[原创]k生素数群的数量公式

独木星空谁 · 发表于 2021-10-23 12:11

素数29 统计12+16 理论占比实际占比占比绝对误差相对误差
0 1143157145167 3.57% 3.57142% 0.000011% 0.00032%
1 1100814844201 3.44% 3.43913% 0.004745% 0.13778%
2 1100869364121 3.44% 3.43930% 0.004575% 0.13283%
3 1100800557792 3.44% 3.43909% 0.004790% 0.13907%
4 1100828943056 3.44% 3.43918% 0.004701% 0.13650%
5 1100796063256 3.44% 3.43907% 0.004804% 0.13948%
6 1100669323745 3.44% 3.43868% 0.005200% 0.15098%
7 1100862306439 3.44% 3.43928% 0.004597% 0.13347%
8 1100828821887 3.44% 3.43918% 0.004701% 0.13651%
9 1100819679584 3.44% 3.43915% 0.004730% 0.13734%
10 1100812873973 3.44% 3.43913% 0.004751% 0.13796%
11 1100825335741 3.44% 3.43917% 0.004712% 0.13683%
12 1100808822959 3.44% 3.43911% 0.004764% 0.13832%
13 1143166018984 3.44% 3.57144% -0.127567% -3.70418%
14 1100795864686 3.44% 3.43907% 0.004804% 0.13950%
15 1100820483185 3.44% 3.43915% 0.004727% 0.13727%
16 1100821473875 3.44% 3.43915% 0.004724% 0.13718%
17 1100797176886 3.44% 3.43908% 0.004800% 0.13938%
18 1100842856160 3.44% 3.43922% 0.004657% 0.13524%
19 1100775688161 3.44% 3.43901% 0.004867% 0.14133%
20 1100854972784 3.44% 3.43926% 0.004620% 0.13414%
21 1100822403144 3.44% 3.43916% 0.004721% 0.13709%
22 1100764156616 3.44% 3.43897% 0.004903% 0.14238%
23 1100922491190 3.44% 3.43947% 0.004409% 0.12801%
24 1100876117022 3.44% 3.43932% 0.004553% 0.13222%
25 1100795027569 3.44% 3.43907% 0.004807% 0.13958%
26 1100822926683 3.44% 3.43916% 0.004720% 0.13704%
27 1100865096068 3.44% 3.43929% 0.004588% 0.13322%
28 1100865096068 3.44% 3.43929% 0.004588% 0.13322%
合计 32008501931002 100.00% 100.00000% 0.000000% -0.00001%

独木星空谁 · 发表于 2021-10-23 14:15

组合105 1 2 3 4 5 10 12 13 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→→→ 3 0 300 303 306 309 312 315
5→→→ 5 -1 499 504 509 514 519 524
6→→→ 5 0 500 505 510 515 520 525
7→→→ 6 -2 598 604 610 616 622 628
8→→→ 5 -2 498 503 508 513 518 523
9→→→ 3 -1 299 302 305 308 311 314
10→→→ 3 -2 298 301 304 307 310 313
11→→→ 3 -1 299 302 305 308 311 314
12→→→ 2 0 200 202 204 206 208 210
13→→→ 4 0 400 404 408 412 416 420
14→→→ 6 0 600 606 612 618 624 630
15→→0 6 0 600 606 612 618 624 630
一周汇总 64 -19 6381 6445 6509 6573 6637 6701

x+y=N 正整数解组数系数及 a,b值

独木星空谁 · 发表于 2021-10-23 14:16

mod(n,15) 2at^2 2bt c 10周 11周 12周 13周 14周
1→→→ 33 -39 3 1458 1785 2145 2538 2964
2→→→ 36 -42 3 1593 1950 2343 2772 3237
3→→→ 40 -44 3 1783 2181 2619 3097 3615
4→→→ 39 -39 3 1758 2148 2577 3045 3552
5→→→ 36 -36 6 1626 1986 2382 2814 3282
6→→→ 32 -20 4 1504 1830 2188 2578 3000
7→→→ 30 -6 3 1473 1785 2127 2499 2901
8→→→ 33 -3 3 1638 1983 2361 2772 3216
9→→→ 35 1 1 1756 2124 2527 2965 3438
10→→→ 36 0 0 1800 2178 2592 3042 3528
11→→→ 36 -6 0 1770 2145 2556 3003 3486
12→→→ 37 -11 0 1795 2178 2598 3055 3549
13→→→ 30 -6 0 1470 1782 2124 2496 2898
14→→→ 27 3 0 1365 1650 1962 2301 2667
15→→0同 32 12 0 1660 2002 2376 2782 3220
一周汇总 512 -236 29 24449 29707 35477 41759 48553
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 2021-10-23 14:16

mod(n,15) 6at^3 6bt^2 6ct d 5周 6周 7周
1→→→ 273 -576 363 -10 3580 6725 11316
2→→→ 264 -480 288 -12 3728 6900 11496
3→→→ 259 -378 197 -13 3972 7240 11936
4→→→ 265 -273 62 -8 4427 7956 12984
5→→→ 279 -216 -3 -6 4904 8739 14176
6→→→ 288 -192 -12 -4 5186 9200 14878
7→→→ 291 -174 9 -1 5344 9440 15224
8→→→ 279 -123 54 0 5345 9360 15008
9→→→ 270 -72 114 0 5420 9402 14980
10→→→ 265 -3 146 0 5630 9668 15295
11→→→ 256 108 116 0 5880 9980 15652
12→→→ 265 159 86 0 6255 10580 16548
13→→→ 282 192 30 0 6700 11334 17724
14→→→ 282 210 -12 0 6740 11400 17822
15→→0同 278 204 -2 0 6640 11230 17556
一周汇总 4096 -1614 1436 -54 79751 139154 222595
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 2021-10-23 14:17

mod(n,15) 24at^4 24bt^3 24ct^2 24dt 6e 6周 7周 8周
1→→→ 2175 -4310 3045 -1510 150 82875 161795 286895
2→→→ 2215 -3970 1925 -530 90 86650 168645 298305
3→→→ 2225 -3610 1375 -230 60 89675 173750 306320
4→→→ 2205 -3170 1275 -430 30 92350 177770 311955
5→→→ 2174 -2508 1186 -852 6 96391 183821 320405
6→→→ 2145 -1610 855 -1270 0 102305 192955 333590
7→→→ 2155 -830 665 -1630 0 109490 204610 351310
8→→→ 2185 -90 215 -1470 0 117135 217315 371070
9→→→ 2205 530 -105 -950 0 123445 227675 387030
10→→→ 2232 868 120 -316 0 128441 235851 399660
11→→→ 2230 1220 530 460 0 132310 241745 408180
12→→→ 2185 1690 1295 950 0 135380 245665 412730
13→→→ 2145 2270 2115 1150 0 139720 251685 420530
14→→→ 2140 3020 2660 1060 0 146995 262990 437100
15→→0同 2152 3760 3032 680 0 154766 275415 455800
一周汇总 32768 -6740 20188 -4888 336 1737928 3221687 5500880
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 2021-10-23 14:18

mod(n,15) 120at^5 120bt^4 120ct^3 120dt^2 120et 6f 10周 11周
1→→→ 17427 -39105 42015 -22455 3918 -90 11595474 19061214
2→→→ 17331 -32550 32985 -24510 7464 -36 11985066 19630242
3→→→ 17331 -25675 21135 -23885 11214 -6 12460071 20338592
4→→→ 17412 -19230 9540 -21630 13908 0 12970134 21107559
5→→→ 17544 -13950 1740 -18810 13476 0 13457448 21845208
6→→→ 17614 -8950 -2970 -13250 7676 0 13897348 22502029
7→→→ 17586 -3870 -2370 -10530 -96 0 14303967 23092938
8→→→ 17511 1530 2505 -10530 -8496 0 14731392 23704428
9→→→ 17419 7925 8155 -11525 -15254 0 15233333 24422244
10→→→ 17346 14970 13770 -13530 -17436 0 15804522 25243878
11→→→ 17382 21840 18090 -12480 -15312 0 16444074 26179560
12→→→ 17514 27960 21630 -6960 -9024 0 17098698 27148814
13→→→ 17589 33285 26505 2715 -174 0 17654373 27963804
14→→→ 17592 37890 34140 16470 8028 0 18116394 28628985
15→→0同 17546 42590 45370 30970 13764 0 18575872 29280394
一周汇总 262144 44660 272240 -139940 13656 -132 224328166 360149889
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 2021-10-23 17:02

组合106 1 2 3 4 5 10 12 14 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→→→ 5 -1 499 504 509 514 519 524
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→→→ 5 -3 497 502 507 512 517 522
10→→→ 1 0 100 101 102 103 104 105
11→→→ 4 -2 398 402 406 410 414 418
12→→→ 2 0 200 202 204 206 208 210
13→→→ 5 -1 499 504 509 514 519 524
14→→→ 4 0 400 404 408 412 416 420
15→→0 6 0 600 606 612 618 624 630
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 2021-10-23 17:03

mod(n,15) 2at^2 2bt c 10周 11周 12周 13周 14周
1→→→ 36 -54 9 1539 1890 2277 2700 3159
2→→→ 36 -48 6 1566 1920 2310 2736 3198
3→→→ 37 -41 3 1648 2016 2421 2863 3342
4→→→ 39 -45 6 1731 2118 2544 3009 3513
5→→→ 33 -21 0 1545 1881 2250 2652 3087
6→→→ 38 -32 7 1747 2130 2551 3010 3507
7→→→ 30 0 0 1500 1815 2160 2535 2940
8→→→ 39 -15 6 1881 2283 2724 3204 3723
9→→→ 31 7 0 1585 1914 2274 2665 3087
10→→→ 39 -9 3 1908 2313 2757 3240 3762
11→→→ 30 0 0 1500 1815 2160 2535 2940
12→→→ 35 -11 1 1696 2058 2455 2887 3354
13→→→ 27 -3 0 1335 1617 1926 2262 2625
14→→→ 33 -3 0 1635 1980 2358 2769 3213
15→→0同 29 9 0 1495 1804 2142 2509 2905
一周汇总 512 -266 41 24311 29554 35309 41576 48355
x+y+z=N 正整数解组数及系数 a,b,c 的值

独舟星海 · 发表于 2021-10-23 21:43

素数29 统计12+17 理论占比实际占比占比绝对误差相对误差
0 1143143747973 3.57% 3.57138% 0.000051% 0.00143%
1 1100832076098 3.44% 3.43919% 0.004689% 0.13616%
2 1100808366954 3.44% 3.43911% 0.004763% 0.13831%
3 1100850679817 3.44% 3.43925% 0.004631% 0.13447%
4 1100762449630 3.44% 3.43897% 0.004907% 0.14247%
5 1100742508748 3.44% 3.43891% 0.004969% 0.14428%
6 1100769486061 3.44% 3.43899% 0.004885% 0.14183%
7 1100791076613 3.44% 3.43906% 0.004817% 0.13988%
8 1100809643431 3.44% 3.43912% 0.004759% 0.13819%
9 1100832964416 3.44% 3.43919% 0.004686% 0.13608%
10 1100846685680 3.44% 3.43923% 0.004643% 0.13483%
11 1100871341124 3.44% 3.43931% 0.004566% 0.13259%
12 1143144809704 3.44% 3.57138% -0.127503% -3.70232%
13 1100801478651 3.44% 3.43909% 0.004785% 0.13893%
14 1100854353461 3.44% 3.43926% 0.004619% 0.13413%
15 1100853735950 3.44% 3.43926% 0.004621% 0.13419%
16 1100814034708 3.44% 3.43913% 0.004745% 0.13779%
17 1100777174157 3.44% 3.43902% 0.004861% 0.14114%
18 1100833467116 3.44% 3.43919% 0.004685% 0.13603%
19 1100865416847 3.44% 3.43929% 0.004585% 0.13313%
20 1100858282367 3.44% 3.43927% 0.004607% 0.13378%
21 1100829403783 3.44% 3.43918% 0.004697% 0.13640%
22 1100838007449 3.44% 3.43921% 0.004671% 0.13562%
23 1100791922294 3.44% 3.43906% 0.004814% 0.13980%
24 1100800760619 3.44% 3.43909% 0.004787% 0.13900%
25 1100794354365 3.44% 3.43907% 0.004807% 0.13958%
26 1100867558451 3.44% 3.43930% 0.004578% 0.13294%
27 1100848711006 3.44% 3.43924% 0.004637% 0.13465%
28 1100848711006 3.44% 3.43924% 0.004637% 0.13465%
合计 32008483208479 100.00% 100.00000% 0.000000% -0.00005%
出现技术故障，m=12时，12的实际占比为1/28，是余数0的占比，问什么？

独舟星海 · 发表于 2021-10-23 22:15

素数29 统计12+12 理论占比实际占比占比绝对误差相对误差
0 1185511956521 3.57% 3.57598% -0.004548% -0.12735%
1 1143146748927 3.44% 3.44819% -0.004309% -0.12512%
2 1143190575212 3.44% 3.44832% -0.004441% -0.12896%
3 1143242906967 3.44% 3.44848% -0.004599% -0.13354%
4 1143084747005 3.44% 3.44800% -0.004122% -0.11969%
5 1143207916089 3.44% 3.44837% -0.004493% -0.13048%
6 1143216917838 3.44% 3.44840% -0.004521% -0.13126%
7 1143192727325 3.44% 3.44833% -0.004448% -0.12914%
8 1143171757448 3.44% 3.44826% -0.004384% -0.12731%
9 1143125277581 3.44% 3.44812% -0.004244% -0.12324%
10 1143148899807 3.44% 3.44819% -0.004315% -0.12531%
11 1143171264645 3.44% 3.44826% -0.004383% -0.12726%
12 1143180898359 3.44% 3.44829% -0.004412% -0.12811%
13 1143202485099 3.44% 3.44835% -0.004477% -0.13000%
14 1143157790494 3.44% 3.44822% -0.004342% -0.12608%
15 1143104957678 3.44% 3.44806% -0.004183% -0.12146%
16 1143241018257 3.44% 3.44847% -0.004593% -0.13337%
17 1143123794016 3.44% 3.44812% -0.004240% -0.12311%
18 1143189015894 3.44% 3.44831% -0.004436% -0.12882%
19 1143132238045 3.44% 3.44814% -0.004265% -0.12385%
20 1143243224238 3.44% 3.44848% -0.004600% -0.13357%
21 1143183247803 3.44% 3.44830% -0.004419% -0.12831%
22 1143206422842 3.44% 3.44837% -0.004489% -0.13034%
23 1143165687723 3.44% 3.44824% -0.004366% -0.12678%
24 1143205415923 3.44% 3.44836% -0.004486% -0.13026%
25 1143284511618 3.44% 3.44860% -0.004724% -0.13718%
26 1143030115628 3.44% 3.44783% -0.003957% -0.11490%
27 1143145906089 3.44% 3.44818% -0.004306% -0.12504%
28 1100906941608 3.44% 3.32077% 0.123103% 3.57455%
合计 33152115366679 100.00% 100.00000% 0.000000% 0.00472%
对于，理论合成来说，是一成不变的；而实际合成，却变化很大，因为实际合成，不缺余数类，有余数0的参与，以前只是1个值而已，现在确实一组数（参与运算）

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[原创]k生素数群的数量公式

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