[原创]k生素数群的数量公式

独木星空谁 · 发表于 2021-10-24 12:13

素数29 统计12+22 理论占比实际占比占比绝对误差相对误差
0 1185512039071 3.57% 3.57143% 0.000002% 0.00005%
1 1143104452910 3.44% 3.44367% 0.000206% 0.00598%
2 1143189748202 3.44% 3.44393% -0.000051% -0.00148%
3 1143193682015 3.44% 3.44394% -0.000063% -0.00182%
4 1143195021093 3.44% 3.44394% -0.000067% -0.00194%
5 1143194496107 3.44% 3.44394% -0.000065% -0.00189%
6 1143155256996 3.44% 3.44382% 0.000053% 0.00154%
7 1143193428120 3.44% 3.44394% -0.000062% -0.00180%
8 1143243063736 3.44% 3.44409% -0.000212% -0.00614%
9 1143182160159 3.44% 3.44391% -0.000028% -0.00081%
10 1143227804502 3.44% 3.44404% -0.000166% -0.00481%
11 1143153792071 3.44% 3.44382% 0.000057% 0.00167%
12 1143139442063 3.44% 3.44378% 0.000101% 0.00292%
13 1143177315379 3.44% 3.44389% -0.000013% -0.00039%
14 1143181534960 3.44% 3.44390% -0.000026% -0.00076%
15 1143178106086 3.44% 3.44389% -0.000016% -0.00046%
16 1143194168651 3.44% 3.44394% -0.000064% -0.00187%
17 1143146503191 3.44% 3.44380% 0.000079% 0.00230%
18 1143199292907 3.44% 3.44396% -0.000080% -0.00231%
19 1143136903976 3.44% 3.44377% 0.000108% 0.00314%
20 1143194926962 3.44% 3.44394% -0.000067% -0.00193%
21 1143077456426 3.44% 3.44359% 0.000287% 0.00834%
22 1143088415121 3.44% 3.44362% 0.000254% 0.00739%
23 1143182898745 3.44% 3.44391% -0.000030% -0.00088%
24 1143157811280 3.44% 3.44383% 0.000045% 0.00131%
25 1143167311379 3.44% 3.44386% 0.000017% 0.00048%
26 1143158359358 3.44% 3.44383% 0.000044% 0.00127%
27 1143194297812 3.44% 3.44394% -0.000065% -0.00188%
28 1143232504838 3.44% 3.44406% -0.000180% -0.00522%
合计 33194352194116 100.00% 100.00000% 0.000000% 0.00000%

独木星空谁 · 发表于 2021-10-24 12:14

素数29 统计12+23 理论占比实际占比占比绝对误差相对误差
0 1185512156492 3.57% 3.57143% 0.000001% 0.00004%
1 1143164673516 3.44% 3.44385% 0.000025% 0.00071%
2 1143170069021 3.44% 3.44387% 0.000008% 0.00024%
3 1143182211696 3.44% 3.44391% -0.000028% -0.00082%
4 1143137105814 3.44% 3.44377% 0.000108% 0.00313%
5 1143115339942 3.44% 3.44370% 0.000173% 0.00503%
6 1143124483344 3.44% 3.44373% 0.000146% 0.00423%
7 1143204113243 3.44% 3.44397% -0.000094% -0.00274%
8 1143216202098 3.44% 3.44401% -0.000131% -0.00379%
9 1143187194164 3.44% 3.44392% -0.000043% -0.00126%
10 1143228096056 3.44% 3.44404% -0.000166% -0.00483%
11 1143222886382 3.44% 3.44403% -0.000151% -0.00438%
12 1143146022754 3.44% 3.44380% 0.000081% 0.00235%
13 1143197761314 3.44% 3.44395% -0.000075% -0.00218%
14 1143170414295 3.44% 3.44387% 0.000007% 0.00021%
15 1143172985375 3.44% 3.44388% 0.000000% -0.00001%
16 1143181919885 3.44% 3.44390% -0.000027% -0.00079%
17 1143167055359 3.44% 3.44386% 0.000017% 0.00051%
18 1143135442067 3.44% 3.44376% 0.000113% 0.00327%
19 1143134207814 3.44% 3.44376% 0.000116% 0.00338%
20 1143211985229 3.44% 3.44400% -0.000118% -0.00342%
21 1143148205912 3.44% 3.44380% 0.000074% 0.00216%
22 1143123590123 3.44% 3.44373% 0.000148% 0.00431%
23 1143152187302 3.44% 3.44382% 0.000062% 0.00181%
24 1143237649625 3.44% 3.44407% -0.000195% -0.00567%
25 1143187691743 3.44% 3.44392% -0.000045% -0.00130%
26 1143148844614 3.44% 3.44381% 0.000072% 0.00210%
27 1143177461971 3.44% 3.44389% -0.000014% -0.00040%
28 1143194236966 3.44% 3.44394% -0.000064% -0.00187%
合计 33194352194116 100.00% 100.00000% 0.000000% 0.00000%

独木星空谁 · 发表于 2021-10-24 16:27

素数 2 3 5 7
0 0 0 0 0
2 0 2 2 2
剩余余数类 1 1 1 1
剩余余数类 3 3
剩余余数类 4 4
5
6
横竖说明对素数2 对素数3 对素数5
选项 1
选项 7
选项 1 13
选项 1 3 19
选项 2 5 25
可选项 1 1 1
可选项 13
可选项 19
周期210 0 30 60 90 120 150 180
1 1 31 61 91 121 151 181
13 13 43 73 103 133 163 193
19 19 49 79 109 139 169 199
周期210 0 30 60 90 120 150 180
1 1 31 61 0 0 151 181
13 13 43 73 103 0 0 193
19 19 0 0 109 139 169 199
这楼数据，过于重要，不便解释，请见谅！

独木星空谁 · 发表于 2021-10-24 16:28

针对素29 针对素29 针对素29
统计12+24 统计12+25 统计12+26
1185512075528 1185512039071 1185512203452
1143144900368 1143158359358 1143128189603
1143166002069 1143182898745 1143166586949
1143189061149 1143194926962 1143175216421
1143178439998 1143146503191 1143168887822
1143144929808 1143181534960 1143158724449
1143155870127 1143153792071 1143125421075
1143241877432 1143243063736 1143183423130
1143196265912 1143194496107 1143218003947
1143128318916 1143189748202 1143100953336
1143215008462 1143232504838 1143262693895
1143192950017 1143167311379 1143209680989
1143125662735 1143088415121 1143215459867
1143156975831 1143136903976 1143146941056
1143230076226 1143194168651 1143212429058
1143097787493 1143177315379 1143185447047
1143207259021 1143227804502 1143164357175
1143150754274 1143193428120 1143114157503
1143206234129 1143195021093 1143203281316
1143137665623 1143104452910 1143143688928
1143233733024 1143194297812 1143212993186
1143128727316 1143157811280 1143165984939
1143116284539 1143077456426 1143105614468
1143175097126 1143199292907 1143174180539
1143168711493 1143178106086 1143186954098
1143168745781 1143139442063 1143151751836
1143190731649 1143182160159 1143169680223
1143193187883 1143155256996 1143224248422
1143198860187 1143193682015 1143165039387

独木星空谁 · 发表于 2021-10-24 16:29

素数29 统计12+24 理论占比实际占比占比绝对误差相对误差
0 1185512075528 3.57% 3.57143% 0.000002% 0.00004%
1 1143144900368 3.44% 3.44379% 0.000084% 0.00244%
2 1143166002069 3.44% 3.44386% 0.000021% 0.00060%
3 1143189061149 3.44% 3.44393% -0.000049% -0.00142%
4 1143178439998 3.44% 3.44389% -0.000017% -0.00049%
5 1143144929808 3.44% 3.44379% 0.000084% 0.00244%
6 1143155870127 3.44% 3.44383% 0.000051% 0.00148%
7 1143241877432 3.44% 3.44409% -0.000208% -0.00604%
8 1143196265912 3.44% 3.44395% -0.000071% -0.00205%
9 1143128318916 3.44% 3.44374% 0.000134% 0.00389%
10 1143215008462 3.44% 3.44400% -0.000127% -0.00369%
11 1143192950017 3.44% 3.44394% -0.000061% -0.00176%
12 1143125662735 3.44% 3.44374% 0.000142% 0.00413%
13 1143156975831 3.44% 3.44383% 0.000048% 0.00139%
14 1143230076226 3.44% 3.44405% -0.000172% -0.00501%
15 1143097787493 3.44% 3.44365% 0.000226% 0.00657%
16 1143207259021 3.44% 3.44398% -0.000104% -0.00301%
17 1143150754274 3.44% 3.44381% 0.000067% 0.00193%
18 1143206234129 3.44% 3.44398% -0.000101% -0.00292%
19 1143137665623 3.44% 3.44377% 0.000106% 0.00308%
20 1143233733024 3.44% 3.44406% -0.000183% -0.00533%
21 1143128727316 3.44% 3.44374% 0.000133% 0.00386%
22 1143116284539 3.44% 3.44371% 0.000170% 0.00495%
23 1143175097126 3.44% 3.44388% -0.000007% -0.00020%
24 1143168711493 3.44% 3.44387% 0.000012% 0.00036%
25 1143168745781 3.44% 3.44387% 0.000012% 0.00036%
26 1143190731649 3.44% 3.44393% -0.000054% -0.00156%
27 1143193187883 3.44% 3.44394% -0.000061% -0.00178%
28 1143198860187 3.44% 3.44396% -0.000078% -0.00228%
合计 33194352194116 100.00% 100.00000% 0.000000% 0.00000%

独木星空谁 · 发表于 2021-10-24 16:29

素数29 统计12+25 理论占比实际占比占比绝对误差相对误差
0 1185512039071 3.57% 3.57143% 0.000002% 0.00005%
1 1143158359358 3.44% 3.44383% 0.000044% 0.00127%
2 1143182898745 3.44% 3.44391% -0.000030% -0.00088%
3 1143194926962 3.44% 3.44394% -0.000067% -0.00193%
4 1143146503191 3.44% 3.44380% 0.000079% 0.00230%
5 1143181534960 3.44% 3.44390% -0.000026% -0.00076%
6 1143153792071 3.44% 3.44382% 0.000057% 0.00167%
7 1143243063736 3.44% 3.44409% -0.000212% -0.00614%
8 1143194496107 3.44% 3.44394% -0.000065% -0.00189%
9 1143189748202 3.44% 3.44393% -0.000051% -0.00148%
10 1143232504838 3.44% 3.44406% -0.000180% -0.00522%
11 1143167311379 3.44% 3.44386% 0.000017% 0.00048%
12 1143088415121 3.44% 3.44362% 0.000254% 0.00739%
13 1143136903976 3.44% 3.44377% 0.000108% 0.00314%
14 1143194168651 3.44% 3.44394% -0.000064% -0.00187%
15 1143177315379 3.44% 3.44389% -0.000013% -0.00039%
16 1143227804502 3.44% 3.44404% -0.000166% -0.00481%
17 1143193428120 3.44% 3.44394% -0.000062% -0.00180%
18 1143195021093 3.44% 3.44394% -0.000067% -0.00194%
19 1143104452910 3.44% 3.44367% 0.000206% 0.00598%
20 1143194297812 3.44% 3.44394% -0.000065% -0.00188%
21 1143157811280 3.44% 3.44383% 0.000045% 0.00131%
22 1143077456426 3.44% 3.44359% 0.000287% 0.00834%
23 1143199292907 3.44% 3.44396% -0.000080% -0.00231%
24 1143178106086 3.44% 3.44389% -0.000016% -0.00046%
25 1143139442063 3.44% 3.44378% 0.000101% 0.00292%
26 1143182160159 3.44% 3.44391% -0.000028% -0.00081%
27 1143155256996 3.44% 3.44382% 0.000053% 0.00154%
28 1143193682015 3.44% 3.44394% -0.000063% -0.00182%
合计 33194352194116 100.00% 100.00000% 0.000000% 0.00000%

独木星空谁 · 发表于 2021-10-24 16:29

素数29 统计12+26 理论占比实际占比占比绝对误差相对误差
0 1185512203452 3.57% 3.57143% 0.000001% 0.00003%
1 1143128189603 3.44% 3.44374% 0.000135% 0.00391%
2 1143166586949 3.44% 3.44386% 0.000019% 0.00055%
3 1143175216421 3.44% 3.44388% -0.000007% -0.00021%
4 1143168887822 3.44% 3.44387% 0.000012% 0.00035%
5 1143158724449 3.44% 3.44384% 0.000043% 0.00124%
6 1143125421075 3.44% 3.44373% 0.000143% 0.00415%
7 1143183423130 3.44% 3.44391% -0.000032% -0.00093%
8 1143218003947 3.44% 3.44401% -0.000136% -0.00395%
9 1143100953336 3.44% 3.44366% 0.000217% 0.00629%
10 1143262693895 3.44% 3.44415% -0.000271% -0.00786%
11 1143209680989 3.44% 3.44399% -0.000111% -0.00322%
12 1143215459867 3.44% 3.44401% -0.000128% -0.00373%
13 1143146941056 3.44% 3.44380% 0.000078% 0.00227%
14 1143212429058 3.44% 3.44400% -0.000119% -0.00346%
15 1143185447047 3.44% 3.44392% -0.000038% -0.00110%
16 1143164357175 3.44% 3.44385% 0.000026% 0.00074%
17 1143114157503 3.44% 3.44370% 0.000177% 0.00513%
18 1143203281316 3.44% 3.44397% -0.000092% -0.00266%
19 1143143688928 3.44% 3.44379% 0.000088% 0.00255%
20 1143212993186 3.44% 3.44400% -0.000121% -0.00351%
21 1143165984939 3.44% 3.44386% 0.000021% 0.00060%
22 1143105614468 3.44% 3.44368% 0.000203% 0.00588%
23 1143174180539 3.44% 3.44388% -0.000004% -0.00012%
24 1143186954098 3.44% 3.44392% -0.000043% -0.00123%
25 1143151751836 3.44% 3.44381% 0.000064% 0.00185%
26 1143169680223 3.44% 3.44387% 0.000010% 0.00028%
27 1143224248422 3.44% 3.44403% -0.000155% -0.00450%
28 1143165039387 3.44% 3.44385% 0.000024% 0.00068%
合计 33194352194116 100.00% 100.00000% 0.000000% 0.00000%

独木星空谁 · 发表于 2021-10-24 16:48

组合107 1 2 3 4 5 10 12 15 mod(n,15)
mod(n,15) at b 100周 101周 102周 103周 104周 105周
1→→→ 4 -4 396 400 404 408 412 416
2→→→ 5 -4 496 501 506 511 516 521
3→→→ 4 -2 398 402 406 410 414 418
4→→→ 5 -2 498 503 508 513 518 523
5→→→ 7 -3 697 704 711 718 725 732
6→→→ 5 0 500 505 510 515 520 525
7→→→ 6 -2 598 604 610 616 622 628
8→→→ 3 0 300 303 306 309 312 315
9→→→ 3 -1 299 302 305 308 311 314
10→→→ 3 -2 298 301 304 307 310 313
11→→→ 2 0 200 202 204 206 208 210
12→→→ 4 -2 398 402 406 410 414 418
13→→→ 4 0 400 404 408 412 416 420
14→→→ 4 0 400 404 408 412 416 420
15→→0 5 -1 499 504 509 514 519 524
一周汇总 64 -23 6377 6441 6505 6569 6633 6697

x+y=N 正整数解组数系数及 a,b值

独木星空谁 · 发表于 2021-10-24 16:49

mod(n,15) 2at^2 2bt c 10周 11周 12周 13周 14周
1→→→ 33 -51 9 1404 1725 2079 2466 2886
2→→→ 39 -63 12 1647 2025 2442 2898 3393
3→→→ 34 -38 3 1513 1851 2223 2629 3069
4→→→ 36 -42 6 1596 1953 2346 2775 3240
5→→→ 36 -36 6 1626 1986 2382 2814 3282
6→→→ 35 -17 1 1666 2025 2419 2848 3312
7→→→ 39 -21 6 1851 2250 2688 3165 3681
8→→→ 36 0 0 1800 2178 2592 3042 3528
9→→→ 37 -5 3 1828 2214 2637 3097 3594
10→→→ 36 -6 3 1773 2148 2559 3006 3489
11→→→ 30 0 0 1500 1815 2160 2535 2940
12→→→ 31 -11 3 1498 1818 2169 2551 2964
13→→→ 27 -3 0 1335 1617 1926 2262 2625
14→→→ 30 0 0 1500 1815 2160 2535 2940
15→→0同 33 3 1 1666 2014 2395 2809 3256
一周汇总 512 -290 53 24203 29434 35177 41432 48199
x+y+z=N 正整数解组数及系数 a,b,c 的值

独木星空谁 · 发表于 2021-10-24 16:49

mod(n,15) 6at^3 6bt^2 6ct d 5周 6周 7周
1→→→ 255 -564 429 -20 3300 6205 10452
2→→→ 268 -576 476 -28 3552 6640 11144
3→→→ 267 -438 201 -5 3900 7180 11916
4→→→ 281 -429 250 -16 4259 7776 12836
5→→→ 283 -348 149 -10 4560 8239 13500
6→→→ 280 -264 68 -4 4786 8560 13926
7→→→ 286 -240 146 -12 5068 8990 14548
8→→→ 273 -105 42 0 5285 9240 14798
9→→→ 280 -72 140 -6 5644 9782 15576
10→→→ 279 3 150 -4 5946 10208 16145
11→→→ 276 84 120 0 6200 10560 16604
12→→→ 281 75 178 -4 6311 10740 16880
13→→→ 264 144 96 0 6180 10464 16380
14→→→ 266 114 100 0 6100 10360 16254
15→→0同 257 150 79 -1 6044 10230 16008
一周汇总 4096 -2466 2624 -110 77135 135174 216967
x+y+z+u=N 正整数解组数及a,b c,d 的值

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[原创]k生素数群的数量公式

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