证明\(P_i+2P_j\)=2N+1(N≥4）在素数集内有解

独舟星海 · 发表于 2021-10-15 20:09

素数31 统计2+27 理论占比实际占比占比绝对误差相对误差
0 1106478005014 3.33% 3.33333% 0.000001% 0.00004%
1 1069578743357 3.22% 3.22217% 0.000051% 0.00159%
2 1069617280613 3.22% 3.22229% -0.000065% -0.00201%
3 1069570214400 3.22% 3.22215% 0.000077% 0.00239%
4 1069588823926 3.22% 3.22220% 0.000021% 0.00065%
5 1069608389268 3.22% 3.22226% -0.000038% -0.00118%
6 1069617120146 3.22% 3.22229% -0.000064% -0.00199%
7 1069624206594 3.22% 3.22231% -0.000086% -0.00266%
8 1069535724127 3.22% 3.22204% 0.000181% 0.00562%
9 1069614133904 3.22% 3.22228% -0.000055% -0.00171%
10 1069594062697 3.22% 3.22222% 0.000005% 0.00016%
11 1069573520781 3.22% 3.22216% 0.000067% 0.00208%
12 1069623417001 3.22% 3.22231% -0.000083% -0.00258%
13 1069632418341 3.22% 3.22233% -0.000110% -0.00342%
14 1069529445706 3.22% 3.22202% 0.000200% 0.00620%
15 1069574083814 3.22% 3.22216% 0.000065% 0.00203%
16 1069583632558 3.22% 3.22219% 0.000037% 0.00114%
17 1069634691406 3.22% 3.22234% -0.000117% -0.00364%
18 1069529597427 3.22% 3.22202% 0.000199% 0.00619%
19 1069591295816 3.22% 3.22221% 0.000014% 0.00042%
20 1069664067702 3.22% 3.22243% -0.000206% -0.00638%
21 1069641860505 3.22% 3.22236% -0.000139% -0.00431%
22 1069579161502 3.22% 3.22217% 0.000050% 0.00155%
23 1069607988207 3.22% 3.22226% -0.000037% -0.00114%
24 1069576912882 3.22% 3.22217% 0.000057% 0.00177%
25 1069642693586 3.22% 3.22236% -0.000141% -0.00438%
26 1069583543300 3.22% 3.22219% 0.000037% 0.00115%
27 1069579123691 3.22% 3.22217% 0.000050% 0.00156%
28 1069634806966 3.22% 3.22234% -0.000118% -0.00365%
29 1069565073459 3.22% 3.22213% 0.000093% 0.00287%
30 1069578155420 3.22% 3.22217% 0.000053% 0.00165%
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+28 理论占比实际占比占比绝对误差相对误差
0 1106477897881 3.33% 3.33333% 0.000002% 0.00005%
1 1069599433599 3.22% 3.22223% -0.000011% -0.00034%
2 1069639729470 3.22% 3.22235% -0.000132% -0.00411%
3 1069599242129 3.22% 3.22223% -0.000010% -0.00032%
4 1069573888562 3.22% 3.22216% 0.000066% 0.00205%
5 1069631128591 3.22% 3.22233% -0.000106% -0.00330%
6 1069547981768 3.22% 3.22208% 0.000144% 0.00447%
7 1069608604598 3.22% 3.22226% -0.000039% -0.00120%
8 1069572501185 3.22% 3.22215% 0.000070% 0.00218%
9 1069654427113 3.22% 3.22240% -0.000177% -0.00548%
10 1069541474456 3.22% 3.22206% 0.000164% 0.00508%
11 1069602199083 3.22% 3.22224% -0.000019% -0.00060%
12 1069599372911 3.22% 3.22223% -0.000011% -0.00033%
13 1069601435251 3.22% 3.22224% -0.000017% -0.00053%
14 1069536127741 3.22% 3.22204% 0.000180% 0.00558%
15 1069643403986 3.22% 3.22237% -0.000143% -0.00445%
16 1069559960840 3.22% 3.22211% 0.000108% 0.00335%
17 1069604092772 3.22% 3.22225% -0.000025% -0.00078%
18 1069578579816 3.22% 3.22217% 0.000052% 0.00161%
19 1069578903296 3.22% 3.22217% 0.000051% 0.00158%
20 1069653870142 3.22% 3.22240% -0.000175% -0.00543%
21 1069645278987 3.22% 3.22237% -0.000149% -0.00463%
22 1069542620609 3.22% 3.22206% 0.000160% 0.00497%
23 1069617501968 3.22% 3.22229% -0.000065% -0.00203%
24 1069572010787 3.22% 3.22215% 0.000072% 0.00222%
25 1069632272896 3.22% 3.22233% -0.000110% -0.00341%
26 1069581941090 3.22% 3.22218% 0.000042% 0.00130%
27 1069571750947 3.22% 3.22215% 0.000072% 0.00225%
28 1069648241697 3.22% 3.22238% -0.000158% -0.00490%
29 1069544609208 3.22% 3.22207% 0.000154% 0.00479%
30 1069591710737 3.22% 3.22221% 0.000012% 0.00038%
合计 33194352194116 100.00% 100.00000% 0.000000% 0.00000%

独舟星海 · 发表于 2021-10-15 20:10

素数31 统计2+29 理论占比实际占比占比绝对误差相对误差
0 1106478441796 3.33% 3.33333% 0.000000% 0.00000%
1 1069578498405 3.22% 3.22217% 0.000052% 0.00162%
2 1069603728186 3.22% 3.22225% -0.000024% -0.00074%
3 1069643711817 3.22% 3.22237% -0.000144% -0.00448%
4 1069564312019 3.22% 3.22213% 0.000095% 0.00294%
5 1069610618907 3.22% 3.22227% -0.000045% -0.00139%
6 1069615915931 3.22% 3.22228% -0.000061% -0.00188%
7 1069602402207 3.22% 3.22224% -0.000020% -0.00062%
8 1069579770484 3.22% 3.22217% 0.000048% 0.00150%
9 1069580705087 3.22% 3.22218% 0.000045% 0.00141%
10 1069625450374 3.22% 3.22231% -0.000089% -0.00277%
11 1069612143778 3.22% 3.22227% -0.000049% -0.00153%
12 1069598698816 3.22% 3.22223% -0.000009% -0.00027%
13 1069581414766 3.22% 3.22218% 0.000043% 0.00134%
14 1069561408458 3.22% 3.22212% 0.000104% 0.00321%
15 1069578096925 3.22% 3.22217% 0.000053% 0.00165%
16 1069578096925 3.22% 3.22217% 0.000053% 0.00165%
17 1069561408458 3.22% 3.22212% 0.000104% 0.00321%
18 1069581414766 3.22% 3.22218% 0.000043% 0.00134%
19 1069598698816 3.22% 3.22223% -0.000009% -0.00027%
20 1069612143778 3.22% 3.22227% -0.000049% -0.00153%
21 1069625450374 3.22% 3.22231% -0.000089% -0.00277%
22 1069580705087 3.22% 3.22218% 0.000045% 0.00141%
23 1069579770484 3.22% 3.22217% 0.000048% 0.00150%
24 1069602402207 3.22% 3.22224% -0.000020% -0.00062%
25 1069615915931 3.22% 3.22228% -0.000061% -0.00188%
26 1069610618907 3.22% 3.22227% -0.000045% -0.00139%
27 1069564312019 3.22% 3.22213% 0.000095% 0.00294%
28 1069643711817 3.22% 3.22237% -0.000144% -0.00448%
29 1069603728186 3.22% 3.22225% -0.000024% -0.00074%
30 1069578498405 3.22% 3.22217% 0.000052% 0.00162%
合计 33194352194116 100.00% 100.00000% 0.000000% 0.00000%

独舟星海 · 发表于 2021-10-15 20:10

素数31 统计2+30 理论占比实际占比占比绝对误差相对误差
0 1106478005014 3.33% 3.33333% 0.000001% 0.00004%
1 1069565073459 3.22% 3.22213% 0.000093% 0.00287%
2 1069579123691 3.22% 3.22217% 0.000050% 0.00156%
3 1069642693586 3.22% 3.22236% -0.000141% -0.00438%
4 1069607988207 3.22% 3.22226% -0.000037% -0.00114%
5 1069641860505 3.22% 3.22236% -0.000139% -0.00431%
6 1069591295816 3.22% 3.22221% 0.000014% 0.00042%
7 1069634691406 3.22% 3.22234% -0.000117% -0.00364%
8 1069574083814 3.22% 3.22216% 0.000065% 0.00203%
9 1069632418341 3.22% 3.22233% -0.000110% -0.00342%
10 1069573520781 3.22% 3.22216% 0.000067% 0.00208%
11 1069614133904 3.22% 3.22228% -0.000055% -0.00171%
12 1069624206594 3.22% 3.22231% -0.000086% -0.00266%
13 1069608389268 3.22% 3.22226% -0.000038% -0.00118%
14 1069570214400 3.22% 3.22215% 0.000077% 0.00239%
15 1069578743357 3.22% 3.22217% 0.000051% 0.00159%
16 1069578155420 3.22% 3.22217% 0.000053% 0.00165%
17 1069634806966 3.22% 3.22234% -0.000118% -0.00365%
18 1069583543300 3.22% 3.22219% 0.000037% 0.00115%
19 1069576912882 3.22% 3.22217% 0.000057% 0.00177%
20 1069579161502 3.22% 3.22217% 0.000050% 0.00155%
21 1069664067702 3.22% 3.22243% -0.000206% -0.00638%
22 1069529597427 3.22% 3.22202% 0.000199% 0.00619%
23 1069583632558 3.22% 3.22219% 0.000037% 0.00114%
24 1069529445706 3.22% 3.22202% 0.000200% 0.00620%
25 1069623417001 3.22% 3.22231% -0.000083% -0.00258%
26 1069594062697 3.22% 3.22222% 0.000005% 0.00016%
27 1069535724127 3.22% 3.22204% 0.000181% 0.00562%
28 1069617120146 3.22% 3.22229% -0.000064% -0.00199%
29 1069588823926 3.22% 3.22220% 0.000021% 0.00065%
30 1069617280613 3.22% 3.22229% -0.000065% -0.00201%
合计 33194352194116 100.00% 100.00000% 0.000000% 0.00000%

独舟星海 · 发表于 2021-10-15 20:11

素数31 统计2+31 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% #DIV/0!
1 1107086431916 3.33% 3.33517% -0.001832% -0.05495%
2 1105928379662 3.33% 3.33168% 0.001657% 0.04971%
3 1106060893104 3.33% 3.33208% 0.001258% 0.03773%
4 1106372011620 3.33% 3.33301% 0.000321% 0.00962%
5 1106429626160 3.33% 3.33319% 0.000147% 0.00441%
6 1106861735210 3.33% 3.33449% -0.001155% -0.03464%
7 1105467463342 3.33% 3.33029% 0.003046% 0.09137%
8 1107224706812 3.33% 3.33558% -0.002248% -0.06745%
9 1105709444410 3.33% 3.33102% 0.002317% 0.06950%
10 1106925111204 3.33% 3.33468% -0.001346% -0.04037%
11 1106700414498 3.33% 3.33400% -0.000669% -0.02006%
12 1106637038504 3.33% 3.33381% -0.000478% -0.01434%
13 1106147314914 3.33% 3.33234% 0.000997% 0.02992%
14 1107662577316 3.33% 3.33690% -0.003567% -0.10702%
15 1106383534528 3.33% 3.33305% 0.000286% 0.00857%
16 1107103716278 3.33% 3.33522% -0.001884% -0.05651%
17 1106325919988 3.33% 3.33287% 0.000459% 0.01378%
18 1107241991174 3.33% 3.33563% -0.002300% -0.06901%
19 1106233736724 3.33% 3.33260% 0.000737% 0.02211%
20 1105761297496 3.33% 3.33117% 0.002160% 0.06481%
21 1105144821918 3.33% 3.32932% 0.004018% 0.12053%
22 1107697146040 3.33% 3.33700% -0.003672% -0.11015%
23 1106216452362 3.33% 3.33254% 0.000789% 0.02367%
24 1107288082806 3.33% 3.33577% -0.002439% -0.07318%
25 1105490509158 3.33% 3.33036% 0.002976% 0.08928%
26 1106083938920 3.33% 3.33214% 0.001188% 0.03565%
27 1107530063874 3.33% 3.33650% -0.003168% -0.09505%
28 1105455940434 3.33% 3.33025% 0.003080% 0.09241%
29 1106792597762 3.33% 3.33428% -0.000947% -0.02840%
30 1106383534528 3.33% 3.33305% 0.000286% 0.00857%
合计 33194352194116 100.00% 100.00000% 0.000000% 0.00000%

独舟星海 · 发表于 2021-10-15 20:12

素数31 统计3+31 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% #DIV/0!
1 1106700414498 3.33% 3.33400% -0.000669% -0.02006%
2 1107697146040 3.33% 3.33700% -0.003672% -0.11015%
3 1105928379662 3.33% 3.33168% 0.001657% 0.04971%
4 1106147314914 3.33% 3.33234% 0.000997% 0.02992%
5 1107288082806 3.33% 3.33577% -0.002439% -0.07318%
6 1106372011620 3.33% 3.33301% 0.000321% 0.00962%
7 1106383534528 3.33% 3.33305% 0.000286% 0.00857%
8 1106083938920 3.33% 3.33214% 0.001188% 0.03565%
9 1106861735210 3.33% 3.33449% -0.001155% -0.03464%
10 1106325919988 3.33% 3.33287% 0.000459% 0.01378%
11 1105455940434 3.33% 3.33025% 0.003080% 0.09241%
12 1107224706812 3.33% 3.33558% -0.002248% -0.06745%
13 1106233736724 3.33% 3.33260% 0.000737% 0.02211%
14 1106383534528 3.33% 3.33305% 0.000286% 0.00857%
15 1106925111204 3.33% 3.33468% -0.001346% -0.04037%
16 1105144821918 3.33% 3.32932% 0.004018% 0.12053%
17 1107086431916 3.33% 3.33517% -0.001832% -0.05495%
18 1106637038504 3.33% 3.33381% -0.000478% -0.01434%
19 1106216452362 3.33% 3.33254% 0.000789% 0.02367%
20 1106060893104 3.33% 3.33208% 0.001258% 0.03773%
21 1107662577316 3.33% 3.33690% -0.003567% -0.10702%
22 1105490509158 3.33% 3.33036% 0.002976% 0.08928%
23 1106429626160 3.33% 3.33319% 0.000147% 0.00441%
24 1107103716278 3.33% 3.33522% -0.001884% -0.05651%
25 1107530063874 3.33% 3.33650% -0.003168% -0.09505%
26 1105467463342 3.33% 3.33029% 0.003046% 0.09137%
27 1107241991174 3.33% 3.33563% -0.002300% -0.06901%
28 1106792597762 3.33% 3.33428% -0.000947% -0.02840%
29 1105709444410 3.33% 3.33102% 0.002317% 0.06950%
30 1105761297496 3.33% 3.33117% 0.002160% 0.06481%
合计 33194352194116 100.00% 100.00000% 0.000000% 0.00000%

独舟星海 · 发表于 2021-10-15 20:13

素数31 统计3+1 理论占比实际占比占比绝对误差相对误差
0 1106478018862 3.33% 3.33333% 0.000001% 0.00004%
1 1069606790252 3.22% 3.22226% -0.000033% -0.00103%
2 1069558715404 3.22% 3.22211% 0.000112% 0.00347%
3 1069601315957 3.22% 3.22224% -0.000017% -0.00052%
4 1069581947894 3.22% 3.22218% 0.000042% 0.00129%
5 1069554063398 3.22% 3.22210% 0.000126% 0.00390%
6 1069594007874 3.22% 3.22222% 0.000005% 0.00017%
7 1069559398652 3.22% 3.22211% 0.000110% 0.00340%
8 1069588175689 3.22% 3.22220% 0.000023% 0.00071%
9 1069557575629 3.22% 3.22211% 0.000115% 0.00357%
10 1069624743597 3.22% 3.22231% -0.000087% -0.00271%
11 1069589279921 3.22% 3.22220% 0.000020% 0.00061%
12 1069543919165 3.22% 3.22207% 0.000156% 0.00485%
13 1069617182451 3.22% 3.22229% -0.000064% -0.00200%
14 1069633001912 3.22% 3.22233% -0.000112% -0.00348%
15 1069583984042 3.22% 3.22219% 0.000036% 0.00110%
16 1069619912497 3.22% 3.22229% -0.000073% -0.00226%
17 1069589556676 3.22% 3.22220% 0.000019% 0.00058%
18 1069592108703 3.22% 3.22221% 0.000011% 0.00034%
19 1069638181819 3.22% 3.22235% -0.000128% -0.00396%
20 1069635252370 3.22% 3.22234% -0.000119% -0.00369%
21 1069548953545 3.22% 3.22208% 0.000141% 0.00438%
22 1069639649035 3.22% 3.22235% -0.000132% -0.00410%
23 1069600632555 3.22% 3.22224% -0.000015% -0.00045%
24 1069580021154 3.22% 3.22217% 0.000048% 0.00147%
25 1069568917534 3.22% 3.22214% 0.000081% 0.00251%
26 1069673995642 3.22% 3.22246% -0.000236% -0.00731%
27 1069578996581 3.22% 3.22217% 0.000051% 0.00157%
28 1069618221313 3.22% 3.22229% -0.000068% -0.00210%
29 1069586368241 3.22% 3.22219% 0.000028% 0.00088%
30 1069609305752 3.22% 3.22226% -0.000041% -0.00126%
合计 33194352194116 100.00% 100.00000% 0.000000% 0.00000%

独木星空谁 · 发表于 2021-10-16 06:01

素数31 统计3+2 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 2021-10-16 06:02

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

独木星空谁 · 发表于 2021-10-16 06:22

在\(vP_i+uP_j\)=N中，可以不限定V，U为互质数，只要V，U为正整数的任意组合都可以（甚至为不是0的整数即可），N的奇偶性与（v+u）的奇偶性相同。当N≥3倍的（v+u）时一般情况下有素数解，只有个别组合在小范围内有一定量的反例，另外N不含大于2的因子，这里的因子指v中或u中所含的因子。希望找到这个问题的致命问题，而不要停留在少量反例身上，因为那些所谓的反例都不是真正意义上的反例，当把范围值稍微放大，排除了它，就不是反例了，比如\(P_i+2P_j\)=N在100内有几个反例，那么我们可以设定N大于100时命题成立，又或者在1000内有反例，我们可以让命题大于1000时成立，总而言之，小范围内出现的反例是暂时的，不是永久的，总可以避开，如果在一个不太确定的大范围内出现反例，则命题不成立。对于含v或u的因子(大于2）的N来说，一般情况无素数解组，有也是唯一的一组解。

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