[原创]k生素数群的数量公式

独木星空谁 · 发表于 2021-10-27 05:04

素数29 统计15+19 理论占比实际占比占比绝对误差相对误差
0 1185512172310 3.57% 3.57143% 0.000001% 0.00003%
1 1143110336390 3.44% 3.44369% 0.000188% 0.00547%
2 1143125241202 3.44% 3.44373% 0.000143% 0.00416%
3 1143230243155 3.44% 3.44405% -0.000173% -0.00502%
4 1143147808477 3.44% 3.44380% 0.000075% 0.00219%
5 1143153189554 3.44% 3.44382% 0.000059% 0.00172%
6 1143176061998 3.44% 3.44389% -0.000010% -0.00028%
7 1143164633951 3.44% 3.44385% 0.000025% 0.00072%
8 1143224420943 3.44% 3.44403% -0.000155% -0.00451%
9 1143189871558 3.44% 3.44393% -0.000051% -0.00149%
10 1143193547513 3.44% 3.44394% -0.000062% -0.00181%
11 1143245483813 3.44% 3.44410% -0.000219% -0.00635%
12 1143206051654 3.44% 3.44398% -0.000100% -0.00290%
13 1143081089666 3.44% 3.44360% 0.000276% 0.00803%
14 1143192384325 3.44% 3.44394% -0.000059% -0.00171%
15 1143174689199 3.44% 3.44388% -0.000006% -0.00016%
16 1143195822706 3.44% 3.44395% -0.000069% -0.00201%
17 1143200297011 3.44% 3.44396% -0.000083% -0.00240%
18 1143138744976 3.44% 3.44377% 0.000103% 0.00298%
19 1143135998598 3.44% 3.44377% 0.000111% 0.00322%
20 1143158641857 3.44% 3.44383% 0.000043% 0.00124%
21 1143203968659 3.44% 3.44397% -0.000094% -0.00272%
22 1143144026865 3.44% 3.44379% 0.000087% 0.00252%
23 1143156579261 3.44% 3.44383% 0.000049% 0.00142%
24 1143118585537 3.44% 3.44371% 0.000163% 0.00475%
25 1143182011627 3.44% 3.44391% -0.000028% -0.00080%
26 1143145407387 3.44% 3.44379% 0.000083% 0.00240%
27 1143250651077 3.44% 3.44411% -0.000234% -0.00681%
28 1143194232847 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 2021-10-27 05:04

素数29 统计15+20 理论占比实际占比占比绝对误差相对误差
0 1185512224657 3.57% 3.57143% 0.000001% 0.00003%
1 1143215552900 3.44% 3.44401% -0.000129% -0.00374%
2 1143163907408 3.44% 3.44385% 0.000027% 0.00078%
3 1143174615431 3.44% 3.44388% -0.000005% -0.00016%
4 1143194313589 3.44% 3.44394% -0.000065% -0.00188%
5 1143178053273 3.44% 3.44389% -0.000016% -0.00046%
6 1143152913392 3.44% 3.44382% 0.000060% 0.00174%
7 1143220965505 3.44% 3.44402% -0.000145% -0.00421%
8 1143210697544 3.44% 3.44399% -0.000114% -0.00331%
9 1143166224821 3.44% 3.44386% 0.000020% 0.00058%
10 1143174227038 3.44% 3.44388% -0.000004% -0.00012%
11 1143198863052 3.44% 3.44396% -0.000078% -0.00228%
12 1143197327651 3.44% 3.44395% -0.000074% -0.00214%
13 1143119030269 3.44% 3.44372% 0.000162% 0.00471%
14 1143163371574 3.44% 3.44385% 0.000029% 0.00083%
15 1143159168198 3.44% 3.44384% 0.000041% 0.00120%
16 1143224178550 3.44% 3.44403% -0.000155% -0.00449%
17 1143189657158 3.44% 3.44393% -0.000051% -0.00147%
18 1143169155182 3.44% 3.44387% 0.000011% 0.00032%
19 1143141461159 3.44% 3.44378% 0.000095% 0.00275%
20 1143158851383 3.44% 3.44384% 0.000042% 0.00122%
21 1143163330760 3.44% 3.44385% 0.000029% 0.00083%
22 1143095005326 3.44% 3.44364% 0.000234% 0.00681%
23 1143183714770 3.44% 3.44391% -0.000033% -0.00095%
24 1143162457279 3.44% 3.44385% 0.000031% 0.00091%
25 1143174236636 3.44% 3.44388% -0.000004% -0.00012%
26 1143157243182 3.44% 3.44383% 0.000047% 0.00136%
27 1143157249939 3.44% 3.44383% 0.000047% 0.00136%
28 1143174196490 3.44% 3.44388% -0.000004% -0.00012%
合计 33194352194116 100.00% 100.00000% 0.000000% 0.00000%

独木星空谁 · 发表于 2021-10-27 06:11

组合111 1 2 3 4 5 11 12 13 mod(n,15)
mod(n,15) at b 100周 101周 102周 103周 104周 105周
1→→→ 6 -6 594 600 606 612 618 624
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→→→ 4 0 400 404 408 412 416 420
6→→→ 5 0 500 505 510 515 520 525
7→→→ 5 -1 499 504 509 514 519 524
8→→→ 5 -2 498 503 508 513 518 523
9→→→ 5 -3 497 502 507 512 517 522
10→→→ 3 -2 298 301 304 307 310 313
11→→→ 1 -1 99 100 101 102 103 104
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 -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 2021-10-27 06:11

mod(n,15) 2at^2 2bt c 10周 11周 12周 13周 14周
1→→→ 30 -36 3 1323 1620 1947 2304 2691
2→→→ 36 -36 0 1620 1980 2376 2808 3276
3→→→ 41 -41 1 1846 2256 2707 3199 3732
4→→→ 42 -42 3 1893 2313 2775 3279 3825
5→→→ 39 -39 6 1761 2151 2580 3048 3555
6→→→ 35 -29 7 1612 1965 2353 2776 3234
7→→→ 30 -12 6 1446 1755 2094 2463 2862
8→→→ 27 3 3 1368 1653 1965 2304 2670
9→→→ 29 7 1 1486 1794 2131 2497 2892
10→→→ 36 0 0 1800 2178 2592 3042 3528
11→→→ 39 -9 0 1905 2310 2754 3237 3759
12→→→ 37 -17 0 1765 2145 2562 3016 3507
13→→→ 33 -15 0 1575 1914 2286 2691 3129
14→→→ 30 -6 0 1470 1782 2124 2496 2898
15→→0同 28 10 0 1450 1749 2076 2431 2814
一周汇总 512 -262 30 24320 29565 35322 41591 48372
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 2021-10-27 06:12

mod(n,15) 6at^3 6bt^2 6ct d 5周 6周 7周
1→→→ 289 -672 443 -10 3580 6805 11540
2→→→ 274 -582 404 -16 3604 6760 11366
3→→→ 261 -438 291 -19 3836 7040 11664
4→→→ 257 -285 130 -16 4259 7656 12500
5→→→ 263 -168 -11 -10 4760 8439 13640
6→→→ 280 -132 -64 -4 5226 9220 14850
7→→→ 297 -150 -21 -1 5544 9770 15728
8→→→ 299 -171 82 0 5585 9820 15792
9→→→ 282 -144 174 0 5420 9462 15148
10→→→ 260 -72 220 0 5300 9148 14532
11→→→ 248 36 196 0 5480 9340 14700
12→→→ 249 135 126 0 5855 9900 15484
13→→→ 262 192 26 0 6280 10610 16576
14→→→ 281 201 -50 0 6650 11272 17647
15→→0同 294 192 -78 0 6860 11658 18284
一周汇总 4096 -2058 1868 -76 78239 136900 219451
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 2021-10-27 06:13

mod(n,15) 24at^4 24bt^3 24ct^2 24dt 6e 6周 7周 8周
1→→→ 2115 -4410 3645 -2430 270 79425 155340 275835
2→→→ 2175 -3910 1605 -590 180 84550 164845 291900
3→→→ 2240 -3720 760 360 90 88725 172600 305095
4→→→ 2275 -3590 1025 170 30 92125 178435 314475
5→→→ 2253 -3182 1695 -766 6 95376 183156 320895
6→→→ 2185 -2370 2135 -1830 0 99405 188545 327430
7→→→ 2125 -1290 1955 -2430 0 105465 197435 339550
8→→→ 2115 -230 1305 -2350 0 113510 210280 358750
9→→→ 2155 550 545 -1570 0 121745 224105 380450
10→→→ 2213 942 151 -402 0 128106 235046 398050
11→→→ 2255 1050 325 810 0 131910 241500 408390
12→→→ 2250 1160 1050 1660 0 133930 244300 412100
13→→→ 2195 1510 2005 1970 0 135620 245840 412830
14→→→ 2125 2190 2795 1650 0 139065 250075 417390
15→→0同 2092 3100 3152 920 0 145826 260295 431880
一周汇总 32768 -12200 24148 -4828 576 1694783 3151797 5395020
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 2021-10-27 06:14

mod(n,15) 120at^5 120bt^4 120ct^3 120dt^2 120et 6f 10周 11周
1→→→ 17685 -46065 54525 -16935 -6690 -126 11338434 18701640
2→→→ 17490 -40140 50250 -29160 2280 -36 11624634 19103925
3→→→ 17265 -32165 39725 -40435 15730 -6 12005739 19648100
4→→→ 17172 -23580 23940 -43380 25848 0 12510504 20393604
5→→→ 17292 -16080 7740 -36480 27528 0 13106394 21297144
6→→→ 17541 -10500 -3065 -24060 20204 0 13698592 22204138
7→→→ 17751 -6525 -4965 -11835 6294 0 14198037 22960938
8→→→ 17796 -2850 1560 -4710 -9276 0 14600802 23547843
9→→→ 17653 1955 12625 -3755 -21758 0 14974016 24064722
10→→→ 17403 8580 23025 -6780 -27108 0 15401466 24649317
11→→→ 17205 16455 29085 -9255 -23970 0 15941415 25409406
12→→→ 17195 24280 30085 -7180 -13260 0 16596120 26364866
13→→→ 17370 30780 28710 1620 1440 0 17280720 27387756
14→→→ 17598 35460 29070 16200 15792 0 17877066 28284762
15→→0同 17728 38860 34820 32900 25212 0 18331351 28955542
一周汇总 262144 -21535 357130 -183245 38266 -168 219485290 352973703
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

独舟星海 · 发表于 2021-10-27 07:13

针对素53 针对素53 针对素53 针对素53
统计1+1 统计1+2 统计1+3 统计1+4
638352549929 638352677045 638352650444 638352668646
626082755577 626086743082 626091383091 626081417330
626042193877 626062431327 626072548258 626066444850
626032437601 626049228189 626057500356 626045539890
626094409686 626068347598 626093254847 626088505579
626106475466 626085242767 626084793369 626097085284
626084714163 626058705061 626063440930 626075326427
626067066112 626089356962 626044827141 626076754638
626088251838 626091376317 626060503180 626065237974
626093363543 626076065463 626063066382 626093355552
626108236859 626107081087 626074210729 626086228475
626083461131 626071134451 626085794866 626083476422
626112881214 626098858269 626103646938 626072742654
626105162369 626083288839 626110542250 626079480463
626058159337 626062766774 626069344500 626084848599
626086075389 626080080707 626095945488 626059452895
626083558246 626085689167 626083565291 626088803747
626032977876 626065738282 626060685971 626025572304
626099688437 626096600609 626092233925 626079389850
626092494376 626097544814 626080554719 626095852238
626022516666 626065356414 626057753106 626064244223
626039716140 626051699133 626053571592 626059815822
626115583022 626099375593 626085145692 626087376578
626084468610 626058428029 626068685809 626088062698
626069288553 626091028749 626078720362 626076940718
626054569410 626071681040 626080143877 626084215468
626104874507 626105336997 626061559722 626082934231
626090775324 626085387124 626092036448 626056534673
626066055871 626062018911 626078279273 626066511236
626064202948 626076362581 626072085288 626065732692
626111090036 626098754116 626109785457 626092741346
626058821943 626076101618 626062289508 626049351059
626059201932 626071250004 626086374138 626073806598
626060857573 626057208460 626072148194 626060536526
626074496593 626053724781 626069266829 626086404101
626098540394 626058138156 626082579331 626106938924
626102815248 626101434138 626107853196 626098064344
626063381969 626071607461 626087458545 626065369894
626032858894 626062516623 626046363347 626067912418
626088260141 626100848001 626096690218 626085959082
626080427485 626051316256 626069575078 626094166389
626088265544 626077588865 626077848249 626103125610
626093274864 626066736322 626075949992 626078310380
626053346844 626056716539 626056441119 626061189756
626017702735 626066709993 626067799244 626050612186
626079723581 626073282020 626082820520 626080547290
626113854029 626098792046 626087396450 626073391241
626066943314 626092382092 626074197520 626060954233
626059876300 626064586810 626071586831 626086483990
626067156463 626074349706 626070768280 626065151946
626117864489 626086290828 626090482163 626103213834
626081423812 626072159175 626057295719 626093280583
626063045856 626084068725 626080750344 626084130230

独舟星海 · 发表于 2021-10-27 07:14

数据分析素数53 素数53 素数53 素数53 素数53
素数53 统计1+1 理论占比实际占比占比绝对误差相对误差
0 638352549929 1.923077% 1.92308% 0.000001% 0.00006%
1 626082755577 1.886095% 1.88611% -0.000018% -0.00093%
2 626042193877 1.886095% 1.88599% 0.000105% 0.00554%
3 626032437601 1.886095% 1.88596% 0.000134% 0.00710%
4 626094409686 1.886095% 1.88615% -0.000053% -0.00280%
5 626106475466 1.886095% 1.88618% -0.000089% -0.00472%
6 626084714163 1.886095% 1.88612% -0.000024% -0.00125%
7 626067066112 1.886095% 1.88607% 0.000030% 0.00157%
8 626088251838 1.886095% 1.88613% -0.000034% -0.00181%
9 626093363543 1.886095% 1.88614% -0.000050% -0.00263%
10 626108236859 1.886095% 1.88619% -0.000094% -0.00500%
11 626083461131 1.886095% 1.88611% -0.000020% -0.00105%
12 626112881214 1.886095% 1.88620% -0.000108% -0.00575%
13 626105162369 1.886095% 1.88618% -0.000085% -0.00451%
14 626058159337 1.886095% 1.88604% 0.000056% 0.00299%
15 626086075389 1.886095% 1.88612% -0.000028% -0.00146%
16 626083558246 1.886095% 1.88611% -0.000020% -0.00106%
17 626032977876 1.886095% 1.88596% 0.000132% 0.00702%
18 626099688437 1.886095% 1.88616% -0.000069% -0.00364%
19 626092494376 1.886095% 1.88614% -0.000047% -0.00249%
20 626022516666 1.886095% 1.88593% 0.000164% 0.00869%
21 626039716140 1.886095% 1.88598% 0.000112% 0.00594%
22 626115583022 1.886095% 1.88621% -0.000117% -0.00618%
23 626084468610 1.886095% 1.88612% -0.000023% -0.00121%
24 626069288553 1.886095% 1.88607% 0.000023% 0.00122%
25 626054569410 1.886095% 1.88603% 0.000067% 0.00357%
26 626104874507 1.886095% 1.88618% -0.000084% -0.00447%
27 626090775324 1.886095% 1.88614% -0.000042% -0.00221%
28 626066055871 1.886095% 1.88606% 0.000033% 0.00173%
29 626064202948 1.886095% 1.88606% 0.000038% 0.00203%
30 626111090036 1.886095% 1.88620% -0.000103% -0.00546%
31 626058821943 1.886095% 1.88604% 0.000054% 0.00289%
32 626059201932 1.886095% 1.88604% 0.000053% 0.00283%
33 626060857573 1.886095% 1.88605% 0.000048% 0.00256%
34 626074496593 1.886095% 1.88609% 0.000007% 0.00039%
35 626098540394 1.886095% 1.88616% -0.000065% -0.00346%
36 626102815248 1.886095% 1.88617% -0.000078% -0.00414%
37 626063381969 1.886095% 1.88605% 0.000041% 0.00216%
38 626032858894 1.886095% 1.88596% 0.000133% 0.00704%
39 626088260141 1.886095% 1.88613% -0.000034% -0.00181%
40 626080427485 1.886095% 1.88611% -0.000011% -0.00056%
41 626088265544 1.886095% 1.88613% -0.000034% -0.00181%
42 626093274864 1.886095% 1.88614% -0.000049% -0.00261%
43 626053346844 1.886095% 1.88602% 0.000071% 0.00376%
44 626017702735 1.886095% 1.88592% 0.000178% 0.00946%
45 626079723581 1.886095% 1.88610% -0.000008% -0.00045%
46 626113854029 1.886095% 1.88621% -0.000111% -0.00590%
47 626066943314 1.886095% 1.88606% 0.000030% 0.00159%
48 626059876300 1.886095% 1.88604% 0.000051% 0.00272%
49 626067156463 1.886095% 1.88607% 0.000029% 0.00156%
50 626117864489 1.886095% 1.88622% -0.000123% -0.00654%
51 626081423812 1.886095% 1.88611% -0.000014% -0.00072%
52 626063045856 1.886095% 1.88605% 0.000042% 0.00221%
合计 33194352194116 100.000000% 100.00000% 0.000000% 0.00000%

独舟星海 · 发表于 2021-10-27 07:40

数据分析素数53 素数53 素数53 素数53 素数53
素数53 统计1+2 理论占比实际占比占比绝对误差相对误差
0 638352677045 1.923077% 1.92308% 0.000001% 0.00004%
1 626086743082 1.886095% 1.88612% -0.000030% -0.00157%
2 626062431327 1.886095% 1.88605% 0.000044% 0.00231%
3 626049228189 1.886095% 1.88601% 0.000083% 0.00442%
4 626068347598 1.886095% 1.88607% 0.000026% 0.00137%
5 626085242767 1.886095% 1.88612% -0.000025% -0.00133%
6 626058705061 1.886095% 1.88604% 0.000055% 0.00291%
7 626089356962 1.886095% 1.88613% -0.000038% -0.00199%
8 626091376317 1.886095% 1.88614% -0.000044% -0.00231%
9 626076065463 1.886095% 1.88609% 0.000003% 0.00013%
10 626107081087 1.886095% 1.88619% -0.000091% -0.00482%
11 626071134451 1.886095% 1.88608% 0.000017% 0.00092%
12 626098858269 1.886095% 1.88616% -0.000066% -0.00351%
13 626083288839 1.886095% 1.88611% -0.000019% -0.00102%
14 626062766774 1.886095% 1.88605% 0.000043% 0.00226%
15 626080080707 1.886095% 1.88610% -0.000010% -0.00051%
16 626085689167 1.886095% 1.88612% -0.000026% -0.00140%
17 626065738282 1.886095% 1.88606% 0.000034% 0.00178%
18 626096600609 1.886095% 1.88615% -0.000059% -0.00315%
19 626097544814 1.886095% 1.88616% -0.000062% -0.00330%
20 626065356414 1.886095% 1.88606% 0.000035% 0.00185%
21 626051699133 1.886095% 1.88602% 0.000076% 0.00403%
22 626099375593 1.886095% 1.88616% -0.000068% -0.00359%
23 626058428029 1.886095% 1.88604% 0.000056% 0.00295%
24 626091028749 1.886095% 1.88614% -0.000043% -0.00226%
25 626071681040 1.886095% 1.88608% 0.000016% 0.00084%
26 626105336997 1.886095% 1.88618% -0.000086% -0.00454%
27 626085387124 1.886095% 1.88612% -0.000026% -0.00135%
28 626062018911 1.886095% 1.88605% 0.000045% 0.00238%
29 626076362581 1.886095% 1.88609% 0.000002% 0.00009%
30 626098754116 1.886095% 1.88616% -0.000066% -0.00349%
31 626076101618 1.886095% 1.88609% 0.000002% 0.00013%
32 626071250004 1.886095% 1.88608% 0.000017% 0.00090%
33 626057208460 1.886095% 1.88604% 0.000059% 0.00315%
34 626053724781 1.886095% 1.88602% 0.000070% 0.00370%
35 626058138156 1.886095% 1.88604% 0.000057% 0.00300%
36 626101434138 1.886095% 1.88617% -0.000074% -0.00392%
37 626071607461 1.886095% 1.88608% 0.000016% 0.00085%
38 626062516623 1.886095% 1.88605% 0.000043% 0.00230%
39 626100848001 1.886095% 1.88617% -0.000072% -0.00382%
40 626051316256 1.886095% 1.88602% 0.000077% 0.00409%
41 626077588865 1.886095% 1.88610% -0.000002% -0.00011%
42 626066736322 1.886095% 1.88606% 0.000031% 0.00162%
43 626056716539 1.886095% 1.88603% 0.000061% 0.00323%
44 626066709993 1.886095% 1.88606% 0.000031% 0.00163%
45 626073282020 1.886095% 1.88608% 0.000011% 0.00058%
46 626098792046 1.886095% 1.88616% -0.000066% -0.00350%
47 626092382092 1.886095% 1.88614% -0.000047% -0.00247%
48 626064586810 1.886095% 1.88606% 0.000037% 0.00197%
49 626074349706 1.886095% 1.88609% 0.000008% 0.00041%
50 626086290828 1.886095% 1.88612% -0.000028% -0.00150%
51 626072159175 1.886095% 1.88608% 0.000014% 0.00076%
52 626084068725 1.886095% 1.88612% -0.000022% -0.00114%
合计 33194352194116 100.000000% 100.00000% 0.000000% 0.00000%

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[原创]k生素数群的数量公式

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