[原创]k生素数群的数量公式

独舟星海 · 发表于 2021-11-18 07:26

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+27 理论占比实际占比占比绝对误差相对误差
0 638352770289 1.923077% 1.92308% 0.000000% 0.00002%
1 626061285738 1.886095% 1.88605% 0.000047% 0.00250%
2 626092575360 1.886095% 1.88614% -0.000047% -0.00250%
3 626071596400 1.886095% 1.88608% 0.000016% 0.00085%
4 626085503040 1.886095% 1.88612% -0.000026% -0.00137%
5 626098173638 1.886095% 1.88616% -0.000064% -0.00340%
6 626089424749 1.886095% 1.88613% -0.000038% -0.00200%
7 626072085200 1.886095% 1.88608% 0.000015% 0.00077%
8 626062796874 1.886095% 1.88605% 0.000043% 0.00225%
9 626096448352 1.886095% 1.88615% -0.000059% -0.00312%
10 626043452716 1.886095% 1.88599% 0.000101% 0.00534%
11 626099427026 1.886095% 1.88616% -0.000068% -0.00360%
12 626050989549 1.886095% 1.88602% 0.000078% 0.00414%
13 626079436081 1.886095% 1.88610% -0.000008% -0.00040%
14 626088482757 1.886095% 1.88613% -0.000035% -0.00185%
15 626072274540 1.886095% 1.88608% 0.000014% 0.00074%
16 626076879118 1.886095% 1.88609% 0.000000% 0.00000%
17 626045961187 1.886095% 1.88600% 0.000093% 0.00494%
18 626080827943 1.886095% 1.88611% -0.000012% -0.00063%
19 626066291081 1.886095% 1.88606% 0.000032% 0.00170%
20 626093236451 1.886095% 1.88614% -0.000049% -0.00261%
21 626086344922 1.886095% 1.88612% -0.000028% -0.00151%
22 626038578009 1.886095% 1.88598% 0.000115% 0.00612%
23 626102859252 1.886095% 1.88617% -0.000078% -0.00414%
24 626072246371 1.886095% 1.88608% 0.000014% 0.00074%
25 626115914773 1.886095% 1.88621% -0.000118% -0.00623%
26 626061838274 1.886095% 1.88605% 0.000045% 0.00241%
27 626052646710 1.886095% 1.88602% 0.000073% 0.00388%
28 626049969570 1.886095% 1.88601% 0.000081% 0.00430%
29 626086638468 1.886095% 1.88612% -0.000029% -0.00155%
30 626070655567 1.886095% 1.88608% 0.000019% 0.00100%
31 626066731375 1.886095% 1.88606% 0.000031% 0.00163%
32 626085858179 1.886095% 1.88612% -0.000027% -0.00143%
33 626082376047 1.886095% 1.88611% -0.000016% -0.00087%
34 626092418893 1.886095% 1.88614% -0.000047% -0.00248%
35 626074157051 1.886095% 1.88609% 0.000008% 0.00044%
36 626092762147 1.886095% 1.88614% -0.000048% -0.00253%
37 626053579038 1.886095% 1.88602% 0.000070% 0.00373%
38 626093434429 1.886095% 1.88614% -0.000050% -0.00264%
39 626069449321 1.886095% 1.88607% 0.000022% 0.00119%
40 626099402176 1.886095% 1.88616% -0.000068% -0.00359%
41 626091202967 1.886095% 1.88614% -0.000043% -0.00228%
42 626060892490 1.886095% 1.88605% 0.000048% 0.00256%
43 626065287709 1.886095% 1.88606% 0.000035% 0.00186%
44 626090831677 1.886095% 1.88614% -0.000042% -0.00222%
45 626072509170 1.886095% 1.88608% 0.000013% 0.00070%
46 626060530521 1.886095% 1.88605% 0.000049% 0.00262%
47 626071615820 1.886095% 1.88608% 0.000016% 0.00085%
48 626083090175 1.886095% 1.88611% -0.000019% -0.00099%
49 626071345171 1.886095% 1.88608% 0.000017% 0.00089%
50 626077699388 1.886095% 1.88610% -0.000002% -0.00013%
51 626086030896 1.886095% 1.88612% -0.000027% -0.00146%
52 626093379471 1.886095% 1.88614% -0.000050% -0.00263%
合计 33194352194116 100.000000% 100.00000% 0.000000% 0.00000%

独舟星海 · 发表于 2021-11-18 09:37

针对素53 针对素53 针对素53 针对素53
统计4+28 统计4+29 统计4+30 统计4+31
638352681135 638352802673 638352686677 638352710821
626091527226 626081848967 626082370830 626096673291
626091369336 626103046139 626102224150 626079984852
626050256388 626059566222 626070867868 626080528658
626057805627 626050263276 626085364328 626071242207
626064130763 626065193430 626090747301 626077654178
626080271152 626085711975 626062555579 626078954776
626083214264 626077769551 626064278061 626072199394
626062970957 626070332911 626048417841 626047817158
626088994299 626103583988 626076575734 626067735253
626078811276 626079537326 626082166341 626061289729
626069106097 626084666311 626085995167 626094231407
626060437111 626068911280 626058015152 626032871409
626035616956 626058401192 626063915742 626085809560
626101024453 626085486685 626102788006 626102378277
626070672604 626058833694 626061813058 626036714603
626104232626 626063815916 626106109422 626077723761
626041113833 626041854616 626020025505 626048804263
626085657736 626073492619 626056009112 626076566043
626079705001 626108850319 626102480146 626091512719
626082534479 626097365183 626104480848 626086039491
626069168530 626085924757 626082219620 626079781714
626088648579 626085309248 626061791999 626060981159
626076571700 626090070492 626077785014 626087723943
626083977423 626073850552 626100151926 626084432234
626088390888 626110921573 626096825119 626106048667
626079796720 626050489604 626073603482 626063936190
626061062986 626040819638 626027610387 626053726069
626074922136 626060406782 626077608610 626083468891
626065102536 626074786982 626062873358 626089176702
626048405688 626093504313 626078589820 626083914410
626036435705 626062081881 626054380787 626061390950
626088316066 626081257405 626077430975 626096761214
626087627140 626069633529 626046438118 626057452112
626102335926 626065592840 626089378903 626080974648
626101866524 626086914046 626111909390 626091260836
626081316089 626074063978 626077032132 626090826706
626067183668 626084937974 626049895885 626044793095
626078205729 626084846635 626103961284 626080953283
626094372892 626095033502 626075798640 626050917981
626100796477 626095741966 626100434704 626070334391
626098850547 626104314058 626105640217 626102001624
626064703812 626048107973 626088110651 626076980047
626076230970 626068325652 626083747418 626078871147
626075143936 626075467196 626094992758 626082331958
626096244091 626090470256 626073666230 626094745542
626069124429 626048646032 626057002461 626074193788
626061034094 626067585673 626047177384 626064537069
626086068248 626097002489 626065271985 626113306235
626074420672 626078112596 626060753225 626084590369
626084897936 626055495240 626075880659 626060670808
626089628769 626081954337 626086155585 626084775623
626069209891 626099190644 626108188522 626096892861

独舟星海 · 发表于 2021-11-18 09:38

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+28 理论占比实际占比占比绝对误差相对误差
0 638352681135 1.923077% 1.92308% 0.000001% 0.00004%
1 626091527226 1.886095% 1.88614% -0.000044% -0.00233%
2 626091369336 1.886095% 1.88614% -0.000044% -0.00231%
3 626050256388 1.886095% 1.88601% 0.000080% 0.00426%
4 626057805627 1.886095% 1.88604% 0.000058% 0.00305%
5 626064130763 1.886095% 1.88606% 0.000038% 0.00204%
6 626080271152 1.886095% 1.88610% -0.000010% -0.00054%
7 626083214264 1.886095% 1.88611% -0.000019% -0.00101%
8 626062970957 1.886095% 1.88605% 0.000042% 0.00223%
9 626088994299 1.886095% 1.88613% -0.000036% -0.00193%
10 626078811276 1.886095% 1.88610% -0.000006% -0.00030%
11 626069106097 1.886095% 1.88607% 0.000024% 0.00125%
12 626060437111 1.886095% 1.88605% 0.000050% 0.00263%
13 626035616956 1.886095% 1.88597% 0.000124% 0.00660%
14 626101024453 1.886095% 1.88617% -0.000073% -0.00385%
15 626070672604 1.886095% 1.88608% 0.000019% 0.00100%
16 626104232626 1.886095% 1.88618% -0.000082% -0.00436%
17 626041113833 1.886095% 1.88599% 0.000108% 0.00572%
18 626085657736 1.886095% 1.88612% -0.000026% -0.00140%
19 626079705001 1.886095% 1.88610% -0.000008% -0.00045%
20 626082534479 1.886095% 1.88611% -0.000017% -0.00090%
21 626069168530 1.886095% 1.88607% 0.000023% 0.00124%
22 626088648579 1.886095% 1.88613% -0.000035% -0.00188%
23 626076571700 1.886095% 1.88609% 0.000001% 0.00005%
24 626083977423 1.886095% 1.88612% -0.000021% -0.00113%
25 626088390888 1.886095% 1.88613% -0.000035% -0.00183%
26 626079796720 1.886095% 1.88610% -0.000009% -0.00046%
27 626061062986 1.886095% 1.88605% 0.000048% 0.00253%
28 626074922136 1.886095% 1.88609% 0.000006% 0.00032%
29 626065102536 1.886095% 1.88606% 0.000036% 0.00189%
30 626048405688 1.886095% 1.88601% 0.000086% 0.00455%
31 626036435705 1.886095% 1.88597% 0.000122% 0.00646%
32 626088316066 1.886095% 1.88613% -0.000034% -0.00182%
33 626087627140 1.886095% 1.88613% -0.000032% -0.00171%
34 626102335926 1.886095% 1.88617% -0.000077% -0.00406%
35 626101866524 1.886095% 1.88617% -0.000075% -0.00399%
36 626081316089 1.886095% 1.88611% -0.000013% -0.00070%
37 626067183668 1.886095% 1.88607% 0.000029% 0.00155%
38 626078205729 1.886095% 1.88610% -0.000004% -0.00021%
39 626094372892 1.886095% 1.88615% -0.000053% -0.00279%
40 626100796477 1.886095% 1.88617% -0.000072% -0.00382%
41 626098850547 1.886095% 1.88616% -0.000066% -0.00350%
42 626064703812 1.886095% 1.88606% 0.000037% 0.00195%
43 626076230970 1.886095% 1.88609% 0.000002% 0.00011%
44 626075143936 1.886095% 1.88609% 0.000005% 0.00028%
45 626096244091 1.886095% 1.88615% -0.000058% -0.00309%
46 626069124429 1.886095% 1.88607% 0.000023% 0.00124%
47 626061034094 1.886095% 1.88605% 0.000048% 0.00254%
48 626086068248 1.886095% 1.88612% -0.000028% -0.00146%
49 626074420672 1.886095% 1.88609% 0.000007% 0.00040%
50 626084897936 1.886095% 1.88612% -0.000024% -0.00128%
51 626089628769 1.886095% 1.88613% -0.000038% -0.00203%
52 626069209891 1.886095% 1.88607% 0.000023% 0.00123%
合计 33194352194116 100.000000% 100.00000% 0.000000% 0.00000%

白新岭 · 发表于 2021-11-18 09:39

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+29 理论占比实际占比占比绝对误差相对误差
0 638352802673 1.923077% 1.92308% 0.000000% 0.00002%
1 626081848967 1.886095% 1.88611% -0.000015% -0.00079%
2 626103046139 1.886095% 1.88617% -0.000079% -0.00417%
3 626059566222 1.886095% 1.88604% 0.000052% 0.00277%
4 626050263276 1.886095% 1.88601% 0.000080% 0.00426%
5 626065193430 1.886095% 1.88606% 0.000035% 0.00187%
6 626085711975 1.886095% 1.88612% -0.000027% -0.00141%
7 626077769551 1.886095% 1.88610% -0.000003% -0.00014%
8 626070332911 1.886095% 1.88607% 0.000020% 0.00105%
9 626103583988 1.886095% 1.88618% -0.000080% -0.00426%
10 626079537326 1.886095% 1.88610% -0.000008% -0.00042%
11 626084666311 1.886095% 1.88612% -0.000023% -0.00124%
12 626068911280 1.886095% 1.88607% 0.000024% 0.00128%
13 626058401192 1.886095% 1.88604% 0.000056% 0.00296%
14 626085486685 1.886095% 1.88612% -0.000026% -0.00137%
15 626058833694 1.886095% 1.88604% 0.000054% 0.00289%
16 626063815916 1.886095% 1.88606% 0.000039% 0.00209%
17 626041854616 1.886095% 1.88599% 0.000106% 0.00560%
18 626073492619 1.886095% 1.88608% 0.000010% 0.00055%
19 626108850319 1.886095% 1.88619% -0.000096% -0.00510%
20 626097365183 1.886095% 1.88616% -0.000062% -0.00327%
21 626085924757 1.886095% 1.88612% -0.000027% -0.00144%
22 626085309248 1.886095% 1.88612% -0.000025% -0.00134%
23 626090070492 1.886095% 1.88613% -0.000040% -0.00210%
24 626073850552 1.886095% 1.88609% 0.000009% 0.00049%
25 626110921573 1.886095% 1.88620% -0.000102% -0.00543%
26 626050489604 1.886095% 1.88602% 0.000080% 0.00422%
27 626040819638 1.886095% 1.88599% 0.000109% 0.00576%
28 626060406782 1.886095% 1.88604% 0.000050% 0.00264%
29 626074786982 1.886095% 1.88609% 0.000006% 0.00034%
30 626093504313 1.886095% 1.88614% -0.000050% -0.00265%
31 626062081881 1.886095% 1.88605% 0.000045% 0.00237%
32 626081257405 1.886095% 1.88611% -0.000013% -0.00069%
33 626069633529 1.886095% 1.88607% 0.000022% 0.00116%
34 626065592840 1.886095% 1.88606% 0.000034% 0.00181%
35 626086914046 1.886095% 1.88612% -0.000030% -0.00160%
36 626074063978 1.886095% 1.88609% 0.000009% 0.00045%
37 626084937974 1.886095% 1.88612% -0.000024% -0.00128%
38 626084846635 1.886095% 1.88612% -0.000024% -0.00127%
39 626095033502 1.886095% 1.88615% -0.000055% -0.00289%
40 626095741966 1.886095% 1.88615% -0.000057% -0.00301%
41 626104314058 1.886095% 1.88618% -0.000083% -0.00438%
42 626048107973 1.886095% 1.88601% 0.000087% 0.00460%
43 626068325652 1.886095% 1.88607% 0.000026% 0.00137%
44 626075467196 1.886095% 1.88609% 0.000004% 0.00023%
45 626090470256 1.886095% 1.88614% -0.000041% -0.00217%
46 626048646032 1.886095% 1.88601% 0.000085% 0.00451%
47 626067585673 1.886095% 1.88607% 0.000028% 0.00149%
48 626097002489 1.886095% 1.88616% -0.000061% -0.00321%
49 626078112596 1.886095% 1.88610% -0.000004% -0.00019%
50 626055495240 1.886095% 1.88603% 0.000065% 0.00342%
51 626081954337 1.886095% 1.88611% -0.000015% -0.00081%
52 626099190644 1.886095% 1.88616% -0.000067% -0.00356%
合计 33194352194116 100.000000% 100.00000% 0.000000% 0.00000%

白新岭 · 发表于 2021-11-18 09:53

截止2021年11月17日周三22:08分浏览量78125,,回复6486热度150度。参照浏览量73213，差距 4912
截止2021年11月18日周四09:44分浏览量78224,,回复6506热度150度。参照浏览量73224，差距 5000
浏览量 ↑ 99, 回复↑ 14热度↑ 。参照浏览量↑ 11, 差距 ↑ 88
上午好!

独舟星海 · 发表于 2021-11-18 19:12

组合187 1 2 3 4 6 10 11 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→→→ 3 0 300 303 306 309 312 315
5→→→ 7 -3 697 704 711 718 725 732
6→→→ 5 -2 498 503 508 513 518 523
7→→→ 5 -1 499 504 509 514 519 524
8→→→ 3 0 300 303 306 309 312 315
9→→→ 4 -2 398 402 406 410 414 418
10→→→ 4 -2 398 402 406 410 414 418
11→→→ 2 0 200 202 204 206 208 210
12→→→ 5 0 500 505 510 515 520 525
13→→→ 5 -1 499 504 509 514 519 524
14→→→ 4 0 400 404 408 412 416 420
15→→0 4 0 400 404 408 412 416 420
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

独舟星海 · 发表于 2021-11-18 19:13

mod(n,15) 2at^2 2bt c 10周 11周 12周 13周 14周
1→→→ 39 -63 12 1647 2025 2442 2898 3393
2→→→ 33 -45 6 1431 1755 2112 2502 2925
3→→→ 33 -33 1 1486 1816 2179 2575 3004
4→→→ 36 -42 6 1596 1953 2346 2775 3240
5→→→ 33 -33 6 1491 1821 2184 2580 3009
6→→→ 34 -20 3 1603 1950 2331 2746 3195
7→→→ 33 -9 0 1605 1947 2322 2730 3171
8→→→ 39 -15 3 1878 2280 2721 3201 3720
9→→→ 37 -11 3 1798 2181 2601 3058 3552
10→→→ 30 0 0 1500 1815 2160 2535 2940
11→→→ 36 -6 0 1770 2145 2556 3003 3486
12→→→ 32 -8 1 1561 1893 2257 2653 3081
13→→→ 33 3 0 1665 2013 2394 2808 3255
14→→→ 30 12 0 1560 1881 2232 2613 3024
15→→0同 34 14 0 1770 2134 2532 2964 3430
一周汇总 512 -256 41 24361 29609 35369 41641 48425
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 2021-11-18 19:13

mod(n,15) 6at^3 6bt^2 6ct d 5周 6周 7周
1→→→ 259 -504 341 -16 3564 6625 11072
2→→→ 272 -444 196 -4 3976 7320 12148
3→→→ 276 -432 216 -10 4120 7550 12492
4→→→ 281 -381 178 -12 4403 7996 13148
5→→→ 272 -288 76 -6 4524 8134 13280
6→→→ 268 -228 20 0 4650 8300 13482
7→→→ 282 -228 90 -4 4996 8870 14360
8→→→ 271 -147 86 -4 5101 8956 14388
9→→→ 265 -24 23 0 5440 9419 14980
10→→→ 279 3 54 0 5870 10116 16037
11→→→ 277 30 83 -1 5964 10234 16176
12→→→ 281 87 58 0 6265 10696 16842
13→→→ 264 156 12 0 6160 10452 16380
14→→→ 273 177 30 0 6450 10920 17087
15→→0同 276 192 84 0 6620 11172 17444
一周汇总 4096 -2031 1547 -57 78103 136760 219316
x+y+z+u=N 正整数解组数及a,b c,d 的值

独舟星海 · 发表于 2021-11-18 19:14

mod(n,15) 24at^4 24bt^3 24ct^2 24dt 6e 6周 7周
1→→→ 2185 -4830 3935 -1530 60 80050 157160
2→→→ 2175 -4430 3585 -1690 90 82550 161120
3→→→ 2195 -3930 3025 -1770 120 87275 169105
4→→→ 2155 -3070 1685 -1010 60 91025 174870
5→→→ 2173 -2438 911 -622 0 96611 184226
6→→→ 2215 -2090 1085 -1210 30 102130 193590
7→→→ 2185 -1430 695 -1210 30 105865 199225
8→→→ 2185 -670 -85 -590 0 111685 208670
9→→→ 2185 -210 35 -450 0 116040 215530
10→→→ 2193 270 567 -510 6 121576 224260
11→→→ 2185 930 875 -270 0 127605 233590
12→→→ 2155 1710 845 210 0 133080 241815
13→→→ 2205 2210 1335 370 0 141055 255010
14→→→ 2205 2650 1995 230 0 145970 262605
15→→0同 2172 3348 2280 264 0 150906 269871
一周汇总 32768 -11980 22768 -9788 396 1693423 3150647
x+y+z+u+v=N 的正整数解组数，及系数 a,b,c,d,e 的值

独舟星海 · 发表于 2021-11-18 19:14

mod(n,15) 120at^5 120bt^4 120ct^3 120dt^2 120et 6f 10周
1→→→ 17493 -42195 47085 -37365 17502 -126 11423925
2→→→ 17547 -36870 38325 -35130 19728 -180 11841714
3→→→ 17417 -30145 24425 -21455 11558 -90 12188694
4→→→ 17475 -24600 15585 -13560 5100 0 12631500
5→→→ 17508 -19770 13500 -18030 7512 -36 13040595
6→→→ 17433 -13530 9295 -18510 6152 -36 13462540
7→→→ 17448 -6990 3720 -12450 -1008 0 13978041
8→→→ 17448 -1290 3120 -11850 -4908 0 14448216
9→→→ 17556 4090 5920 -15730 -4996 -6 15006641
10→→→ 17487 10230 7425 -15630 -5112 0 15473424
11→→→ 17433 16635 8445 -9075 -6798 0 15975996
12→→→ 17528 21770 15000 -4070 -6308 0 16541916
13→→→ 17478 27120 24150 -120 -3108 0 17025891
14→→→ 17445 33750 31875 7650 0 0 17622000
15→→0同 17448 39810 40820 17550 1492 0 18212416
一周汇总 262144 -21985 288690 -187775 36806 -474 218873509
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

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