[原创]k生素数群的数量公式

独木星空谁 · 发表于 2021-11-7 12:10

数据分析素数53 素数53 素数53 素数53 素数53
素数53 统计3+45 理论占比实际占比占比绝对误差相对误差
0 638352625268 1.923077% 1.92308% 0.000001% 0.00005%
1 626080457700 1.886095% 1.88611% -0.000011% -0.00057%
2 626104116471 1.886095% 1.88618% -0.000082% -0.00435%
3 626098140250 1.886095% 1.88616% -0.000064% -0.00339%
4 626098728230 1.886095% 1.88616% -0.000066% -0.00349%
5 626074118384 1.886095% 1.88609% 0.000008% 0.00045%
6 626065231416 1.886095% 1.88606% 0.000035% 0.00187%
7 626057469924 1.886095% 1.88604% 0.000059% 0.00310%
8 626047926074 1.886095% 1.88601% 0.000087% 0.00463%
9 626045927965 1.886095% 1.88600% 0.000093% 0.00495%
10 626076402103 1.886095% 1.88609% 0.000002% 0.00008%
11 626083754551 1.886095% 1.88612% -0.000021% -0.00109%
12 626074522696 1.886095% 1.88609% 0.000007% 0.00038%
13 626110737343 1.886095% 1.88620% -0.000102% -0.00540%
14 626056506775 1.886095% 1.88603% 0.000061% 0.00326%
15 626103017446 1.886095% 1.88617% -0.000079% -0.00417%
16 626082722514 1.886095% 1.88611% -0.000018% -0.00093%
17 626073683747 1.886095% 1.88608% 0.000010% 0.00052%
18 626084037356 1.886095% 1.88612% -0.000021% -0.00114%
19 626043507793 1.886095% 1.88599% 0.000101% 0.00533%
20 626081287948 1.886095% 1.88611% -0.000013% -0.00070%
21 626080850969 1.886095% 1.88611% -0.000012% -0.00063%
22 626059175464 1.886095% 1.88604% 0.000053% 0.00283%
23 626043166985 1.886095% 1.88599% 0.000102% 0.00539%
24 626103009549 1.886095% 1.88617% -0.000079% -0.00417%
25 626108302623 1.886095% 1.88619% -0.000095% -0.00501%
26 626063073690 1.886095% 1.88605% 0.000042% 0.00221%
27 626073499239 1.886095% 1.88608% 0.000010% 0.00054%
28 626087375341 1.886095% 1.88613% -0.000032% -0.00167%
29 626056128410 1.886095% 1.88603% 0.000063% 0.00332%
30 626105551022 1.886095% 1.88618% -0.000086% -0.00457%
31 626074510274 1.886095% 1.88609% 0.000007% 0.00038%
32 626090344621 1.886095% 1.88614% -0.000040% -0.00215%
33 626073784622 1.886095% 1.88609% 0.000009% 0.00050%
34 626078784676 1.886095% 1.88610% -0.000006% -0.00030%
35 626080195274 1.886095% 1.88610% -0.000010% -0.00052%
36 626114089964 1.886095% 1.88621% -0.000112% -0.00594%
37 626076849101 1.886095% 1.88609% 0.000000% 0.00001%
38 626079210643 1.886095% 1.88610% -0.000007% -0.00037%
39 626095712008 1.886095% 1.88615% -0.000057% -0.00300%
40 626059467364 1.886095% 1.88604% 0.000053% 0.00279%
41 626066543932 1.886095% 1.88606% 0.000031% 0.00166%
42 626073329201 1.886095% 1.88608% 0.000011% 0.00057%
43 626073716094 1.886095% 1.88609% 0.000010% 0.00051%
44 626078774156 1.886095% 1.88610% -0.000006% -0.00030%
45 626084414242 1.886095% 1.88612% -0.000023% -0.00120%
46 626067610588 1.886095% 1.88607% 0.000028% 0.00149%
47 626069816643 1.886095% 1.88607% 0.000021% 0.00113%
48 626075165252 1.886095% 1.88609% 0.000005% 0.00028%
49 626082561350 1.886095% 1.88611% -0.000017% -0.00090%
50 626065148869 1.886095% 1.88606% 0.000035% 0.00188%
51 626056663849 1.886095% 1.88603% 0.000061% 0.00323%
52 626060446147 1.886095% 1.88605% 0.000050% 0.00263%
合计 33194352194116 100.000000% 100.00000% 0.000000% 0.00000%

独木星空谁 · 发表于 2021-11-7 12:10

数据分析素数53 素数53 素数53 素数53 素数53
素数53 统计3+46 理论占比实际占比占比绝对误差相对误差
0 638352641644 1.923077% 1.92308% 0.000001% 0.00004%
1 626092909361 1.886095% 1.88614% -0.000048% -0.00256%
2 626107011081 1.886095% 1.88619% -0.000091% -0.00481%
3 626080982813 1.886095% 1.88611% -0.000012% -0.00065%
4 626079787312 1.886095% 1.88610% -0.000009% -0.00046%
5 626089588972 1.886095% 1.88613% -0.000038% -0.00203%
6 626052849211 1.886095% 1.88602% 0.000072% 0.00384%
7 626042816024 1.886095% 1.88599% 0.000103% 0.00545%
8 626045694655 1.886095% 1.88600% 0.000094% 0.00499%
9 626048487145 1.886095% 1.88601% 0.000086% 0.00454%
10 626028871630 1.886095% 1.88595% 0.000145% 0.00767%
11 626086226024 1.886095% 1.88612% -0.000028% -0.00149%
12 626067136173 1.886095% 1.88607% 0.000029% 0.00156%
13 626109254879 1.886095% 1.88619% -0.000097% -0.00517%
14 626080821752 1.886095% 1.88611% -0.000012% -0.00062%
15 626105826756 1.886095% 1.88618% -0.000087% -0.00462%
16 626075004998 1.886095% 1.88609% 0.000006% 0.00030%
17 626071086532 1.886095% 1.88608% 0.000018% 0.00093%
18 626095401555 1.886095% 1.88615% -0.000056% -0.00295%
19 626045793605 1.886095% 1.88600% 0.000094% 0.00497%
20 626095891959 1.886095% 1.88615% -0.000057% -0.00303%
21 626092567219 1.886095% 1.88614% -0.000047% -0.00250%
22 626083843895 1.886095% 1.88612% -0.000021% -0.00111%
23 626071853966 1.886095% 1.88608% 0.000015% 0.00081%
24 626090766633 1.886095% 1.88614% -0.000042% -0.00221%
25 626099803508 1.886095% 1.88616% -0.000069% -0.00366%
26 626055095163 1.886095% 1.88603% 0.000066% 0.00348%
27 626083799854 1.886095% 1.88612% -0.000021% -0.00110%
28 626078867737 1.886095% 1.88610% -0.000006% -0.00031%
29 626081498820 1.886095% 1.88611% -0.000014% -0.00073%
30 626106612804 1.886095% 1.88618% -0.000089% -0.00474%
31 626076845104 1.886095% 1.88609% 0.000000% 0.00001%
32 626073148729 1.886095% 1.88608% 0.000011% 0.00060%
33 626091663025 1.886095% 1.88614% -0.000044% -0.00236%
34 626062630374 1.886095% 1.88605% 0.000043% 0.00228%
35 626063494518 1.886095% 1.88605% 0.000040% 0.00214%
36 626110467272 1.886095% 1.88620% -0.000101% -0.00536%
37 626083096078 1.886095% 1.88611% -0.000019% -0.00099%
38 626070192202 1.886095% 1.88607% 0.000020% 0.00107%
39 626073692049 1.886095% 1.88608% 0.000010% 0.00051%
40 626045914996 1.886095% 1.88600% 0.000093% 0.00495%
41 626063263334 1.886095% 1.88605% 0.000041% 0.00218%
42 626062681160 1.886095% 1.88605% 0.000043% 0.00227%
43 626076195298 1.886095% 1.88609% 0.000002% 0.00011%
44 626093459232 1.886095% 1.88614% -0.000050% -0.00264%
45 626087247765 1.886095% 1.88613% -0.000031% -0.00165%
46 626071904589 1.886095% 1.88608% 0.000015% 0.00080%
47 626082345309 1.886095% 1.88611% -0.000016% -0.00087%
48 626071140616 1.886095% 1.88608% 0.000017% 0.00092%
49 626094064461 1.886095% 1.88615% -0.000052% -0.00274%
50 626075823516 1.886095% 1.88609% 0.000003% 0.00017%
51 626058546014 1.886095% 1.88604% 0.000055% 0.00293%
52 626065584795 1.886095% 1.88606% 0.000034% 0.00181%
合计 33194352194116 100.000000% 100.00000% 0.000000% 0.00000%

独木星空谁 · 发表于 2021-11-7 12:12

组合147 1 2 3 4 6 7 13 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→→→ 7 -4 696 703 710 717 724 731
5→→→ 6 -2 598 604 610 616 622 628
6→→→ 5 -2 498 503 508 513 518 523
7→→→ 6 -2 598 604 610 616 622 628
8→→→ 5 0 500 505 510 515 520 525
9→→→ 4 0 400 404 408 412 416 420
10→→→ 4 0 400 404 408 412 416 420
11→→→ 3 -1 299 302 305 308 311 314
12→→→ 1 0 100 101 102 103 104 105
13→→→ 4 -2 398 402 406 410 414 418
14→→→ 3 0 300 303 306 309 312 315
15→→0 3 -1 299 302 305 308 311 314
一周汇总 64 -24 6376 6440 6504 6568 6632 6696

x+y=N 正整数解组数系数及 a,b值

独木星空谁 · 发表于 2021-11-7 12:12

mod(n,15) 2at^2 2bt c 10周 11周 12周 13周 14周
1→→→ 27 -45 9 1134 1395 1683 1998 2340
2→→→ 33 -57 12 1377 1695 2046 2430 2847
3→→→ 29 -39 6 1261 1546 1860 2203 2575
4→→→ 33 -45 9 1434 1758 2115 2505 2928
5→→→ 39 -39 6 1761 2151 2580 3048 3555
6→→→ 38 -24 3 1783 2170 2595 3058 3559
7→→→ 39 -21 3 1848 2247 2685 3162 3678
8→→→ 42 -12 0 2040 2475 2952 3471 4032
9→→→ 38 -2 1 1891 2289 2725 3199 3711
10→→→ 36 6 0 1830 2211 2628 3081 3570
11→→→ 39 3 3 1968 2379 2829 3318 3846
12→→→ 31 13 0 1615 1947 2310 2704 3129
13→→→ 30 0 3 1503 1818 2163 2538 2943
14→→→ 30 6 0 1530 1848 2196 2574 2982
15→→0同 28 6 1 1431 1728 2053 2406 2787
一周汇总 512 -250 56 24406 29657 35420 41695 48482
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 2021-11-7 12:13

mod(n,15) 6at^3 6bt^2 6ct d 5周 6周 7周
1→→→ 249 -456 327 -20 3540 6535 10872
2→→→ 256 -492 404 -28 3592 6640 11060
3→→→ 256 -432 272 -16 3744 6880 11408
4→→→ 249 -393 246 -16 3739 6836 11296
5→→→ 260 -384 220 -12 3988 7264 11972
6→→→ 272 -312 124 -4 4466 8040 13142
7→→→ 271 -222 101 -5 4800 8520 13792
8→→→ 287 -159 58 0 5365 9436 15176
9→→→ 297 -72 63 -4 5936 10319 16460
10→→→ 286 42 32 0 6160 10580 16730
11→→→ 296 72 124 -6 6564 11206 17648
12→→→ 293 183 94 0 6945 11740 18354
13→→→ 279 216 177 -4 6856 11513 17916
14→→→ 274 246 152 0 6860 11492 17850
15→→0同 271 258 173 -1 6864 11476 17800
一周汇总 4096 -1905 2567 -116 79419 138477 221476
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 2021-11-7 12:13

mod(n,15) 24at^4 24bt^3 24ct^2 24dt 6e 6周 7周
1→→→ 2205 -4430 4815 -3670 270 85550 166085
2→→→ 2160 -4000 4620 -4100 330 86600 167215
3→→→ 2155 -3630 3905 -3270 210 88775 170765
4→→→ 2125 -3110 3095 -2710 150 90750 173695
5→→→ 2094 -2704 2634 -2504 126 92086 175511
6→→→ 2125 -2390 1955 -1690 30 95755 181935
7→→→ 2125 -1790 1295 -1510 60 100215 189220
8→→→ 2130 -1200 870 -960 0 105285 197435
9→→→ 2195 -650 925 -1150 60 113790 211865
10→→→ 2211 286 561 -514 0 122681 226275
11→→→ 2225 950 1315 -890 60 130460 238605
12→→→ 2265 1750 1515 -130 0 140300 254660
13→→→ 2265 2550 2475 -90 30 148955 268070
14→→→ 2235 3270 3225 630 0 155115 277095
15→→0同 2253 3758 4215 934 6 162041 287981
一周汇总 32768 -11340 37420 -21624 1332 1718358 3186412
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 2021-11-7 12:14

mod(n,15) 120at^5 120bt^4 120ct^3 120dt^2 120et 6f 10周
1→→→ 17784 -40830 58440 -68610 44736 -576 11850957
2→→→ 17679 -34080 49665 -63660 41916 -576 12256722
3→→→ 17592 -28450 43500 -57230 32628 -402 12606627
4→→→ 17553 -23160 37035 -48480 21372 -216 12967470
5→→→ 17364 -17490 31140 -43350 16656 -216 13237227
6→→→ 17277 -13030 27455 -36710 5848 -36 13510348
7→→→ 17277 -8355 22905 -32685 4098 -126 13865208
8→→→ 17175 -2940 17925 -25860 -3780 0 14195010
9→→→ 17209 1655 17845 -26855 -734 -120 14604998
10→→→ 17331 7530 15405 -18330 -7536 0 15182472
11→→→ 17370 13890 19230 -18930 -3120 -90 15776700
12→→→ 17480 20340 23980 -10080 -7080 0 16452510
13→→→ 17664 27150 32820 -4830 -2964 -36 17251722
14→→→ 17661 34710 43335 7950 -2136 0 17977572
15→→0同 17728 41090 58760 20470 3672 -6 18704530
一周汇总 262144 -21970 499440 -427190 143576 -2400 220440073
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 2021-11-7 12:15

组合148 1 2 3 4 6 7 14 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→→→ 6 -4 596 602 608 614 620 626
4→→→ 5 -2 498 503 508 513 518 523
5→→→ 6 -2 598 604 610 616 622 628
6→→→ 7 -4 696 703 710 717 724 731
7→→→ 6 -2 598 604 610 616 622 628
8→→→ 5 0 500 505 510 515 520 525
9→→→ 4 0 400 404 408 412 416 420
10→→→ 4 0 400 404 408 412 416 420
11→→→ 2 0 200 202 204 206 208 210
12→→→ 1 0 100 101 102 103 104 105
13→→→ 3 -1 299 302 305 308 311 314
14→→→ 3 -2 298 301 304 307 310 313
15→→0 3 -1 299 302 305 308 311 314
一周汇总 64 -26 6374 6438 6502 6566 6630 6694

x+y=N 正整数解组数系数及 a,b值

独木星空谁 · 发表于 2021-11-7 12:15

mod(n,15) 2at^2 2bt c 10周 11周 12周 13周 14周
1→→→ 27 -51 12 1107 1365 1650 1962 2301
2→→→ 30 -54 12 1242 1530 1848 2196 2574
3→→→ 29 -45 9 1234 1516 1827 2167 2536
4→→→ 33 -39 6 1461 1788 2148 2541 2967
5→→→ 39 -45 9 1734 2121 2547 3012 3516
6→→→ 41 -39 9 1864 2275 2727 3220 3754
7→→→ 42 -24 3 1983 2412 2883 3396 3951
8→→→ 42 -12 0 2040 2475 2952 3471 4032
9→→→ 43 -5 0 2125 2574 3066 3601 4179
10→→→ 39 3 0 1965 2376 2826 3315 3843
11→→→ 33 15 0 1725 2079 2466 2886 3339
12→→→ 32 10 1 1651 1992 2365 2770 3207
13→→→ 30 0 3 1503 1818 2163 2538 2943
14→→→ 27 3 3 1368 1653 1965 2304 2670
15→→0同 25 3 1 1266 1530 1819 2133 2472
一周汇总 512 -280 68 24268 29504 35252 41512 48284
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 2021-11-7 12:16

mod(n,15) 6at^3 6bt^2 6ct d 5周 6周 7周
1→→→ 253 -516 455 -32 3468 6435 10748
2→→→ 240 -468 396 -28 3352 6200 10332
3→→→ 236 -420 304 -20 3400 6260 10396
4→→→ 245 -441 322 -20 3515 6476 10760
5→→→ 256 -432 344 -24 3796 6944 11484
6→→→ 266 -366 256 -16 4214 7620 12500
7→→→ 278 -288 154 -4 4716 8430 13716
8→→→ 297 -213 102 0 5385 9516 15358
9→→→ 305 -120 79 0 5920 10339 16548
10→→→ 302 18 40 0 6400 11020 17458
11→→→ 303 114 45 -1 6824 11636 18304
12→→→ 299 153 142 -4 6981 11820 18504
13→→→ 287 204 193 -6 6984 11743 18292
14→→→ 270 246 180 -4 6796 11372 17650
15→→0同 259 258 185 -1 6624 11056 17128
一周汇总 4096 -2271 3197 -160 78375 136867 219178
x+y+z+u=N 正整数解组数及a,b c,d 的值

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