[原创]k生素数群的数量公式

独木星空谁 · 发表于 2021-11-10 07:52

数据分析素数53 素数53 素数53 素数53 素数53
素数53 统计4+10 理论占比实际占比占比绝对误差相对误差
0 638352709569 1.923077% 1.92308% 0.000001% 0.00003%
1 626081662701 1.886095% 1.88611% -0.000014% -0.00076%
2 626074949268 1.886095% 1.88609% 0.000006% 0.00031%
3 626059213989 1.886095% 1.88604% 0.000053% 0.00283%
4 626082966469 1.886095% 1.88611% -0.000018% -0.00097%
5 626089620566 1.886095% 1.88613% -0.000038% -0.00203%
6 626059710944 1.886095% 1.88604% 0.000052% 0.00275%
7 626085297799 1.886095% 1.88612% -0.000025% -0.00134%
8 626078816920 1.886095% 1.88610% -0.000006% -0.00030%
9 626063143316 1.886095% 1.88605% 0.000041% 0.00220%
10 626073528687 1.886095% 1.88608% 0.000010% 0.00054%
11 626058138741 1.886095% 1.88604% 0.000057% 0.00300%
12 626046767392 1.886095% 1.88600% 0.000091% 0.00481%
13 626060236113 1.886095% 1.88604% 0.000050% 0.00266%
14 626112106388 1.886095% 1.88620% -0.000106% -0.00562%
15 626049496221 1.886095% 1.88601% 0.000083% 0.00438%
16 626056099682 1.886095% 1.88603% 0.000063% 0.00332%
17 626042471779 1.886095% 1.88599% 0.000104% 0.00550%
18 626071408321 1.886095% 1.88608% 0.000017% 0.00088%
19 626094229879 1.886095% 1.88615% -0.000052% -0.00277%
20 626074150910 1.886095% 1.88609% 0.000008% 0.00044%
21 626089797298 1.886095% 1.88613% -0.000039% -0.00206%
22 626066725742 1.886095% 1.88606% 0.000031% 0.00163%
23 626105129084 1.886095% 1.88618% -0.000085% -0.00451%
24 626095136309 1.886095% 1.88615% -0.000055% -0.00291%
25 626088913045 1.886095% 1.88613% -0.000036% -0.00192%
26 626070303933 1.886095% 1.88607% 0.000020% 0.00105%
27 626055338429 1.886095% 1.88603% 0.000065% 0.00345%
28 626068299552 1.886095% 1.88607% 0.000026% 0.00138%
29 626073580698 1.886095% 1.88608% 0.000010% 0.00053%
30 626053537810 1.886095% 1.88602% 0.000070% 0.00373%
31 626066096297 1.886095% 1.88606% 0.000033% 0.00173%
32 626093339609 1.886095% 1.88614% -0.000049% -0.00262%
33 626070760498 1.886095% 1.88608% 0.000019% 0.00098%
34 626078439561 1.886095% 1.88610% -0.000005% -0.00024%
35 626113439606 1.886095% 1.88620% -0.000110% -0.00583%
36 626103375354 1.886095% 1.88617% -0.000080% -0.00423%
37 626080393922 1.886095% 1.88611% -0.000010% -0.00056%
38 626078880430 1.886095% 1.88610% -0.000006% -0.00031%
39 626086069879 1.886095% 1.88612% -0.000028% -0.00146%
40 626101265364 1.886095% 1.88617% -0.000073% -0.00389%
41 626070021060 1.886095% 1.88607% 0.000021% 0.00110%
42 626083296137 1.886095% 1.88611% -0.000019% -0.00102%
43 626066120198 1.886095% 1.88606% 0.000033% 0.00172%
44 626084699789 1.886095% 1.88612% -0.000023% -0.00124%
45 626070078552 1.886095% 1.88607% 0.000021% 0.00109%
46 626049970946 1.886095% 1.88601% 0.000081% 0.00430%
47 626081541911 1.886095% 1.88611% -0.000014% -0.00074%
48 626108980494 1.886095% 1.88619% -0.000097% -0.00512%
49 626078240715 1.886095% 1.88610% -0.000004% -0.00021%
50 626096955571 1.886095% 1.88616% -0.000060% -0.00320%
51 626072460534 1.886095% 1.88608% 0.000013% 0.00071%
52 626084280135 1.886095% 1.88612% -0.000022% -0.00118%
合计 33194352194116 100.000000% 100.00000% 0.000000% 0.00000%

独木星空谁 · 发表于 2021-11-10 07:52

数据分析素数53 素数53 素数53 素数53 素数53
素数53 统计4+11 理论占比实际占比占比绝对误差相对误差
0 638352742800 1.923077% 1.92308% 0.000001% 0.00003%
1 626072337453 1.886095% 1.88608% 0.000014% 0.00073%
2 626098648665 1.886095% 1.88616% -0.000065% -0.00347%
3 626066232378 1.886095% 1.88606% 0.000032% 0.00171%
4 626095433468 1.886095% 1.88615% -0.000056% -0.00296%
5 626088089704 1.886095% 1.88613% -0.000034% -0.00179%
6 626075920643 1.886095% 1.88609% 0.000003% 0.00016%
7 626051984475 1.886095% 1.88602% 0.000075% 0.00398%
8 626032315333 1.886095% 1.88596% 0.000134% 0.00712%
9 626080326891 1.886095% 1.88610% -0.000010% -0.00055%
10 626059457102 1.886095% 1.88604% 0.000053% 0.00279%
11 626083249002 1.886095% 1.88611% -0.000019% -0.00101%
12 626072026276 1.886095% 1.88608% 0.000015% 0.00078%
13 626069160153 1.886095% 1.88607% 0.000023% 0.00124%
14 626104779505 1.886095% 1.88618% -0.000084% -0.00445%
15 626058183795 1.886095% 1.88604% 0.000056% 0.00299%
16 626087457611 1.886095% 1.88613% -0.000032% -0.00168%
17 626050558100 1.886095% 1.88602% 0.000079% 0.00421%
18 626069250492 1.886095% 1.88607% 0.000023% 0.00122%
19 626069779216 1.886095% 1.88607% 0.000021% 0.00114%
20 626112129166 1.886095% 1.88620% -0.000106% -0.00563%
21 626092331044 1.886095% 1.88614% -0.000046% -0.00246%
22 626050758712 1.886095% 1.88602% 0.000079% 0.00418%
23 626075520941 1.886095% 1.88609% 0.000004% 0.00022%
24 626075974602 1.886095% 1.88609% 0.000003% 0.00015%
25 626108546743 1.886095% 1.88619% -0.000095% -0.00505%
26 626086951689 1.886095% 1.88612% -0.000030% -0.00160%
27 626055420464 1.886095% 1.88603% 0.000065% 0.00343%
28 626050054117 1.886095% 1.88601% 0.000081% 0.00429%
29 626090318954 1.886095% 1.88614% -0.000040% -0.00214%
30 626094807917 1.886095% 1.88615% -0.000054% -0.00286%
31 626060606219 1.886095% 1.88605% 0.000049% 0.00260%
32 626089357241 1.886095% 1.88613% -0.000038% -0.00199%
33 626046054305 1.886095% 1.88600% 0.000093% 0.00493%
34 626078969912 1.886095% 1.88610% -0.000006% -0.00033%
35 626101843987 1.886095% 1.88617% -0.000075% -0.00398%
36 626078541704 1.886095% 1.88610% -0.000005% -0.00026%
37 626086278238 1.886095% 1.88612% -0.000028% -0.00150%
38 626098064224 1.886095% 1.88616% -0.000064% -0.00338%
39 626091946114 1.886095% 1.88614% -0.000045% -0.00240%
40 626087706728 1.886095% 1.88613% -0.000033% -0.00172%
41 626101059620 1.886095% 1.88617% -0.000073% -0.00386%
42 626062979186 1.886095% 1.88605% 0.000042% 0.00222%
43 626067448100 1.886095% 1.88607% 0.000029% 0.00151%
44 626088839367 1.886095% 1.88613% -0.000036% -0.00191%
45 626071269884 1.886095% 1.88608% 0.000017% 0.00090%
46 626063144177 1.886095% 1.88605% 0.000041% 0.00220%
47 626043550348 1.886095% 1.88599% 0.000100% 0.00533%
48 626085484390 1.886095% 1.88612% -0.000026% -0.00137%
49 626058200119 1.886095% 1.88604% 0.000056% 0.00299%
50 626090400468 1.886095% 1.88614% -0.000041% -0.00215%
51 626082487738 1.886095% 1.88611% -0.000017% -0.00089%
52 626087214636 1.886095% 1.88613% -0.000031% -0.00165%
合计 33194352194116 100.000000% 100.00000% 0.000000% 0.00000%

独木星空谁 · 发表于 2021-11-10 12:34

组合159 1 2 3 4 6 8 10 15 mod(n,15)
mod(n,15) at b 100周 101周 102周 103周 104周 105周
1→→→ 5 -5 495 500 505 510 515 520
2→→→ 3 -2 298 301 304 307 310 313
3→→→ 6 -4 596 602 608 614 620 626
4→→→ 5 -2 498 503 508 513 518 523
5→→→ 5 -1 499 504 509 514 519 524
6→→→ 5 -2 498 503 508 513 518 523
7→→→ 4 0 400 404 408 412 416 420
8→→→ 5 -2 498 503 508 513 518 523
9→→→ 4 0 400 404 408 412 416 420
10→→→ 6 -2 598 604 610 616 622 628
11→→→ 4 0 400 404 408 412 416 420
12→→→ 5 0 500 505 510 515 520 525
13→→→ 2 0 200 202 204 206 208 210
14→→→ 4 0 400 404 408 412 416 420
15→→0 1 -1 99 100 101 102 103 104
一周汇总 64 -21 6379 6443 6507 6571 6635 6699

x+y=N 正整数解组数系数及 a,b值

独木星空谁 · 发表于 2021-11-10 12:35

mod(n,15) 2at^2 2bt c 10周 11周 12周 13周 14周
1→→→ 33 -57 12 1377 1695 2046 2430 2847
2→→→ 27 -33 3 1188 1455 1749 2070 2418
3→→→ 35 -51 9 1504 1846 2223 2635 3082
4→→→ 30 -30 3 1353 1653 1983 2343 2733
5→→→ 39 -33 3 1788 2181 2613 3084 3594
6→→→ 31 -17 3 1468 1785 2133 2512 2922
7→→→ 39 -15 0 1875 2277 2718 3198 3717
8→→→ 30 -6 3 1473 1785 2127 2499 2901
9→→→ 38 -6 0 1870 2266 2700 3172 3682
10→→→ 33 -3 3 1638 1983 2361 2772 3216
11→→→ 39 3 0 1965 2376 2826 3315 3843
12→→→ 37 7 0 1885 2277 2706 3172 3675
13→→→ 36 18 0 1890 2277 2700 3159 3654
14→→→ 36 12 0 1860 2244 2664 3120 3612
15→→0同 29 23 1 1566 1882 2227 2601 3004
一周汇总 512 -188 40 24700 29982 35776 42082 48900
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 2021-11-10 12:35

mod(n,15) 6at^3 6bt^2 6ct d 5周 6周 7周
1→→→ 265 -432 299 -22 3948 7225 11948
2→→→ 277 -399 146 -4 4226 7720 12743
3→→→ 260 -372 208 -16 4024 7320 12052
4→→→ 267 -315 78 -4 4311 7796 12778
5→→→ 270 -312 102 -6 4404 7944 13000
6→→→ 266 -186 4 -4 4766 8460 13688
7→→→ 280 -192 32 0 5060 8960 14476
8→→→ 261 -33 -18 -4 5281 9176 14626
9→→→ 281 -60 43 0 5640 9799 15624
10→→→ 257 69 34 -4 5666 9696 15291
11→→→ 286 60 62 0 6260 10718 16912
12→→→ 265 159 74 0 6245 10568 16534
13→→→ 296 216 64 0 7120 12016 18760
14→→→ 272 276 148 0 6940 11596 17976
15→→0同 293 366 115 -1 7724 12858 19872
一周汇总 4096 -1155 1391 -65 81615 141852 226280
x+y+z+u=N 正整数解组数及a,b c,d 的值

独木星空谁 · 发表于 2021-11-10 12:36

mod(n,15) 24at^4 24bt^3 24ct^2 24dt 6e 6周 7周
1→→→ 2175 -3770 2745 -1990 210 87175 168770
2→→→ 2250 -3660 2670 -1380 30 92225 177840
3→→→ 2150 -2620 1570 -1700 150 94475 180380
4→→→ 2225 -2490 1315 -1170 30 99425 189355
5→→→ 2133 -1758 891 -1482 60 100336 189661
6→→→ 2215 -1390 65 -890 30 106980 201605
7→→→ 2145 -810 315 -1290 0 108690 203280
8→→→ 2210 -120 -650 -720 30 117110 217845
9→→→ 2155 350 305 -1250 0 119665 220850
10→→→ 2182 1164 -190 -732 30 127841 234330
11→→→ 2160 1480 900 -820 0 131105 238840
12→→→ 2160 2320 960 -400 0 138860 251090
13→→→ 2195 2630 1705 70 0 144775 260680
14→→→ 2170 3580 2450 80 0 153095 273280
15→→0同 2243 3998 3085 994 6 161981 288121
一周汇总 32768 -1096 18136 -12680 576 1783738 3295927
x+y+z+u+v=N 的正整数解组数，及系数 a,b,c,d,e 的值

独木星空谁 · 发表于 2021-11-10 12:36

mod(n,15) 120at^5 120bt^4 120ct^3 120dt^2 120et 6f 10周
1→→→ 17550 -33360 25170 -23880 20640 -306 12036519
2→→→ 17493 -28110 24435 -30930 17832 -36 12414330
3→→→ 17540 -20610 10920 -18030 14500 -216 12976314
4→→→ 17553 -16110 13035 -24030 10272 -36 13374450
5→→→ 17445 -8655 5145 -20505 8370 -90 13842720
6→→→ 17571 -4900 6505 -18980 644 -36 14272606
7→→→ 17373 2385 3345 -23625 1242 0 14684541
8→→→ 17616 6300 3480 -16380 -7776 -36 15219696
9→→→ 17353 13585 5745 -25825 -4138 0 15618926
10→→→ 17625 18240 7695 -16980 -11460 -36 16256514
11→→→ 17310 24870 16050 -22350 -9240 0 16611855
12→→→ 17557 30160 20755 -12700 -11852 0 17305554
13→→→ 17280 35670 33300 -7950 -12060 0 17642370
14→→→ 17517 41910 40155 1650 -6912 0 18425424
15→→0同 17361 46925 56105 15595 -7946 -6 18857791
一周汇总 262144 108300 271840 -244920 2116 -798 229539610
x+y+z+u+v+w=N 的正整数解组数，及系数 a,b,c,d,e,f 的值

独木星空谁 · 发表于 2021-11-10 14:59

组合160 1 2 3 4 6 8 11 12 mod(n,15)
mod(n,15) at b 100周 101周 102周 103周 104周 105周
1→→→ 3 -3 297 300 303 306 309 312
2→→→ 3 -2 298 301 304 307 310 313
3→→→ 4 -2 398 402 406 410 414 418
4→→→ 5 -2 498 503 508 513 518 523
5→→→ 6 -2 598 604 610 616 622 628
6→→→ 3 0 300 303 306 309 312 315
7→→→ 5 -1 499 504 509 514 519 524
8→→→ 5 -2 498 503 508 513 518 523
9→→→ 5 -1 499 504 509 514 519 524
10→→→ 4 0 400 404 408 412 416 420
11→→→ 2 0 200 202 204 206 208 210
12→→→ 5 0 500 505 510 515 520 525
13→→→ 4 0 400 404 408 412 416 420
14→→→ 6 0 600 606 612 618 624 630
15→→0 4 0 400 404 408 412 416 420
一周汇总 64 -15 6385 6449 6513 6577 6641 6705

x+y=N 正整数解组数系数及 a,b值

独木星空谁 · 发表于 2021-11-10 15:00

mod(n,15) 2at^2 2bt c 10周 11周 12周 13周 14周
1→→→ 39 -51 6 1701 2085 2508 2970 3471
2→→→ 33 -39 3 1458 1785 2145 2538 2964
3→→→ 33 -33 1 1486 1816 2179 2575 3004
4→→→ 30 -30 3 1353 1653 1983 2343 2733
5→→→ 36 -30 3 1653 2016 2415 2850 3321
6→→→ 35 -17 1 1666 2025 2419 2848 3312
7→→→ 33 -9 0 1605 1947 2322 2730 3171
8→→→ 33 -3 0 1635 1980 2358 2769 3213
9→→→ 35 -3 0 1735 2101 2502 2938 3409
10→→→ 36 0 0 1800 2178 2592 3042 3528
11→→→ 39 3 0 1965 2376 2826 3315 3843
12→→→ 31 7 0 1585 1914 2274 2665 3087
13→→→ 33 15 0 1725 2079 2466 2886 3339
14→→→ 30 18 0 1590 1914 2268 2652 3066
15→→0同 36 24 0 1920 2310 2736 3198 3696
一周汇总 512 -148 17 24877 30179 35993 42319 49157
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 2021-11-10 15:00

mod(n,15) 6at^3 6bt^2 6ct d 5周 6周 7周
1→→→ 265 -396 167 -6 4004 7325 12104
2→→→ 283 -369 110 -4 4446 8080 13289
3→→→ 273 -294 27 -1 4484 8090 13236
4→→→ 279 -243 -30 0 4775 8556 13930
5→→→ 264 -192 -48 0 4660 8304 13468
6→→→ 272 -156 -56 0 4970 8800 14210
7→→→ 278 -108 -50 0 5300 9310 14952
8→→→ 273 -45 -42 0 5465 9516 15190
9→→→ 273 36 -45 0 5800 9999 15848
10→→→ 262 102 -28 0 5860 10016 15778
11→→→ 272 156 -20 0 6300 10708 16800
12→→→ 283 201 14 0 6745 11408 17836
13→→→ 282 240 30 0 6900 11622 18116
14→→→ 273 309 66 0 7030 11748 18207
15→→0同 264 348 108 0 7040 11700 18060
一周汇总 4096 -411 203 -11 83779 145182 231024
x+y+z+u=N 正整数解组数及a,b c,d 的值

		自动登录	找回密码
密码			注册

[原创]k生素数群的数量公式

评分

点评

评分

评分