[原创]k生素数群的数量公式

独木星空谁 · 发表于 2021-11-7 19:37

mod(n,15) 24at^4 24bt^3 24ct^2 24dt 6e 6周 7周
1→→→ 2165 -2310 -1145 1290 0 94725 181615
2→→→ 2155 -1670 -1435 950 0 99425 189070
3→→→ 2265 -1270 -1605 610 0 108625 205345
4→→→ 2135 -390 -1895 150 0 108975 204190
5→→→ 2232 -52 -1920 -236 0 117121 218561
6→→→ 2165 650 -1985 -710 0 119605 221620
7→→→ 2130 1220 -1890 -1100 0 122890 226345
8→→→ 2235 1730 -1755 -1370 0 133285 244335
9→→→ 2125 2450 -1345 -1670 0 134365 244370
10→→→ 2253 2938 -969 -1678 0 146231 264915
11→→→ 2205 3570 -345 -1710 0 150255 270410
12→→→ 2165 4030 355 -1510 0 153335 274470
13→→→ 2240 4580 1120 -1220 0 163555 291480
14→→→ 2095 5050 2225 -730 0 161735 286090
15→→0同 2203 5686 3389 -94 0 175196 308546
一周汇总 32768 26212 -9200 -9028 0 1989323 3631362
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 19:37

mod(n,15) 120at^5 120bt^4 120ct^3 120dt^2 120et 6f 10周
1→→→ 17553 -12405 -32775 10245 17382 0 13330611
2→→→ 17433 -6000 -35745 5100 19212 0 13735476
3→→→ 17291 115 -35925 -475 18994 0 14120562
4→→→ 17721 5190 -34425 -5550 17064 0 14909922
5→→→ 17310 12150 -31650 -12150 14340 0 15164820
6→→→ 17648 17130 -27060 -17130 9532 0 15895186
7→→→ 17502 23340 -21510 -22980 4368 0 16331964
8→→→ 17280 29040 -13980 -27780 -2040 0 16680180
9→→→ 17635 34665 -6005 -31305 -8270 0 17507765
10→→→ 17205 40950 4875 -33750 -14880 0 17761260
11→→→ 17598 46770 15930 -33450 -20208 0 18665691
12→→→ 17548 53080 29260 -31120 -24848 0 19262496
13→→→ 17400 58620 43500 -25500 -27780 0 19723935
14→→→ 17760 64620 58200 -17100 -28440 0 20653380
15→→0同 17260 69600 75400 -4200 -27260 0 20805895
一周汇总 262144 436865 -11910 -247145 -52834 0 254549143
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 19:38

组合151 1 2 3 4 6 8 9 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→→→ 5 -3 497 502 507 512 517 522
4→→→ 3 0 300 303 306 309 312 315
5→→→ 6 -2 598 604 610 616 622 628
6→→→ 5 -2 498 503 508 513 518 523
7→→→ 4 0 400 404 408 412 416 420
8→→→ 3 0 300 303 306 309 312 315
9→→→ 5 -1 499 504 509 514 519 524
10→→→ 6 0 600 606 612 618 624 630
11→→→ 4 0 400 404 408 412 416 420
12→→→ 5 0 500 505 510 515 520 525
13→→→ 4 0 400 404 408 412 416 420
14→→→ 4 0 400 404 408 412 416 420
15→→0 4 0 400 404 408 412 416 420
一周汇总 64 -13 6387 6451 6515 6579 6643 6707

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 19:38

mod(n,15) 2at^2 2bt c 10周 11周 12周 13周 14周
1→→→ 33 -33 0 1485 1815 2178 2574 3003
2→→→ 33 -39 3 1458 1785 2145 2538 2964
3→→→ 35 -39 3 1558 1906 2289 2707 3160
4→→→ 33 -27 0 1515 1848 2214 2613 3045
5→→→ 30 -18 0 1410 1716 2052 2418 2814
6→→→ 35 -17 1 1666 2025 2419 2848 3312
7→→→ 36 -12 0 1740 2112 2520 2964 3444
8→→→ 33 -3 0 1635 1980 2358 2769 3213
9→→→ 35 -3 0 1735 2101 2502 2938 3409
10→→→ 30 6 0 1530 1848 2196 2574 2982
11→→→ 36 12 0 1860 2244 2664 3120 3612
12→→→ 35 15 0 1825 2200 2610 3055 3535
13→→→ 36 24 0 1920 2310 2736 3198 3696
14→→→ 36 24 0 1920 2310 2736 3198 3696
15→→0同 36 24 0 1920 2310 2736 3198 3696
一周汇总 512 -86 7 25177 30510 36355 42712 49581
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 19:39

mod(n,15) 6at^3 6bt^2 6ct d 5周 6周 7周
1→→→ 275 -336 61 0 4380 7945 13048
2→→→ 275 -273 -2 0 4590 8260 13489
3→→→ 273 -246 -21 -1 4644 8330 13572
4→→→ 275 -195 -74 0 4855 8656 14042
5→→→ 274 -144 -106 0 5020 8894 14364
6→→→ 273 -111 -102 0 5140 9060 14581
7→→→ 268 -24 -124 0 5380 9380 14980
8→→→ 275 9 -98 0 5685 9856 15680
9→→→ 273 72 -81 0 5920 10179 16100
10→→→ 274 138 -76 0 6220 10616 16702
11→→→ 268 168 -28 0 6260 10628 16660
12→→→ 273 231 18 0 6665 11232 17514
13→→→ 268 312 44 0 6920 11564 17920
14→→→ 268 372 128 0 7240 12008 18508
15→→0同 284 432 172 0 7860 12988 19964
一周汇总 4096 405 -289 -1 86779 149596 237124
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 19:40

mod(n,15) 24at^4 24bt^3 24ct^2 24dt 6e 6周 7周
1→→→ 2185 -2670 -385 870 0 93600 179900
2→→→ 2185 -2090 -745 650 0 98225 187390
3→→→ 2195 -1490 -1055 350 0 103625 196245
4→→→ 2185 -850 -1525 190 0 108100 203385
5→→→ 2182 -332 -1510 -316 0 112496 210371
6→→→ 2195 250 -1715 -610 0 118055 219485
7→→→ 2180 840 -1820 -840 0 122340 226135
8→→→ 2185 1390 -1525 -1210 0 127910 234990
9→→→ 2195 1910 -1235 -1310 0 133540 243985
10→→→ 2182 2564 -910 -1292 0 139216 252700
11→→→ 2180 3160 -260 -1360 0 145430 262325
12→→→ 2195 3610 385 -1150 0 151310 271635
13→→→ 2180 4240 1180 -880 0 157430 280840
14→→→ 2180 4800 2140 -480 0 164010 290920
15→→0同 2164 5360 3380 160 0 170206 300041
一周汇总 32768 20692 -5600 -7228 0 1945493 3560347
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 19:40

mod(n,15) 120at^5 120bt^4 120ct^3 120dt^2 120et 6f 10周
1→→→ 17451 -16185 -23625 10425 11934 0 13006557
2→→→ 17451 -10380 -25935 4620 14244 0 13466412
3→→→ 17481 -4685 -27475 1325 13354 0 13950342
4→→→ 17451 1590 -27975 -2850 11784 0 14440482
5→→→ 17490 7350 -25950 -9150 10260 0 14964480
6→→→ 17481 12980 -22445 -14180 6284 0 15450832
7→→→ 17484 19140 -18900 -18780 1776 0 15991998
8→→→ 17451 24930 -13095 -24030 -2736 0 16490622
9→→→ 17481 30605 -5395 -27605 -8366 0 17049257
10→→→ 17490 36600 2550 -29400 -12840 0 17620680
11→→→ 17484 42300 13020 -28980 -17184 0 18177918
12→→→ 17481 48250 24995 -26350 -20456 0 18772962
13→→→ 17484 54000 37620 -20880 -21984 0 19364268
14→→→ 17484 59700 52620 -12180 -22584 0 19971468
15→→0同 17500 65400 68500 0 -20600 0 20602450
一周汇总 262144 371595 8510 -198015 -57114 0 249320728
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 19:43

针对素53 针对素53 针对素53 针对素53
统计3+47 统计3+48 统计3+49 统计3+50
638352574769 638352742800 638352686677 638353368106
626058673173 626069779216 626102480146 626099250258
626100658919 626098064224 626103961284 626068075624
626093777610 626095433468 626085364328 626072899456
626062695857 626075520941 626077785014 626083169389
626075730451 626062979186 626088110651 626073341983
626052605395 626032315333 626048417841 626061456401
626037996846 626055420464 626027610387 626041622428
626053614326 626063144177 626057002461 626059416720
626043822504 626072026276 626058015152 626075296867
626061704597 626060606219 626054380787 626049516690
626077849805 626090400468 626075880659 626073293797
626087939784 626087457611 626106109422 626081013559
626104463251 626101843987 626111909390 626087122017
626070693386 626072337453 626082370830 626092780018
626087678976 626112129166 626104480848 626083011929
626084931421 626091946114 626075798640 626097766025
626086509328 626088089704 626090747301 626100639563
626101340576 626075974602 626100151926 626075800171
626078637424 626067448100 626083747418 626066827684
626076299597 626080326891 626076575734 626088445209
626075491089 626050054117 626077608610 626090445589
626056540323 626043550348 626047177384 626060232592
626079853562 626069160153 626063915742 626080709675
626077656952 626089357241 626077430975 626083911749
626092602886 626082487738 626086155585 626097899026
626038278307 626050558100 626020025505 626055468586
626104438526 626078541704 626077032132 626055468586
626098038609 626098648665 626102224150 626097899026
626087042073 626092331044 626082219620 626083911749
626084145572 626087706728 626100434704 626080709675
626077099543 626075920643 626062555579 626060232592
626112525650 626108546743 626096825119 626090445589
626061754784 626088839367 626094992758 626088445209
626088514013 626059457102 626082166341 626066827684
626049847122 626090318954 626062873358 626075800171
626089847883 626085484390 626065271985 626100639563
626071980185 626104779505 626102788006 626097766025
626062005409 626046054305 626046438118 626083011929
626063785613 626087214636 626108188522 626092780018
626070993749 626069250492 626056009112 626087122017
626054670223 626086278238 626049895885 626081013559
626086127889 626066232378 626070867868 626073293797
626061397693 626050758712 626061791999 626049516690
626091985183 626101059620 626105640217 626075296867
626089213220 626051984475 626064278061 626059416720
626084722891 626086951689 626073603482 626041622428
626082235064 626071269884 626073666230 626061456401
626081525456 626083249002 626085995167 626073341983
626088603777 626094807917 626078589820 626083169389
626076802252 626058200119 626060753225 626072899456
626066390967 626058183795 626061813058 626068075624
626095879656 626078969912 626089378903 626099250258

独木星空谁 · 发表于 2021-11-7 19:43

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+47 理论占比实际占比占比绝对误差相对误差
0 638352574769 1.923077% 1.92308% 0.000001% 0.00006%
1 626058673173 1.886095% 1.88604% 0.000055% 0.00291%
2 626100658919 1.886095% 1.88617% -0.000072% -0.00379%
3 626093777610 1.886095% 1.88615% -0.000051% -0.00269%
4 626062695857 1.886095% 1.88605% 0.000043% 0.00227%
5 626075730451 1.886095% 1.88609% 0.000004% 0.00019%
6 626052605395 1.886095% 1.88602% 0.000073% 0.00388%
7 626037996846 1.886095% 1.88598% 0.000117% 0.00622%
8 626053614326 1.886095% 1.88602% 0.000070% 0.00372%
9 626043822504 1.886095% 1.88599% 0.000100% 0.00528%
10 626061704597 1.886095% 1.88605% 0.000046% 0.00243%
11 626077849805 1.886095% 1.88610% -0.000003% -0.00015%
12 626087939784 1.886095% 1.88613% -0.000033% -0.00176%
13 626104463251 1.886095% 1.88618% -0.000083% -0.00440%
14 626070693386 1.886095% 1.88608% 0.000019% 0.00099%
15 626087678976 1.886095% 1.88613% -0.000032% -0.00172%
16 626084931421 1.886095% 1.88612% -0.000024% -0.00128%
17 626086509328 1.886095% 1.88612% -0.000029% -0.00153%
18 626101340576 1.886095% 1.88617% -0.000074% -0.00390%
19 626078637424 1.886095% 1.88610% -0.000005% -0.00028%
20 626076299597 1.886095% 1.88609% 0.000002% 0.00010%
21 626075491089 1.886095% 1.88609% 0.000004% 0.00023%
22 626056540323 1.886095% 1.88603% 0.000061% 0.00325%
23 626079853562 1.886095% 1.88610% -0.000009% -0.00047%
24 626077656952 1.886095% 1.88610% -0.000002% -0.00012%
25 626092602886 1.886095% 1.88614% -0.000047% -0.00251%
26 626038278307 1.886095% 1.88598% 0.000116% 0.00617%
27 626104438526 1.886095% 1.88618% -0.000083% -0.00440%
28 626098038609 1.886095% 1.88616% -0.000064% -0.00337%
29 626087042073 1.886095% 1.88613% -0.000031% -0.00162%
30 626084145572 1.886095% 1.88612% -0.000022% -0.00116%
31 626077099543 1.886095% 1.88610% -0.000001% -0.00003%
32 626112525650 1.886095% 1.88620% -0.000107% -0.00569%
33 626061754784 1.886095% 1.88605% 0.000046% 0.00242%
34 626088514013 1.886095% 1.88613% -0.000035% -0.00185%
35 626049847122 1.886095% 1.88601% 0.000082% 0.00432%
36 626089847883 1.886095% 1.88613% -0.000039% -0.00207%
37 626071980185 1.886095% 1.88608% 0.000015% 0.00079%
38 626062005409 1.886095% 1.88605% 0.000045% 0.00238%
39 626063785613 1.886095% 1.88606% 0.000040% 0.00210%
40 626070993749 1.886095% 1.88608% 0.000018% 0.00094%
41 626054670223 1.886095% 1.88603% 0.000067% 0.00355%
42 626086127889 1.886095% 1.88612% -0.000028% -0.00147%
43 626061397693 1.886095% 1.88605% 0.000047% 0.00248%
44 626091985183 1.886095% 1.88614% -0.000045% -0.00241%
45 626089213220 1.886095% 1.88613% -0.000037% -0.00197%
46 626084722891 1.886095% 1.88612% -0.000024% -0.00125%
47 626082235064 1.886095% 1.88611% -0.000016% -0.00085%
48 626081525456 1.886095% 1.88611% -0.000014% -0.00074%
49 626088603777 1.886095% 1.88613% -0.000035% -0.00187%
50 626076802252 1.886095% 1.88609% 0.000000% 0.00002%
51 626066390967 1.886095% 1.88606% 0.000032% 0.00168%
52 626095879656 1.886095% 1.88615% -0.000057% -0.00303%
合计 33194352194116 100.000000% 100.00000% 0.000000% 0.00000%

独木星空谁 · 发表于 2021-11-7 19:43

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

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