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 19:47

针对素31 针对素31 针对素31 针对素31 针对素31
统计3+16 统计3+17 统计3+18 统计3+19 统计3+20
1106477987456 1106478054858 1106477987456 1106477950816 1106478119475
1069591935630 1069547650823 1069622099982 1069589949295 1069622431707
1069530363836 1069566317564 1069515744311 1069540332281 1069587953683
1069608717578 1069617666792 1069658590776 1069617309461 1069573519094
1069586011306 1069619918904 1069641021608 1069630738389 1069614997997
1069592804705 1069573785791 1069572226812 1069601763552 1069547971077
1069572226812 1069574568884 1069591935630 1069602499486 1069610396836
1069632997221 1069602071775 1069573589040 1069602472434 1069584016802
1069588733350 1069653431187 1069641807454 1069634545514 1069642633678
1069584643857 1069577624320 1069562766500 1069543553164 1069586623994
1069626442512 1069614881001 1069575944866 1069608967936 1069580556453
1069641021608 1069662705638 1069632997221 1069602934225 1069619370145
1069575944866 1069550128982 1069530363836 1069560390498 1069584257371
1069648484992 1069637593658 1069593362916 1069617841675 1069612695496
1069631925523 1069588505745 1069600739078 1069574117269 1069622651725
1069570332313 1069604755156 1069575518812 1069591906113 1069586120458
1069658590776 1069632928478 1069648484992 1069614847244 1069600724679
1069562766500 1069593704163 1069588733350 1069584307933 1069568125764
1069575518812 1069563586871 1069608717578 1069624684506 1069565636746
1069564940099 1069607748208 1069630224489 1069622838353 1069606247831
1069584343837 1069596939054 1069588899751 1069643382790 1069627988875
1069515744311 1069590445406 1069564940099 1069551129966 1069559437868
1069641807454 1069636936221 1069631925523 1069633655414 1069593650180
1069600739078 1069582418958 1069584643857 1069556731570 1069570455615
1069588899751 1069554749369 1069586011306 1069539960475 1069619494352
1069594399620 1069569488059 1069584593886 1069540376857 1069535244691
1069622099982 1069590022666 1069594399620 1069616773658 1069632523811
1069573589040 1069571924210 1069584343837 1069562929484 1069565087358
1069593362916 1069550297817 1069570332313 1069564539975 1069611093617
1069630224489 1069595970048 1069626442512 1069665888680 1069608458862
1069584593886 1069645373510 1069592804705 1069632875103 1069633707876

独木星空谁 · 发表于 2021-10-15 19:47

针对素31 针对素31 针对素31 针对素31 针对素31
统计3+21 统计3+22 统计3+23 统计3+24 统计3+25
1106478075328 1106477984614 1106478083143 1106478089176 1106478005014
1069575590414 1069593483127 1069597140999 1069599379277 1069573520781
1069549811687 1069569137004 1069558371719 1069568368159 1069579161502
1069588633507 1069637931246 1069647778162 1069589350050 1069617280613
1069580008406 1069594095134 1069610019002 1069651281347 1069632418341
1069571818769 1069577538949 1069528055749 1069582653476 1069576912882
1069601072316 1069625037800 1069559836996 1069578605837 1069588823926
1069591611246 1069612055114 1069586181799 1069588424965 1069574083814
1069613999032 1069603579040 1069598552563 1069601604312 1069583543300
1069591711810 1069572575482 1069627451097 1069556001907 1069617120146
1069590542213 1069603962411 1069611924450 1069588161489 1069634691406
1069633216623 1069609611332 1069631560000 1069638012426 1069634806966
1069556055353 1069545522307 1069605019400 1069550616856 1069535724127
1069583094245 1069607531469 1069627788103 1069564483911 1069591295816
1069558326278 1069643544396 1069593612559 1069563908521 1069578155420
1069615005117 1069614503340 1069584456991 1069606558777 1069594062697
1069654331218 1069613164798 1069605129930 1069599561996 1069641860505
1069601058626 1069560619484 1069583688733 1069579051540 1069578743357
1069593639801 1069555581413 1069583123076 1069595638710 1069623417001
1069649053493 1069615529589 1069618434015 1069607617090 1069607988207
1069574575910 1069612873766 1069622858813 1069604439917 1069570214400
1069574524081 1069535457099 1069530837637 1069589339164 1069529445706
1069603924144 1069647130485 1069613829128 1069662358749 1069642693586
1069557891208 1069605546249 1069615916024 1069621289566 1069608389268
1069598807379 1069576524530 1069607849788 1069593323816 1069583632558
1069573990603 1069520121252 1069565827971 1069563798720 1069579123691
1069609171886 1069604668063 1069655116687 1069663587679 1069624206594
1069604066461 1069603261427 1069550003844 1069555453593 1069529597427
1069596479586 1069577894642 1069558276820 1069594003002 1069565073459
1069629545043 1069655427270 1069600627584 1069622944134 1069614133904
1069652562333 1069580301284 1069594841334 1069594285954 1069664067702

独木星空谁 · 发表于 2021-10-15 19:47

针对素31 针对素31 针对素31
统计3+26 统计3+27 统计3+28
1106478083143 1106478075328 1106478441796
1069583123076 1069591611246 1069612143778
1069528055749 1069558326278 1069580705087
1069615916024 1069574524081 1069603728186
1069611924450 1069596479586 1069581414766
1069558276820 1069580008406 1069602402207
1069584456991 1069633216623 1069564312019
1069558371719 1069593639801 1069578096925
1069622858813 1069573990603 1069610618907
1069586181799 1069575590414 1069615915931
1069565827971 1069613999032 1069561408458
1069605019400 1069615005117 1069643711817
1069594841334 1069603924144 1069579770484
1069583688733 1069629545043 1069598698816
1069610019002 1069571818769 1069578498405
1069613829128 1069556055353 1069625450374
1069627451097 1069649053493 1069625450374
1069550003844 1069609171886 1069578498405
1069593612559 1069549811687 1069598698816
1069597140999 1069591711810 1069579770484
1069618434015 1069654331218 1069643711817
1069559836996 1069557891208 1069561408458
1069607849788 1069652562333 1069615915931
1069631560000 1069601072316 1069610618907
1069600627584 1069583094245 1069578096925
1069605129930 1069574575910 1069564312019
1069647778162 1069604066461 1069602402207
1069530837637 1069588633507 1069581414766
1069598552563 1069590542213 1069603728186
1069655116687 1069601058626 1069580705087
1069627788103 1069598807379 1069612143778

独木星空谁 · 发表于 2021-10-15 19:48

针对素31 针对素31 针对素31
统计3+29 统计3+30 统计3+31
1106477897881 1106477984614 5761454
1069591710737 1069577894642 1106700414498
1069544609208 1069520121252 1107697146040
1069648241697 1069647130485 1105928379662
1069571750947 1069615529589 1106147314914
1069581941090 1069613164798 1107288082806
1069632272896 1069607531469 1106372011620
1069572010787 1069603962411 1106383534528
1069617501968 1069612055114 1106083938920
1069542620609 1069594095134 1106861735210
1069645278987 1069593483127 1106325919988
1069653870142 1069655427270 1105455940434
1069578903296 1069604668063 1107224706812
1069578579816 1069605546249 1106233736724
1069604092772 1069612873766 1106383534528
1069559960840 1069560619484 1106925111204
1069643403986 1069643544396 1105144821918
1069536127741 1069609611332 1107086431916
1069601435251 1069603579040 1106637038504
1069599372911 1069577538949 1106216452362
1069602199083 1069569137004 1106060893104
1069541474456 1069580301284 1107662577316
1069654427113 1069603261427 1105490509158
1069572501185 1069576524530 1106429626160
1069608604598 1069535457099 1107103716278
1069547981768 1069555581413 1107530063874
1069631128591 1069614503340 1105467463342
1069573888562 1069545522307 1107241991174
1069599242129 1069572575482 1106792597762
1069639729470 1069625037800 1105709444410
1069599433599 1069637931246 1105761297496

独舟星海 · 发表于 2021-10-15 20:06

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

独舟星海 · 发表于 2021-10-15 20:07

统计2+23
1106477950816
1069584307933
1069617309461
1069643382790
1069602499486
1069556731570
1069543553164
1069616773658
1069560390498
1069665888680
1069591906113
1069589949295
1069624684506
1069630738389
1069551129966
1069602472434
1069539960475
1069608967936
1069562929484
1069617841675
1069632875103
1069614847244
1069540332281
1069622838353
1069601763552
1069633655414
1069634545514
1069540376857
1069602934225
1069564539975
1069574117269

独舟星海 · 发表于 2021-10-15 20:07

素数31 统计2+23 理论占比实际占比占比绝对误差相对误差
0 1106477950816 3.33% 3.33333% 0.000001% 0.00004%
1 1069584307933 3.22% 3.22219% 0.000035% 0.00107%
2 1069617309461 3.22% 3.22229% -0.000065% -0.00201%
3 1069643382790 3.22% 3.22237% -0.000143% -0.00445%
4 1069602499486 3.22% 3.22224% -0.000020% -0.00063%
5 1069556731570 3.22% 3.22210% 0.000118% 0.00365%
6 1069543553164 3.22% 3.22206% 0.000157% 0.00488%
7 1069616773658 3.22% 3.22229% -0.000063% -0.00196%
8 1069560390498 3.22% 3.22212% 0.000107% 0.00331%
9 1069665888680 3.22% 3.22243% -0.000211% -0.00655%
10 1069591906113 3.22% 3.22221% 0.000012% 0.00036%
11 1069589949295 3.22% 3.22220% 0.000018% 0.00055%
12 1069624684506 3.22% 3.22231% -0.000087% -0.00270%
13 1069630738389 3.22% 3.22233% -0.000105% -0.00327%
14 1069551129966 3.22% 3.22209% 0.000135% 0.00418%
15 1069602472434 3.22% 3.22224% -0.000020% -0.00062%
16 1069539960475 3.22% 3.22205% 0.000168% 0.00522%
17 1069608967936 3.22% 3.22226% -0.000040% -0.00123%
18 1069562929484 3.22% 3.22212% 0.000099% 0.00307%
19 1069617841675 3.22% 3.22229% -0.000066% -0.00206%
20 1069632875103 3.22% 3.22233% -0.000112% -0.00347%
21 1069614847244 3.22% 3.22228% -0.000057% -0.00178%
22 1069540332281 3.22% 3.22206% 0.000167% 0.00519%
23 1069622838353 3.22% 3.22230% -0.000081% -0.00253%
24 1069601763552 3.22% 3.22224% -0.000018% -0.00056%
25 1069633655414 3.22% 3.22234% -0.000114% -0.00354%
26 1069634545514 3.22% 3.22234% -0.000117% -0.00362%
27 1069540376857 3.22% 3.22206% 0.000167% 0.00518%
28 1069602934225 3.22% 3.22224% -0.000022% -0.00067%
29 1069564539975 3.22% 3.22213% 0.000094% 0.00292%
30 1069574117269 3.22% 3.22216% 0.000065% 0.00203%
合计 33194352194116 100.00% 100.00000% 0.000000% 0.00000%

独舟星海 · 发表于 2021-10-15 20:08

素数31 统计2+24 理论占比实际占比占比绝对误差相对误差
0 1106477992335 3.33% 3.33333% 0.000001% 0.00004%
1 1069586592677 3.22% 3.22219% 0.000028% 0.00086%
2 1069627214282 3.22% 3.22232% -0.000095% -0.00294%
3 1069584749081 3.22% 3.22219% 0.000033% 0.00103%
4 1069643800376 3.22% 3.22237% -0.000145% -0.00449%
5 1069611328237 3.22% 3.22227% -0.000047% -0.00145%
6 1069562040366 3.22% 3.22212% 0.000102% 0.00316%
7 1069619062500 3.22% 3.22229% -0.000070% -0.00218%
8 1069563441798 3.22% 3.22212% 0.000097% 0.00302%
9 1069594439382 3.22% 3.22222% 0.000004% 0.00013%
10 1069568096063 3.22% 3.22214% 0.000083% 0.00259%
11 1069596567552 3.22% 3.22222% -0.000002% -0.00007%
12 1069570278073 3.22% 3.22215% 0.000077% 0.00239%
13 1069567342708 3.22% 3.22214% 0.000086% 0.00266%
14 1069521289363 3.22% 3.22200% 0.000224% 0.00697%
15 1069624572485 3.22% 3.22231% -0.000087% -0.00269%
16 1069534293824 3.22% 3.22204% 0.000185% 0.00575%
17 1069604431333 3.22% 3.22225% -0.000026% -0.00081%
18 1069575419634 3.22% 3.22216% 0.000061% 0.00190%
19 1069607036429 3.22% 3.22226% -0.000034% -0.00105%
20 1069614410279 3.22% 3.22228% -0.000056% -0.00174%
21 1069673218584 3.22% 3.22246% -0.000233% -0.00724%
22 1069588850540 3.22% 3.22220% 0.000021% 0.00065%
23 1069628448187 3.22% 3.22232% -0.000098% -0.00305%
24 1069587192674 3.22% 3.22220% 0.000026% 0.00080%
25 1069631968363 3.22% 3.22233% -0.000109% -0.00338%
26 1069643052378 3.22% 3.22236% -0.000142% -0.00442%
27 1069545844093 3.22% 3.22207% 0.000150% 0.00467%
28 1069638675965 3.22% 3.22235% -0.000129% -0.00401%
29 1069586906336 3.22% 3.22220% 0.000027% 0.00083%
30 1069573638219 3.22% 3.22216% 0.000067% 0.00207%
合计 33194352194116 100.00% 100.00000% 0.000000% 0.00000%

独舟星海 · 发表于 2021-10-15 20:08

素数31 统计2+25 理论占比实际占比占比绝对误差相对误差
0 1106477984614 3.33% 3.33333% 0.000001% 0.00004%
1 1069560619484 3.22% 3.22212% 0.000106% 0.00329%
2 1069637931246 3.22% 3.22235% -0.000127% -0.00394%
3 1069612873766 3.22% 3.22227% -0.000051% -0.00160%
4 1069625037800 3.22% 3.22231% -0.000088% -0.00273%
5 1069605546249 3.22% 3.22225% -0.000029% -0.00091%
6 1069572575482 3.22% 3.22215% 0.000070% 0.00217%
7 1069604668063 3.22% 3.22225% -0.000027% -0.00083%
8 1069545522307 3.22% 3.22207% 0.000151% 0.00470%
9 1069655427270 3.22% 3.22240% -0.000180% -0.00558%
10 1069614503340 3.22% 3.22228% -0.000056% -0.00175%
11 1069593483127 3.22% 3.22222% 0.000007% 0.00022%
12 1069555581413 3.22% 3.22210% 0.000121% 0.00376%
13 1069594095134 3.22% 3.22222% 0.000005% 0.00016%
14 1069535457099 3.22% 3.22204% 0.000182% 0.00564%
15 1069612055114 3.22% 3.22227% -0.000049% -0.00152%
16 1069576524530 3.22% 3.22216% 0.000058% 0.00180%
17 1069603962411 3.22% 3.22225% -0.000025% -0.00076%
18 1069603261427 3.22% 3.22224% -0.000022% -0.00070%
19 1069607531469 3.22% 3.22226% -0.000035% -0.00110%
20 1069580301284 3.22% 3.22218% 0.000047% 0.00145%
21 1069613164798 3.22% 3.22227% -0.000052% -0.00162%
22 1069569137004 3.22% 3.22214% 0.000080% 0.00249%
23 1069615529589 3.22% 3.22228% -0.000059% -0.00185%
24 1069577538949 3.22% 3.22217% 0.000055% 0.00171%
25 1069647130485 3.22% 3.22238% -0.000155% -0.00480%
26 1069603579040 3.22% 3.22225% -0.000023% -0.00073%
27 1069520121252 3.22% 3.22199% 0.000228% 0.00707%
28 1069609611332 3.22% 3.22226% -0.000042% -0.00129%
29 1069577894642 3.22% 3.22217% 0.000054% 0.00167%
30 1069643544396 3.22% 3.22237% -0.000144% -0.00446%
合计 33194352194116 100.00% 100.00000% 0.000000% 0.00000%

独舟星海 · 发表于 2021-10-15 20:09

素数31 统计2+26 理论占比实际占比占比绝对误差相对误差
0 1106477992335 3.33% 3.33333% 0.000001% 0.00004%
1 1069570278073 3.22% 3.22215% 0.000077% 0.00239%
2 1069587192674 3.22% 3.22220% 0.000026% 0.00080%
3 1069611328237 3.22% 3.22227% -0.000047% -0.00145%
4 1069604431333 3.22% 3.22225% -0.000026% -0.00081%
5 1069586906336 3.22% 3.22220% 0.000027% 0.00083%
6 1069568096063 3.22% 3.22214% 0.000083% 0.00259%
7 1069588850540 3.22% 3.22220% 0.000021% 0.00065%
8 1069584749081 3.22% 3.22219% 0.000033% 0.00103%
9 1069624572485 3.22% 3.22231% -0.000087% -0.00269%
10 1069545844093 3.22% 3.22207% 0.000150% 0.00467%
11 1069563441798 3.22% 3.22212% 0.000097% 0.00302%
12 1069614410279 3.22% 3.22228% -0.000056% -0.00174%
13 1069586592677 3.22% 3.22219% 0.000028% 0.00086%
14 1069567342708 3.22% 3.22214% 0.000086% 0.00266%
15 1069631968363 3.22% 3.22233% -0.000109% -0.00338%
16 1069562040366 3.22% 3.22212% 0.000102% 0.00316%
17 1069575419634 3.22% 3.22216% 0.000061% 0.00190%
18 1069573638219 3.22% 3.22216% 0.000067% 0.00207%
19 1069596567552 3.22% 3.22222% -0.000002% -0.00007%
20 1069628448187 3.22% 3.22232% -0.000098% -0.00305%
21 1069643800376 3.22% 3.22237% -0.000145% -0.00449%
22 1069534293824 3.22% 3.22204% 0.000185% 0.00575%
23 1069638675965 3.22% 3.22235% -0.000129% -0.00401%
24 1069594439382 3.22% 3.22222% 0.000004% 0.00013%
25 1069673218584 3.22% 3.22246% -0.000233% -0.00724%
26 1069627214282 3.22% 3.22232% -0.000095% -0.00294%
27 1069521289363 3.22% 3.22200% 0.000224% 0.00697%
28 1069643052378 3.22% 3.22236% -0.000142% -0.00442%
29 1069619062500 3.22% 3.22229% -0.000070% -0.00218%
30 1069607036429 3.22% 3.22226% -0.000034% -0.00105%
合计 33194352194116 100.00% 100.00000% 0.000000% 0.00000%

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