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 2021-10-15 08:04

也许历史会忘记了我，但是不会忘记合成方法论。

独木星空谁 · 发表于 2021-10-15 08:06

素数31 统计2+1 理论占比实际占比占比绝对误差相对误差
0 1106478054858 3.33% 3.33333% 0.000001% 0.00003%
1 1069593704163 3.22% 3.22222% 0.000006% 0.00020%
2 1069617666792 3.22% 3.22229% -0.000066% -0.00205%
3 1069596939054 3.22% 3.22223% -0.000003% -0.00011%
4 1069574568884 3.22% 3.22216% 0.000064% 0.00198%
5 1069582418958 3.22% 3.22218% 0.000040% 0.00125%
6 1069577624320 3.22% 3.22217% 0.000055% 0.00170%
7 1069590022666 3.22% 3.22220% 0.000017% 0.00054%
8 1069550128982 3.22% 3.22208% 0.000138% 0.00427%
9 1069595970048 3.22% 3.22222% -0.000001% -0.00002%
10 1069604755156 3.22% 3.22225% -0.000027% -0.00084%
11 1069547650823 3.22% 3.22208% 0.000145% 0.00450%
12 1069563586871 3.22% 3.22213% 0.000097% 0.00301%
13 1069619918904 3.22% 3.22229% -0.000073% -0.00226%
14 1069590445406 3.22% 3.22221% 0.000016% 0.00050%
15 1069602071775 3.22% 3.22224% -0.000019% -0.00059%
16 1069554749369 3.22% 3.22210% 0.000124% 0.00384%
17 1069614881001 3.22% 3.22228% -0.000058% -0.00178%
18 1069571924210 3.22% 3.22215% 0.000072% 0.00223%
19 1069637593658 3.22% 3.22235% -0.000126% -0.00391%
20 1069645373510 3.22% 3.22237% -0.000149% -0.00464%
21 1069632928478 3.22% 3.22233% -0.000112% -0.00347%
22 1069566317564 3.22% 3.22213% 0.000089% 0.00276%
23 1069607748208 3.22% 3.22226% -0.000036% -0.00112%
24 1069573785791 3.22% 3.22216% 0.000066% 0.00206%
25 1069636936221 3.22% 3.22235% -0.000124% -0.00385%
26 1069653431187 3.22% 3.22240% -0.000174% -0.00539%
27 1069569488059 3.22% 3.22214% 0.000079% 0.00246%
28 1069662705638 3.22% 3.22242% -0.000202% -0.00626%
29 1069550297817 3.22% 3.22209% 0.000137% 0.00425%
30 1069588505745 3.22% 3.22220% 0.000022% 0.00068%
合计 33194352194116 100.00% 100.00000% 0.000000% 0.00000%

独木星空谁 · 发表于 2021-10-15 08:06

素数31 统计2+2 理论占比实际占比占比绝对误差相对误差
0 1106477810737 3.33% 3.33333% 0.000002% 0.00005%
1 1069555436535 3.22% 3.22210% 0.000122% 0.00377%
2 1069632425326 3.22% 3.22233% -0.000110% -0.00342%
3 1069623583140 3.22% 3.22231% -0.000084% -0.00260%
4 1069602865215 3.22% 3.22224% -0.000021% -0.00066%
5 1069599015341 3.22% 3.22223% -0.000010% -0.00030%
6 1069570228940 3.22% 3.22215% 0.000077% 0.00239%
7 1069663277024 3.22% 3.22243% -0.000203% -0.00631%
8 1069545861788 3.22% 3.22207% 0.000150% 0.00467%
9 1069647180838 3.22% 3.22238% -0.000155% -0.00480%
10 1069566065266 3.22% 3.22213% 0.000090% 0.00278%
11 1069580971001 3.22% 3.22218% 0.000045% 0.00139%
12 1069585162201 3.22% 3.22219% 0.000032% 0.00099%
13 1069617802658 3.22% 3.22229% -0.000066% -0.00206%
14 1069516907423 3.22% 3.22198% 0.000238% 0.00738%
15 1069602191033 3.22% 3.22224% -0.000019% -0.00060%
16 1069554075028 3.22% 3.22210% 0.000126% 0.00390%
17 1069605856951 3.22% 3.22225% -0.000030% -0.00094%
18 1069544990275 3.22% 3.22207% 0.000153% 0.00475%
19 1069611987887 3.22% 3.22227% -0.000049% -0.00151%
20 1069643737766 3.22% 3.22237% -0.000144% -0.00448%
21 1069684449568 3.22% 3.22249% -0.000267% -0.00829%
22 1069514667909 3.22% 3.22198% 0.000244% 0.00758%
23 1069613289405 3.22% 3.22227% -0.000053% -0.00164%
24 1069541824688 3.22% 3.22206% 0.000163% 0.00505%
25 1069661646531 3.22% 3.22242% -0.000198% -0.00616%
26 1069622074849 3.22% 3.22230% -0.000079% -0.00246%
27 1069525633859 3.22% 3.22201% 0.000211% 0.00656%
28 1069664184296 3.22% 3.22243% -0.000206% -0.00639%
29 1069574664686 3.22% 3.22216% 0.000064% 0.00198%
30 1069602325952 3.22% 3.22224% -0.000020% -0.00061%
合计 33194352194116 100.00% 100.00000% 0.000000% 0.00000%

独木星空谁 · 发表于 2021-10-15 08:07

素数31 统计2+3 理论占比实际占比占比绝对误差相对误差
0 1106478119475 3.33% 3.33333% 0.000001% 0.00003%
1 1069568125764 3.22% 3.22214% 0.000083% 0.00259%
2 1069573519094 3.22% 3.22216% 0.000067% 0.00208%
3 1069627988875 3.22% 3.22232% -0.000097% -0.00301%
4 1069610396836 3.22% 3.22227% -0.000044% -0.00137%
5 1069570455615 3.22% 3.22215% 0.000076% 0.00237%
6 1069586623994 3.22% 3.22219% 0.000028% 0.00086%
7 1069632523811 3.22% 3.22233% -0.000111% -0.00343%
8 1069584257371 3.22% 3.22219% 0.000035% 0.00108%
9 1069608458862 3.22% 3.22226% -0.000038% -0.00118%
10 1069586120458 3.22% 3.22219% 0.000029% 0.00090%
11 1069622431707 3.22% 3.22230% -0.000080% -0.00249%
12 1069565636746 3.22% 3.22213% 0.000091% 0.00282%
13 1069614997997 3.22% 3.22228% -0.000058% -0.00180%
14 1069559437868 3.22% 3.22211% 0.000110% 0.00340%
15 1069584016802 3.22% 3.22219% 0.000035% 0.00110%
16 1069619494352 3.22% 3.22229% -0.000071% -0.00222%
17 1069580556453 3.22% 3.22218% 0.000046% 0.00142%
18 1069565087358 3.22% 3.22213% 0.000093% 0.00287%
19 1069612695496 3.22% 3.22227% -0.000051% -0.00158%
20 1069633707876 3.22% 3.22234% -0.000114% -0.00354%
21 1069600724679 3.22% 3.22224% -0.000015% -0.00046%
22 1069587953683 3.22% 3.22220% 0.000024% 0.00073%
23 1069606247831 3.22% 3.22225% -0.000031% -0.00098%
24 1069547971077 3.22% 3.22208% 0.000144% 0.00447%
25 1069593650180 3.22% 3.22222% 0.000006% 0.00020%
26 1069642633678 3.22% 3.22236% -0.000141% -0.00438%
27 1069535244691 3.22% 3.22204% 0.000182% 0.00566%
28 1069619370145 3.22% 3.22229% -0.000071% -0.00220%
29 1069611093617 3.22% 3.22227% -0.000046% -0.00143%
30 1069622651725 3.22% 3.22230% -0.000081% -0.00251%
合计 33194352194116 100.00% 100.00000% 0.000000% 0.00000%

独木星空谁 · 发表于 2021-10-15 08:07

素数31 统计2+4 理论占比实际占比占比绝对误差相对误差
0 1106478054858 3.33% 3.33333% 0.000001% 0.00003%
1 1069554749369 3.22% 3.22210% 0.000124% 0.00384%
2 1069593704163 3.22% 3.22222% 0.000006% 0.00020%
3 1069614881001 3.22% 3.22228% -0.000058% -0.00178%
4 1069617666792 3.22% 3.22229% -0.000066% -0.00205%
5 1069571924210 3.22% 3.22215% 0.000072% 0.00223%
6 1069596939054 3.22% 3.22223% -0.000003% -0.00011%
7 1069637593658 3.22% 3.22235% -0.000126% -0.00391%
8 1069574568884 3.22% 3.22216% 0.000064% 0.00198%
9 1069645373510 3.22% 3.22237% -0.000149% -0.00464%
10 1069582418958 3.22% 3.22218% 0.000040% 0.00125%
11 1069632928478 3.22% 3.22233% -0.000112% -0.00347%
12 1069577624320 3.22% 3.22217% 0.000055% 0.00170%
13 1069566317564 3.22% 3.22213% 0.000089% 0.00276%
14 1069590022666 3.22% 3.22220% 0.000017% 0.00054%
15 1069607748208 3.22% 3.22226% -0.000036% -0.00112%
16 1069550128982 3.22% 3.22208% 0.000138% 0.00427%
17 1069573785791 3.22% 3.22216% 0.000066% 0.00206%
18 1069595970048 3.22% 3.22222% -0.000001% -0.00002%
19 1069636936221 3.22% 3.22235% -0.000124% -0.00385%
20 1069604755156 3.22% 3.22225% -0.000027% -0.00084%
21 1069653431187 3.22% 3.22240% -0.000174% -0.00539%
22 1069547650823 3.22% 3.22208% 0.000145% 0.00450%
23 1069569488059 3.22% 3.22214% 0.000079% 0.00246%
24 1069563586871 3.22% 3.22213% 0.000097% 0.00301%
25 1069662705638 3.22% 3.22242% -0.000202% -0.00626%
26 1069619918904 3.22% 3.22229% -0.000073% -0.00226%
27 1069550297817 3.22% 3.22209% 0.000137% 0.00425%
28 1069590445406 3.22% 3.22221% 0.000016% 0.00050%
29 1069588505745 3.22% 3.22220% 0.000022% 0.00068%
30 1069602071775 3.22% 3.22224% -0.000019% -0.00059%
合计 33194352194116 100.00% 100.00000% 0.000000% 0.00000%

独木星空谁 · 发表于 2021-10-15 10:12

对于\(P_i+12P_j\)=2N+1(N≥19后，有素数解），存在反例61和85两个。

独木星空谁 · 发表于 2021-10-15 10:25

对于\(P_i+14P_j\)=2N+1(N≥22后有素数解），存在51,57,67,69,97,163这六个反例。另外2N+1不能整除7，整除时无解。

独木星空谁 · 发表于 2021-10-15 11:36

对于\(P_i+15P_j\)=2N(N≥24后有素数解），不存在反例，2N不整除3或者5，个别的有唯一的一组解。

yangchuanju · 发表于 2021-10-15 11:50

陈景运的哥猜证明终止于1+2，即任何一个≥6的偶数都可以表示成一个奇素数与一个不超过2个因子的2合数之后。
今白新岭先生导出任一个≥10的偶数都可以表示成一个奇素数p1，加另一个奇素数p2的m倍之和，简称“1+m”，式中m是奇数，如m=3、5、7。
白老师可否顺藤摸瓜，令m=1直接导得哥德巴赫猜想？

独木星空谁 · 发表于 2021-10-15 19:12

第八个命题:\(vP_i+uP_j\)=N,N大于等于3倍的（v+m）时有素数解，v，u为互质数，N不含v，u中大于2的因子，N的奇偶性与（v+u）的奇偶性相同。公式解组数已列出。

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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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