证明\(P_i+2P_j\)=2N+1(N≥4）在素数集内有解

独木星空谁 · 发表于 2021-10-13 11:09

素数11 统计1+9 理论占比实际占比占比绝对误差相对误差
0 107360164 10.00% 9.99930% 0.000695% 0.00695%
1 96632189 9.00% 9.00012% -0.000123% -0.00137%
2 96550407 9.00% 8.99251% 0.007494% 0.08326%
3 96674856 9.00% 9.00410% -0.004097% -0.04552%
4 96744293 9.00% 9.01056% -0.010564% -0.11738%
5 96641401 9.00% 9.00098% -0.000981% -0.01090%
6 96673698 9.00% 9.00399% -0.003989% -0.04433%
7 96501528 9.00% 8.98795% 0.012046% 0.13385%
8 96566986 9.00% 8.99405% 0.005950% 0.06611%
9 96701553 9.00% 9.00658% -0.006584% -0.07315%
10 96629214 9.00% 8.99985% 0.000154% 0.00171%
合计 1073676289 100.00% 100.00000% 0.000000% -0.00077%

独木星空谁 · 发表于 2021-10-13 11:09

素数11 统计1+10 理论占比实际占比占比绝对误差相对误差
0 107362745 10.00% 9.99955% 0.000455% 0.00455%
1 96595762 9.00% 8.99673% 0.003270% 0.03633%
2 96654446 9.00% 9.00220% -0.002196% -0.02440%
3 96652064 9.00% 9.00197% -0.001974% -0.02194%
4 96589059 9.00% 8.99611% 0.003894% 0.04326%
5 96665441 9.00% 9.00322% -0.003220% -0.03578%
6 96665441 9.00% 9.00322% -0.003220% -0.03578%
7 96589059 9.00% 8.99611% 0.003894% 0.04326%
8 96652064 9.00% 9.00197% -0.001974% -0.02194%
9 96654446 9.00% 9.00220% -0.002196% -0.02440%
10 96595762 9.00% 8.99673% 0.003270% 0.03633%
合计 1073676289 100.00% 100.00000% 0.000000% -0.00051%

独木星空谁 · 发表于 2021-10-13 11:12

素数11 统计1+11 理论占比实际占比占比绝对误差相对误差
0 32767 0.00% 0.00305% -0.003052% 0.00000%
1 107410226 10.00% 10.00397% -0.003967% -0.03967%
2 107868964 10.00% 10.04669% -0.046693% -0.46693%
3 107311925 10.00% 9.99481% 0.005188% 0.05188%
4 106984255 10.00% 9.96429% 0.035707% 0.35707%
5 107311925 10.00% 9.99481% 0.005188% 0.05188%
6 107082556 10.00% 9.97345% 0.026551% 0.26551%
7 108163867 10.00% 10.07416% -0.074160% -0.74160%
8 107213624 10.00% 9.98566% 0.014344% 0.14344%
9 106623818 10.00% 9.93072% 0.069277% 0.69277%
10 107672362 10.00% 10.02838% -0.028382% -0.28382%
合计 1073676289 100.00% 100.00000% 0.000000% 0.03052%
本楼打回了素数11的“原形”，另外以上各楼参与运算的素数个数为：32767

独木星空谁 · 发表于 2021-10-13 11:16

明显比以前的248个素数参与运算时精度提高不少，无论是绝对误差，还是相对误差；这才3万多个素数参与运算，如果一亿的素数都参与运算，则会大幅度提高计算精度。下来试一试。

独木星空谁 · 发表于 2021-10-13 11:19

如果针对其他素数又如何？我想，与这个结果无二，精度的高低只取决于参与运算的素数个数，随着素数量的扩大，精度会无限制的提高，直到逼近1（100%）。

独木星空谁 · 发表于 2021-10-13 12:06

针对素11 针对素11 针对素11 针对素11
统计1+1 统计1+2 统计1+3 统计1+4
3319433696689 3319434268742 3319434016200 3319434016200
2987540869800 2987567632041 2987704737114 2987673461592
2987277811715 2987408974554 2987369504683 2987436302966
2987806610671 2987452348130 2987673461592 2987775151155
2987869149901 2987573360553 2987572985942 2987704737114
2987276420678 2987368996480 2987510043069 2987572985942
2987594781062 2987700754830 2987436302966 2987346455276
2987098390335 2987420461071 2987346455276 2987174141140
2987460898040 2987664932358 2987355394979 2987369504683
2987743452521 2987496833270 2987775151155 2987510043069
2987250112704 2987263632087 2987174141140 2987355394979

独木星空谁 · 发表于 2021-10-13 12:07

针对素11 针对素11 针对素11 针对素11
统计1+5 统计1+6 统计1+7 统计1+8
3319433848310 3319434268742 3319434085440 3319434085440
2987642104473 2987408974554 2987500987955 2987319273196
2987188170084 2987573360553 2987277212823 2987542318462
2987541504537 2987700754830 2987542318462 2987528645081
2987837939633 2987664932358 2987559611118 2987731695042
2987408549096 2987263632087 2987187272564 2987277212823
2987422272151 2987567632041 2987731695042 2987669043443
2987279698971 2987452348130 2987319273196 2987187272564
2987527838733 2987368996480 2987602048992 2987500987955
2987806204473 2987420461071 2987669043443 2987602048992
2987264063655 2987496833270 2987528645081 2987559611118

独木星空谁 · 发表于 2021-10-13 12:07

针对素11 针对素11 针对素11
统计1+9 统计1+10 统计1+11
3319433848310 3319434537146 5761454
2987408549096 2987395246212 3319190933762
2987264063655 2987510507534 3320504545274
2987837939633 2987633995275 3317860037888
2987806204473 2987483231154 3317548919372
2987541504537 2987435848310 3320510306728
2987527838733 2987435848310 3318920145424
2987188170084 2987483231154 3321403332098
2987279698971 2987633995275 3319588474088
2987642104473 2987510507534 3318176917858
2987422272151 2987395246212 3320642820170

独木星空谁 · 发表于 2021-10-13 12:10

素数11 统计1+11 理论占比实际占比占比绝对误差相对误差
0 5761454 0.00% 0.00002% -0.000017% 0.00000%
1 3319190933762 10.00% 9.99926% 0.000736% 0.00736%
2 3320504545274 10.00% 10.00322% -0.003221% -0.03221%
3 3317860037888 10.00% 9.99525% 0.004745% 0.04745%
4 3317548919372 10.00% 9.99432% 0.005683% 0.05683%
5 3320510306728 10.00% 10.00324% -0.003239% -0.03239%
6 3318920145424 10.00% 9.99845% 0.001552% 0.01552%
7 3321403332098 10.00% 10.00593% -0.005929% -0.05929%
8 3319588474088 10.00% 10.00046% -0.000462% -0.00462%
9 3318176917858 10.00% 9.99621% 0.003791% 0.03791%
10 3320642820170 10.00% 10.00364% -0.003638% -0.03638%
合计 33194352194116 100.00% 100.00000% 0.000000% 0.00017%
参与运算的素数个数为：5761454
以下几楼也是这个量的素数参与运算的

独木星空谁 · 发表于 2021-10-13 12:11

素数11 统计1+1 理论占比实际占比占比绝对误差相对误差
0 3319433696689 10.00% 10.00000% 0.000005% 100.00005%
1 2987540869800 9.00% 9.00015% -0.000148% -0.00165%
2 2987277811715 9.00% 8.99936% 0.000644% 0.00716%
3 2987806610671 9.00% 9.00095% -0.000949% -0.01054%
4 2987869149901 9.00% 9.00114% -0.001137% -0.01263%
5 2987276420678 9.00% 8.99935% 0.000649% 0.00721%
6 2987594781062 9.00% 9.00031% -0.000311% -0.00345%
7 2987098390335 9.00% 8.99882% 0.001185% 0.01317%
8 2987460898040 9.00% 8.99991% 0.000093% 0.00103%
9 2987743452521 9.00% 9.00076% -0.000758% -0.00843%
10 2987250112704 9.00% 8.99927% 0.000728% 0.00809%
合计 33194352194116 100.00% 100.00000% 0.000000% 99.99999%

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证明\(P_i+2P_j\)=2N+1(N≥4）在素数集内有解

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