+13 1.29702E+13 7.56564E+11
17 2.62356E+15 1.21171E+14 1.14892E+14 6.27939E+12
18 2.474E+16 1.0775E+15 1.02481E+15 5.26905E+13
19 2.34058E+17 9.64417E+15 9.19773E+15 4.46443E+14
20 2.22082E+18 8.68252E+16 8.30095E+16 3.81569E+15
21 2.11273E+19 7.85789E+17 7.52921E+17 3.28683E+16
22 2.01467E+20 7.14543E+18 6.86029E+18 2.85139E+17
23 1.92532E+21 6.52567E+19 6.27671E+19 2.4896E+18
24 1.84356E+22 5.9832E+20 5.76455E+20 2.18654E+19
25 1.76846E+23 5.50568E+21 5.31261E+21 1.93075E+20
26 1.69925E+24 5.08314E+22 4.9118E+22 1.71335E+21
27 1.63525E+25 4.70745E+23 4.5547E+23 1.52741E+22
这是从网上查到10^n内素数个数，第一列是n值，第二列是素数个数，第三列是用调节系数*素数个数^2/范围值得到的素数对，第四列是用调节系数*范围值/（LN(范围值））^2得到的素数对（也就是用哈代公式得到的值），最后一列是它们的差，数量级仅差一位，说明两种计算方式的相对误差在10%左右，非常大，不知道素数对的真值更接近那个值，我虽然没有真实数据，但是我倾向用素数个数计算出来的值更接近真实值。

作者: 白新岭 时间: 2019-2-16 17:56
10^n 素数个数 1.760431509 1.760431509 差值占比
1 3 1.584388358 3.320379744 -1.735991386 -1.095685522
2 24 10.14008549 8.300949359 1.839136132 0.181372843
3 167 49.09667435 36.89310826 12.20356609 0.24856197
4 1228 265.4702549 207.523734 57.94652087 0.218278771
5 9591 1619.373079 1328.151897 291.2211814 0.179835756
6 78497 10847.38992 9223.277066 1624.112853 0.149723838
7 664578 77751.90778 67762.85191 9989.055863 0.12847345
8 5761454 584363.8352 518809.335 65554.50025 0.112180967
9 50847533 4551545.692 4099234.251 452311.44 0.099375349
10 455052510 36453745.86 33203797.44 3249948.425 0.08915266
11 4118054812 298540584.6 274411549.1 24129035.49 0.080823301
12 37607912017 2489875188 2305819266 184055921.8 0.073921746
13 3.46066E+11 21083166428 19647217418 1435949009 0.068108793
14 3.20494E+12 1.80825E+11 1.69407E+11 11418261930 0.063145235
15 2.98446E+13 1.56801E+12 1.47572E+12 92289169100 0.058857382
16 2.79238E+14 1.37268E+13 1.29702E+13 7.56564E+11 0.055115861
从这里可以看出，除了10的时候，是负误差，其它10的次幂时，皆是正误差，随着次幂的增大相对误差在减小。

作者: 白新岭 时间: 2019-2-16 18:41
10^n →→ G（10^n）
1 →→ 3.00000000000000E+00
2 →→ 1.40000000000000E+01
3 →→ 5.60000000000000E+01
4 →→ 2.82000000000000E+02
5 →→ 1.66100000000000E+03
6 →→ 1.09930000000000E+04
7 →→ 7.83350000000000E+04
8 →→ 5.87153000000000E+05
9 →→ 4.56707300000000E+06
10 →→ 3.65485520000000E+07
11 →→ 2.99158483000000E+08
12 →→ 2.49407981800000E+09
13 →→ 2.11127977360000E+10
14 →→ 1.81040353189000E+11
15 →→ 1.56961132247700E+12
16 →→ 1.37389234059900E+13
17 →→ 1.21265111014650E+14
18 →→ 1.07823453532480E+15
19 →→ 9.65002408367160E+15
20 →→ 8.68723539049495E+16
21 →→ 7.86173278229553E+17
22 →→ 7.14859128401663E+18
23 →→ 6.52829861091019E+19
24 →→ 5.98540295787833E+20
25 →→ 5.50753926555204E+21
26 →→ 5.08471751563008E+22
27 →→ 4.70879543316114E+23
28 →→ 4.37308292519866E+24
29 →→ 4.07204193011379E+25
30 →→ 3.80105624750587E+26
31 →→ 3.55625329945931E+27
32 →→ 3.33436484838541E+28
33 →→ 3.13261723372195E+29
34 →→ 2.94864418675847E+30
35 →→ 2.78041706665415E+31
36 →→ 2.62618864920244E+32
37 →→ 2.48444754029461E+33
38 →→ 2.35388097907588E+34
39 →→ 2.23334431121631E+35
40 →→ 2.12183579935978E+36
41 →→ 2.01847573020612E+37
42 →→ 1.92248900049638E+38
43 →→ 1.83319053520075E+39
44 →→ 1.74997302339157E+40
45 →→ 1.67229656011145E+41
46 →→ 1.59967986303503E+42
47 →→ 1.53169279609694E+43
48 →→ 1.46794998243866E+44
49 →→ 1.40810532897322E+45
50 →→ 1.35184731682872E+46
51 →→ 1.29889493763103E+47
52 →→ 1.24899417634670E+48
53 →→ 1.20191495825314E+49
54 →→ 1.15744849133167E+50
55 →→ 1.11540494661338E+51
56 →→ 1.07561142823703E+52
57 →→ 1.03791019258972E+53
58 →→ 1.00215708220083E+54
59 →→ 9.68220145292820E+54
60 →→ 9.35978416253581E+55
61 →→ 9.05320835942033E+56
62 →→ 8.76145293797591E+57
63 →→ 8.48357776297965E+58
64 →→ 8.21871608481628E+59
65 →→ 7.96606777089306E+60
66 →→ 7.72489325438495E+61
这是用积分法得到的素数对，比其用素数个数计算出的素数对都多。

作者: 白新岭 时间: 2019-2-17 16:27
今天查了一下两个素数和的分布表：得到G（10）=3，G（100）=12，G（1000）=56，G（10000）=254；

当是10与1000时，素数对与积分值完全一致，100与10000时，实际素数对小于积分值，所以随位数增多，积分值应该大于实际值（也大于用素数个数求出来的素数对）。

作者: 白新岭 时间: 2019-2-18 10:10
10^n 积分值实际统计统计/积分值
1 6.00000000000000E+00 3.00000000000000E+00 0.500000000000000
2 2.90000000000000E+01 2.40000000000000E+01 0.827586206896552
3 1.77000000000000E+02 1.67000000000000E+02 0.943502824858757
4 1.24600000000000E+03 1.22800000000000E+03 0.985553772070626
5 9.62900000000000E+03 9.59100000000000E+03 0.996053588119223
6 7.86270000000000E+04 7.84970000000000E+04 0.998346623933254
7 6.64918000000000E+05 6.64578000000000E+05 0.999488658751906
8 5.76220900000000E+06 5.76145400000000E+06 0.999868973860546
9 5.08492340000000E+07 5.08475330000000E+07 0.999966548168651
10 4.55055614000000E+08 4.55052510000000E+08 0.999993178855717
11 4.11806640000000E+09 4.11805481200000E+09 0.999997186058000
12 3.76079502800000E+10 3.76079120170000E+10 0.999998982582148
13 3.46065645809000E+11 3.46065536838000E+11 0.999999685114656
14 3.20494206569200E+12 3.20494175080100E+12 0.999999901748302
15 2.98445714752870E+13 2.98445704226680E+13 0.999999964729968
16 2.79238344248557E+14 2.79238341033924E+14 0.999999988487853
17 2.62355716561082E+15 2.62355715765423E+15 0.999999996967251
18 2.47399543096904E+16 2.47399542877408E+16 0.999999999112787
19 2.34057667376222E+17 2.34057667276344E+17 0.999999999573276
20 2.22081960278366E+18 2.22081960256091E+18 0.999999999899699
21 2.11272694866161E+19 2.11272694860187E+19 0.999999999971724
22 2.01467286691248E+20 2.01467286689315E+20 0.999999999990405
23 1.92532039161405E+21 1.92532039160680E+21 0.999999999996234
24 1.84355997673663E+22 1.84355997673492E+22 0.999999999999072
25 1.76846309399199E+23 1.76846309399143E+23 0.999999999999683
26 1.69924675087259E+24 1.69924675087243E+24 0.999999999999906
27 1.63524604268422E+25 1.63524604268416E+25 0.999999999999963
28 1.57589269275975E+26
29 1.52069810971428E+27
30 1.46923988977204E+28
31 1.42115097348081E+29
32 1.37611086699377E+30
33 1.33383848331044E+31
34 1.29408626505159E+32
35 1.25663532881832E+33
36 1.22129142976194E+34
37 1.18788158912168E+35
38 1.15625126102652E+36
39 1.12626194055592E+37
40 1.09778913489828E+38
41 1.07072063488004E+39
42 1.04495503622646E+40
43 1.02040046944366E+41
44 9.96973504768770E+41
45 9.74598204664929E+42
46 9.53205301174764E+43
47 9.32731479347381E+44
48 9.13118751116142E+45
49 8.94313906580259E+46
50 8.76268031750784E+47
51 8.58936083553667E+48
52 8.42276514312127E+49
53 8.26250939115126E+50
54 8.10823840464122E+51
55 7.95962305413021E+52
56 7.81635791105613E+53
57 7.67815915194389E+54
58 7.54476268113578E+55
59 7.41592244592971E+56
60 7.29140892150319E+57
61 7.17100774599038E+58
62 7.05451848863218E+59
63 6.94175353610429E+60
64 6.83253708400362E+61
65 6.72670422208763E+62
66 6.62410010325301E+63
随着n的增大，很快积分值与实际统计值就有高度吻合，到n=27时，小数点后已经有13个9，可见接近度，精度是多高。

作者: 白新岭 时间: 2019-2-23 18:01
Pi10（n)→→1731.79315527582这是最密5家村的系数，素数式为0,2,4,2,10,2,10,2,4,2（数字表示相邻两个素数的距离）。
10^n 积分值
11 2.00000000000000E+00
12 1.00000000000000E+01
13 4.60000000000000E+01
14 2.12000000000000E+02
15 1.02800000000000E+03
16 5.24200000000000E+03
17 2.79050000000000E+04
18 1.54307000000000E+05
19 8.82439000000000E+05
20 5.19981300000000E+06
21 3.14739650000000E+07
22 1.95179436000000E+08
23 1.23724682000000E+09
24 8.00150300600000E+09
25 5.27038336390000E+10
26 3.53038179850000E+11
27 2.40181651006300E+12
28 1.65764381666330E+13
29 1.15937946231775E+14
30 8.20994235145442E+14
31 5.88129235487700E+15
32 4.25889702171590E+16
33 3.11542833857058E+17
34 2.30073375954359E+18
35 1.71434638090752E+19
36 1.28822339698477E+20
37 9.75752656922001E+20
38 7.44657421639768E+21
39 5.72359273307466E+22
40 4.42911477317930E+23
41 3.44948115921183E+24
42 2.70297932618277E+25
43 2.13037989362070E+26
44 1.68841397024750E+27
45 1.34523640875228E+28
46 1.07724298867865E+29
47 8.66819011459531E+29
48 7.00734182503486E+30
49 5.68989637496804E+31
50 4.63983783529086E+32
51 3.79904637193229E+33
52 3.12284235619149E+34
53 2.57669823412196E+35
54 2.13379736792040E+36
55 1.77321109816512E+37
56 1.47852982026902E+38
57 1.23682944706308E+39
58 1.03788702945369E+40
59 8.73582486657053E+40
60 7.37440082942806E+41
61 6.24275369986034E+42
62 5.29922112978888E+43
63 4.51020162176988E+44
64 3.84849975343357E+45
65 3.29203007003361E+46
66 2.82279791155501E+47
不知以前是否发表过，这是间距38的自对称5家村。

作者: 白新岭 时间: 2019-2-24 10:15
到素数19时，相邻素数式差为8的有128810组，2素数式相差为8的有378675组，它们之间的关系是什么？相邻素数差为8的是2素数差为8的一部分，2素数差为8的还包括3生素数为8的，4生素数为8的，所以相邻素数式差为8的=2素数差为8-3素数为8的-4素数为8的，而3素数为8的同样包括4素数为8的（且3素数为8的有两种形式），所以相邻素数为8的=2素数为8的-2倍3素数为8+4素数为8的（在减3素数为8的当中，有去4素数为8的情况，减减为加，所以等于加2倍的4素数为8的，再去一个4素数为8的后，等于加上一个4素数为8的）。

所以378675-2*143360（3素数为8的,在未去4素数为8的之前）+36855（4素数为8的）=128810
由此得到求相邻素数为8的公式=孪生素数对个数-2*最密3生素数个数+最密4生素数个数。

作者: 白新岭 时间: 2019-2-24 12:57
10^n 2生素数积分值 3生素数积分值 4生素数积分值相邻差为8的素数对
1 2.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 2.00000000000000E+00
2 1.00000000000000E+01 4.00000000000000E+00 0.00000000000000E+00 2.00000000000000E+00
3 4.20000000000000E+01 1.60000000000000E+01 3.00000000000000E+00 1.30000000000000E+01
4 2.11000000000000E+02 6.00000000000000E+01 1.10000000000000E+01 1.02000000000000E+02
5 1.24600000000000E+03 2.70000000000000E+02 4.00000000000000E+01 7.46000000000000E+02
6 8.24500000000000E+03 1.43700000000000E+03 1.70000000000000E+02 5.54100000000000E+03
7 5.87510000000000E+04 8.58200000000000E+03 8.50000000000000E+02 4.24370000000000E+04
8 4.40365000000000E+05 5.54820000000000E+04 4.72200000000000E+03 3.34123000000000E+05
9 3.42530500000000E+06 3.79793000000000E+05 2.83840000000000E+04 2.69410300000000E+06
10 2.74114160000000E+07 2.71528400000000E+06 1.81062000000000E+05 2.21619100000000E+07
11 2.24368877000000E+08 2.00896490000000E+07 1.20994400000000E+06 1.85399523000000E+08
12 1.87055999000000E+09 1.52830589000000E+08 8.39456800000000E+06 1.57329338000000E+09
13 1.58345993750000E+10 1.18976333800000E+09 6.00754500000000E+07 1.35151481490000E+10
14 1.35780274094000E+11 9.44389232400000E+09 4.41290899000000E+08 1.17333780345000E+11
15 1.17720857164500E+12 7.62177954860000E+10 3.31455162500000E+09 1.02808753229800E+12
16 1.03041932528750E+13 6.24025314376000E+11 2.53794516430000E+10 9.08152207576600E+12
17 9.09488394251850E+13 5.17368778200500E+12 1.97622493144000E+11 8.07990863543190E+13
18 8.08675956302867E+14 4.33713953109410E+13 1.56177243700000E+12 7.23494938117985E+14
19 7.23751855328771E+15 3.67175721215464E+14 1.25056009324990E+13 6.51567271178928E+15
20 6.51542698446435E+16 3.13588380228085E+15 1.01318973598611E+14 5.89838212136804E+16
21 5.89629998635250E+17 2.69946618183503E+16 8.29588089136792E+14 5.36470263087686E+17
22 5.36144382639262E+18 2.34045046069285E+17 6.85772585781442E+15 4.90021146011186E+18
23 4.89622429003181E+19 2.04240297303743E+18 5.71826853616852E+16 4.49346196396049E+19
24 4.48905252266123E+20 1.79290708961908E+19 4.80603132430811E+17 4.13527713606172E+20
25 4.13065472912555E+21 1.58246230697159E+20 4.06872698422031E+18 3.81823099471545E+21
26 3.81353839519102E+22 1.40371521890257E+21 3.46758761873661E+19 3.53626293902924E+22
27 3.53159681423029E+23 1.25091388312333E+22 2.97351193606394E+20 3.28438754954169E+23
28 3.27981241619335E+24 1.11951512460133E+23 2.56440527376364E+21 3.05847379654685E+24
29 3.05403165457706E+25 1.00589817651362E+24 2.22331571235695E+22 2.85507533498669E+25
30 2.85079237884626E+26 9.07153321314230E+24 1.93711005712835E+23 2.67129882464054E+26
31 2.66719015536742E+27 8.20924131522523E+25 1.69552135401899E+24 2.50470085041693E+27
32 2.50077380578287E+28 7.45288486897691E+26 1.49045559838141E+25 2.35320656400171E+28
33 2.34946308452995E+29 6.78667964292004E+27 1.31548156560022E+26 2.21504497323715E+29
34 2.21148328995555E+30 6.19758208427067E+28 1.16545155188245E+27 2.08869709982202E+30
35 2.08531294132592E+31 5.67474971509747E+29 1.03621673520777E+28 1.97285416375918E+31
36 1.96964162039733E+32 5.20911963209356E+30 9.24411634219414E+28 1.86638363938968E+32
37 1.86333578151142E+33 4.79307680201278E+31 8.27289516674936E+29 1.76830153498784E+33
38 1.76541085396036E+34 4.42019118867108E+32 7.42595718236183E+30 1.67774962590517E+34
39 1.67500834693851E+35 4.08500804841166E+33 6.68469411571155E+31 1.59397665538185E+35
40 1.59137695737787E+36 3.78287959375271E+34 6.03366899229309E+32 1.51632273240205E+36
41 1.51385690025858E+37 3.50982906501237E+35 5.46001314650209E+33 1.44420632027298E+37
42 1.44186684809704E+38 3.26244035551446E+36 4.95294922061421E+34 1.37711333590881E+38
43 1.37489299458606E+39 3.03776790987013E+37 4.50341156725430E+35 1.31458797754538E+39
44 1.31247985649903E+40 2.83326280009472E+38 4.10374244595071E+36 1.25622497474173E+40
45 1.25422250509046E+41 2.64671178334713E+39 3.74744756347486E+37 1.20166301417986E+41
46 1.19975997859186E+42 2.47618683166226E+40 3.42899835163514E+38 1.15057914179378E+42
47 1.14876967493235E+43 2.32000315180180E+41 3.14367126065979E+39 1.10268397902238E+43
48 1.10096256144843E+44 2.17668412153300E+42 2.88741652544276E+40 1.05771762067031E+44
49 1.05607906830731E+45 2.04493188621645E+43 2.65675051885220E+41 1.01544610563487E+45
50 1.01388555633920E+46 1.92360260805324E+44 2.44866707393182E+42 9.75658370885528E+45
51 9.74171269249236E+46 1.81168555579433E+45 2.26056413234535E+43 9.38163614546584E+46
52 9.36745695749414E+47 1.70828537725722E+46 2.09018283137315E+44 9.02789006487407E+47
53 9.01436279786093E+48 1.61260701979356E+47 1.93555672919195E+45 8.69377695063141E+48
54 8.68086427334653E+49 1.52394286189039E+48 1.79496932759942E+46 8.37787067029605E+49
55 8.36553766658759E+50 1.44166169771357E+49 1.66691841245810E+47 8.07887224545734E+50
56 8.06708625853697E+51 1.36519927973583E+50 1.55008601732178E+48 7.79559648860713E+51
57 7.78432697201769E+52 1.29405017582088E+51 1.44331304196684E+49 7.52696024989548E+52
58 7.51617862592685E+53 1.22776073874045E+52 1.34557773785042E+50 7.27197205591661E+53
59 7.26165158186581E+54 1.16592302002200E+53 1.25597741680093E+51 7.02972295527821E+54
60 7.01983859768228E+55 1.10816948778414E+54 1.17371285518155E+52 6.79937841298063E+55
61 6.78990672976167E+56 1.05416843101521E+55 1.09807495928997E+53 6.58017111851792E+56
62 6.57109014884773E+57 1.00361995154042E+56 1.02843333348780E+54 6.37139459187313E+57
63 6.36268375347547E+58 9.56252460460582E+56 9.64226454099809E+54 6.17239748783745E+58
64 6.16403748138939E+59 9.11819608735616E+57 9.04953202321241E+55 5.98257851284459E+59
65 5.97455123310425E+60 8.70097592313475E+58 8.50165550451812E+56 5.80138188019201E+60
66 5.79367033346368E+61 8.30882781159487E+59 7.99462229506832E+57 5.62829323946129E+61
实际个数
0.00000000000000E+00
1.00000000000000E+00
1.50000000000000E+01
1.01000000000000E+02
7.73000000000000E+02
5.56900000000000E+03
4.23520000000000E+04
以上是用公式计算的邻差为8的素数对数量，后边给出了部分实际个数。

作者: 白新岭 时间: 2019-3-9 20:32
本帖最后由白新岭于 2019-3-9 12:33 编辑

4生素数必定产生在3生素数之中，不是三生素数的一定不是四生素数，而每一组四生素数都是两种三生素数；5生素数产生在对应的三生素数之中，有了3生素数表可以直接产生5生素数；6生素数产生在5生素数之中，也可以有三生素数直接产生；这种方法与在素数表中找k生素数是一样的；为了减少运算量，我们要一步一步的提炼，有了基础数列，我们就可以筛选更高一阶的素数，k生素数看似线性，实际上是以ln（N）的速度在下降，虽然比它慢点，但是有限。

作者: 白新岭 时间: 2019-3-21 13:11
808675888577436这是网上查到的10^18以下孪生素数对的数量，与用积分得到808675956302870 ，前5位数字是一致的

欢迎光临数学中国 (http://www.mathchina.com/bbs/)