[原创]k生素数群的数量公式

独木星空谁 · 发表于 2021-10-26 04:11

素数29 统计13+27 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 1143141461159 3.44% 3.44378% 0.000095% 0.00275%
2 1143166224821 3.44% 3.44386% 0.000020% 0.00058%
3 1143174196490 3.44% 3.44388% -0.000004% -0.00012%
4 1143169155182 3.44% 3.44387% 0.000011% 0.00032%
5 1143210697544 3.44% 3.44399% -0.000114% -0.00331%
6 1143157249939 3.44% 3.44383% 0.000047% 0.00136%
7 1143189657158 3.44% 3.44393% -0.000051% -0.00147%
8 1143220965505 3.44% 3.44402% -0.000145% -0.00421%
9 1143157243182 3.44% 3.44383% 0.000047% 0.00136%
10 1143224178550 3.44% 3.44403% -0.000155% -0.00449%
11 1143152913392 3.44% 3.44382% 0.000060% 0.00174%
12 1143174236636 3.44% 3.44388% -0.000004% -0.00012%
13 1143159168198 3.44% 3.44384% 0.000041% 0.00120%
14 1143178053273 3.44% 3.44389% -0.000016% -0.00046%
15 1143162457279 3.44% 3.44385% 0.000031% 0.00091%
16 1143163371574 3.44% 3.44385% 0.000029% 0.00083%
17 1143194313589 3.44% 3.44394% -0.000065% -0.00188%
18 1143183714770 3.44% 3.44391% -0.000033% -0.00095%
19 1143119030269 3.44% 3.44372% 0.000162% 0.00471%
20 1143174615431 3.44% 3.44388% -0.000005% -0.00016%
21 1143095005326 3.44% 3.44364% 0.000234% 0.00681%
22 1143197327651 3.44% 3.44395% -0.000074% -0.00214%
23 1143163907408 3.44% 3.44385% 0.000027% 0.00078%
24 1143163330760 3.44% 3.44385% 0.000029% 0.00083%
25 1143198863052 3.44% 3.44396% -0.000078% -0.00228%
26 1143215552900 3.44% 3.44401% -0.000129% -0.00374%
27 1143158851383 3.44% 3.44384% 0.000042% 0.00122%
28 1143174227038 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 2021-10-26 04:12

素数29 统计13+28 理论占比实际占比占比绝对误差相对误差
0 1185512252119 3.57% 3.57143% 0.000001% 0.00003%
1 1143134393226 3.44% 3.44376% 0.000116% 0.00336%
2 1143167351644 3.44% 3.44386% 0.000017% 0.00048%
3 1143087937215 3.44% 3.44362% 0.000256% 0.00743%
4 1143238818264 3.44% 3.44408% -0.000199% -0.00577%
5 1143223054895 3.44% 3.44403% -0.000151% -0.00439%
6 1143225020595 3.44% 3.44403% -0.000157% -0.00456%
7 1143207215794 3.44% 3.44398% -0.000104% -0.00301%
8 1143170433599 3.44% 3.44387% 0.000007% 0.00021%
9 1143204379004 3.44% 3.44397% -0.000095% -0.00276%
10 1143187580920 3.44% 3.44392% -0.000044% -0.00129%
11 1143184892613 3.44% 3.44391% -0.000036% -0.00105%
12 1143153590211 3.44% 3.44382% 0.000058% 0.00168%
13 1143193624894 3.44% 3.44394% -0.000063% -0.00182%
14 1143127115035 3.44% 3.44374% 0.000138% 0.00400%
15 1143145083805 3.44% 3.44379% 0.000084% 0.00243%
16 1143173037031 3.44% 3.44388% -0.000001% -0.00002%
17 1143176266313 3.44% 3.44389% -0.000010% -0.00030%
18 1143147606067 3.44% 3.44380% 0.000076% 0.00221%
19 1143089676207 3.44% 3.44363% 0.000251% 0.00728%
20 1143171017744 3.44% 3.44387% 0.000005% 0.00016%
21 1143138405814 3.44% 3.44377% 0.000104% 0.00301%
22 1143199176721 3.44% 3.44396% -0.000079% -0.00230%
23 1143150830156 3.44% 3.44381% 0.000066% 0.00193%
24 1143205196456 3.44% 3.44398% -0.000097% -0.00283%
25 1143145690038 3.44% 3.44380% 0.000082% 0.00238%
26 1143216798596 3.44% 3.44401% -0.000132% -0.00385%
27 1143180827910 3.44% 3.44390% -0.000024% -0.00070%
28 1143194921230 3.44% 3.44394% -0.000067% -0.00193%
合计 33194352194116 100.00% 100.00000% 0.000000% 0.00000%

独木星空谁 · 发表于 2021-10-26 06:06

mod(n,15) 2at^2 2bt c 10周 11周 12周 13周 14周
1→→→ 33 -57 12 1377 1695 2046 2430 2847
2→→→ 33 -51 9 1404 1725 2079 2466 2886
3→→→ 40 -62 12 1702 2091 2520 2989 3498
4→→→ 36 -36 3 1623 1983 2379 2811 3279
5→→→ 39 -39 6 1761 2151 2580 3048 3555
6→→→ 40 -26 3 1873 2280 2727 3214 3741
7→→→ 36 -6 0 1770 2145 2556 3003 3486
8→→→ 39 -15 6 1881 2283 2724 3204 3723
9→→→ 35 1 1 1756 2124 2527 2965 3438
10→→→ 33 -3 3 1638 1983 2361 2772 3216
11→→→ 30 -6 3 1473 1785 2127 2499 2901
12→→→ 28 -2 0 1390 1683 2004 2353 2730
13→→→ 30 -12 3 1443 1752 2091 2460 2859
14→→→ 27 -3 0 1335 1617 1926 2262 2625
15→→0同 33 -3 1 1636 1981 2359 2770 3214
一周汇总 512 -320 62 24062 29278 35006 41246 47998
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 2021-10-26 06:07

mod(n,15) 6at^3 6bt^2 6ct d 5周 6周 7周
1→→→ 261 -648 591 -34 3196 6065 10284
2→→→ 256 -540 380 -16 3384 6340 10652
3→→→ 274 -576 470 -28 3672 6850 11480
4→→→ 277 -453 230 -8 4067 7476 12396
5→→→ 283 -384 185 -10 4440 8059 13248
6→→→ 290 -330 172 -12 4798 8620 14072
7→→→ 287 -198 37 -1 5184 9180 14832
8→→→ 293 -165 154 -12 5533 9700 15570
9→→→ 282 -48 102 -4 5756 9962 15844
10→→→ 283 3 146 -4 6026 10348 16369
11→→→ 276 48 192 -6 6104 10410 16388
12→→→ 261 99 150 0 5975 10140 15904
13→→→ 268 60 200 -4 5996 10204 16040
14→→→ 252 120 108 0 5840 9900 15512
15→→0同 253 102 107 -1 5784 9826 15420
一周汇总 4096 -2910 3224 -140 75755 133080 214011
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 2021-10-26 06:08

mod(n,15) 24at^4 24bt^3 24ct^2 24dt 6e 6周 7周 8周
1→→→ 2135 -5770 8365 -6770 510 74300 146315 261415
2→→→ 2115 -5130 6045 -3750 180 76200 149550 266420
3→→→ 2140 -4920 5840 -4380 330 79000 154475 274435
4→→→ 2145 -4290 4155 -2610 150 82825 161025 284795
5→→→ 2174 -3668 2986 -1852 96 88416 170641 300140
6→→→ 2210 -3080 2650 -2380 180 95030 181820 317770
7→→→ 2210 -2140 1390 -1220 30 101865 192995 334825
8→→→ 2255 -1590 1765 -2070 120 109610 205890 354970
9→→→ 2240 -640 1300 -1460 60 116795 217185 371630
10→→→ 2232 48 1680 -1176 30 123191 227071 386045
11→→→ 2240 600 2440 -1080 60 129760 237345 401250
12→→→ 2190 1420 2490 20 0 134780 244475 410700
13→→→ 2190 1660 3630 80 30 138670 250255 418885
14→→→ 2160 2220 3480 1020 0 142095 255220 425620
15→→0同 2132 2596 3676 1196 6 144306 258245 429445
一周汇总 32768 -22684 51892 -26432 1782 1636843 3052507 5238345
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 2021-10-26 06:09

mod(n,15) 120at^5 120bt^4 120ct^3 120dt^2 120et 6f 10周 11周
1→→→ 17397 -50085 96465 -118755 77298 -1116 11034918 18194694
2→→→ 17277 -44310 78915 -83130 39168 -396 11296548 18576129
3→→→ 17301 -40255 70485 -76985 41094 -582 11589465 19015922
4→→→ 17277 -35010 56415 -59130 28368 -396 11903148 19484454
5→→→ 17283 -29625 43335 -43815 16062 -162 12259674 20018796
6→→→ 17414 -24800 36830 -45700 23576 -360 12715738 20709904
7→→→ 17424 -17700 24480 -30900 9216 -90 13224003 21466254
8→→→ 17556 -11970 23880 -36630 13284 -180 13802052 22330443
9→→→ 17634 -4850 20630 -30550 6256 -120 14437793 23273274
10→→→ 17643 2520 21345 -25560 -108 -36 15069060 24196947
11→→→ 17712 8490 29640 -26130 1608 -90 15692844 25109520
12→→→ 17642 15840 32490 -9180 -5672 0 16284294 25960385
13→→→ 17619 21405 44055 -2685 246 -36 16831152 26743854
14→→→ 17532 27090 52140 15570 1788 0 17315124 27428940
15→→0同 17433 32605 59485 33515 7322 -6 17768830 28069018
一周汇总 262144 -150655 690590 -540065 259506 -3570 211224643 340578534
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 2021-10-26 06:42

针对素29 针对素29 针对素29 针对素29
统计14+14 统计14+15 统计14+16 统计14+17
1185511956521 1185512618542 1185512039071 1185512126411
1143145906089 1143168190329 1143194496107 1143163286150
1143284511618 1143184680699 1143227804502 1143244931167
1143165687723 1143191113458 1143178106086 1143179139018
1143183247803 1143177340382 1143194926962 1143157706465
1143132238045 1143140582864 1143167311379 1143161526285
1143123794016 1143152369135 1143104452910 1143140751682
1143104957678 1143131358172 1143155256996 1143067516597
1143202485099 1143221686363 1143153792071 1143163886743
1143171264645 1143180229396 1143194168651 1143177133783
1143125277581 1143184277436 1143077456426 1143105155917
1143192727325 1143199790034 1143158359358 1143216879943
1143207916089 1143206672214 1143189748202 1143175771368
1143242906967 1143136481764 1143193428120 1143207156225
1143146748927 1143145015541 1143139442063 1143156079152
1143143769045 1143145015541 1143146503191 1143180398132
1143030115628 1143136481764 1143088415121 1143109548781
1143205415923 1143206672214 1143194297812 1143176011841
1143206422842 1143199790034 1143193682015 1143204612964
1143243224238 1143184277436 1143243063736 1143263828525
1143189015894 1143180229396 1143177315379 1143180269353
1143241018257 1143221686363 1143199292907 1143242136025
1143157790494 1143131358172 1143182898745 1143200316137
1143180898359 1143152369135 1143232504838 1143143058312
1143148899807 1143140582864 1143195021093 1143147491991
1143171757448 1143177340382 1143182160159 1143160175095
1143216917838 1143191113458 1143181534960 1143211791828
1143084747005 1143184680699 1143136903976 1143146245858
1143190575212 1143168190329 1143157811280 1143157262368

独舟星海 · 发表于 2021-10-26 06:43

针对素29 针对素29 针对素29 针对素29
统计14+18 统计14+19 统计14+20 统计14+21
1185512191410 1185512252119 1185511975239 1185512252119
1143164464469 1143087937215 1143193315399 1143167351644
1143243485584 1143225020595 1143263617598 1143238818264
1143186711936 1143204379004 1143148926314 1143225020595
1143106756314 1143153590211 1143200218506 1143170433599
1143160634777 1143145083805 1143169408058 1143187580920
1143136287128 1143147606067 1143124568587 1143153590211
1143147891069 1143138405814 1143194811867 1143127115035
1143183894226 1143205196456 1143191685695 1143173037031
1143138315674 1143180827910 1143157545600 1143147606067
1143158962143 1143134393226 1143114977673 1143171017744
1143168229663 1143238818264 1143191497854 1143199176721
1143225572516 1143207215794 1143198379334 1143205196456
1143211691201 1143187580920 1143225495712 1143216798596
1143115801436 1143193624894 1143164960412 1143194921230
1143214169257 1143173037031 1143157750453 1143134393226
1143077033981 1143089676207 1143117788669 1143087937215
1143165329654 1143199176721 1143188251662 1143223054895
1143176634594 1143145690038 1143176164442 1143207215794
1143224966108 1143194921230 1143200495427 1143204379004
1143173451312 1143167351644 1143167905732 1143184892613
1143228928332 1143223054895 1143182322520 1143193624894
1143151655121 1143170433599 1143121307306 1143145083805
1143156496791 1143184892613 1143211910006 1143176266313
1143160223728 1143127115035 1143170828801 1143089676207
1143207216605 1143176266313 1143168826148 1143138405814
1143211172106 1143171017744 1143183104368 1143150830156
1143162867972 1143150830156 1143057529231 1143145690038
1143181159009 1143216798596 1143196625503 1143180827910

独舟星海 · 发表于 2021-10-26 06:44

素数29 统计14+14 理论占比实际占比占比绝对误差相对误差
0 1185511956521 3.57% 3.57143% 0.000002% 0.00005%
1 1143145906089 3.44% 3.44380% 0.000081% 0.00236%
2 1143284511618 3.44% 3.44421% -0.000336% -0.00977%
3 1143165687723 3.44% 3.44386% 0.000022% 0.00063%
4 1143183247803 3.44% 3.44391% -0.000031% -0.00091%
5 1143132238045 3.44% 3.44376% 0.000122% 0.00355%
6 1143123794016 3.44% 3.44373% 0.000148% 0.00429%
7 1143104957678 3.44% 3.44367% 0.000205% 0.00594%
8 1143202485099 3.44% 3.44397% -0.000089% -0.00259%
9 1143171264645 3.44% 3.44387% 0.000005% 0.00014%
10 1143125277581 3.44% 3.44373% 0.000143% 0.00416%
11 1143192727325 3.44% 3.44394% -0.000060% -0.00174%
12 1143207916089 3.44% 3.44398% -0.000106% -0.00307%
13 1143242906967 3.44% 3.44409% -0.000211% -0.00613%
14 1143146748927 3.44% 3.44380% 0.000079% 0.00228%
15 1143143769045 3.44% 3.44379% 0.000088% 0.00254%
16 1143030115628 3.44% 3.44345% 0.000430% 0.01249%
17 1143205415923 3.44% 3.44398% -0.000098% -0.00285%
18 1143206422842 3.44% 3.44398% -0.000101% -0.00294%
19 1143243224238 3.44% 3.44409% -0.000212% -0.00616%
20 1143189015894 3.44% 3.44393% -0.000049% -0.00141%
21 1143241018257 3.44% 3.44408% -0.000205% -0.00596%
22 1143157790494 3.44% 3.44383% 0.000045% 0.00132%
23 1143180898359 3.44% 3.44390% -0.000024% -0.00070%
24 1143148899807 3.44% 3.44381% 0.000072% 0.00209%
25 1143171757448 3.44% 3.44387% 0.000003% 0.00009%
26 1143216917838 3.44% 3.44401% -0.000133% -0.00386%
27 1143084747005 3.44% 3.44361% 0.000265% 0.00771%
28 1143190575212 3.44% 3.44393% -0.000053% -0.00155%
合计 33194352194116 100.00% 100.00000% 0.000000% 0.00000%

独舟星海 · 发表于 2021-10-26 06:44

素数29 统计14+15 理论占比实际占比占比绝对误差相对误差
0 1185512618542 3.57% 3.57143% 0.000000% 0.00000%
1 1143168190329 3.44% 3.44386% 0.000014% 0.00041%
2 1143184680699 3.44% 3.44391% -0.000036% -0.00104%
3 1143191113458 3.44% 3.44393% -0.000055% -0.00160%
4 1143177340382 3.44% 3.44389% -0.000014% -0.00039%
5 1143140582864 3.44% 3.44378% 0.000097% 0.00282%
6 1143152369135 3.44% 3.44382% 0.000062% 0.00179%
7 1143131358172 3.44% 3.44375% 0.000125% 0.00363%
8 1143221686363 3.44% 3.44402% -0.000147% -0.00427%
9 1143180229396 3.44% 3.44390% -0.000022% -0.00065%
10 1143184277436 3.44% 3.44391% -0.000034% -0.00100%
11 1143199790034 3.44% 3.44396% -0.000081% -0.00236%
12 1143206672214 3.44% 3.44398% -0.000102% -0.00296%
13 1143136481764 3.44% 3.44377% 0.000110% 0.00318%
14 1143145015541 3.44% 3.44379% 0.000084% 0.00243%
15 1143145015541 3.44% 3.44379% 0.000084% 0.00243%
16 1143136481764 3.44% 3.44377% 0.000110% 0.00318%
17 1143206672214 3.44% 3.44398% -0.000102% -0.00296%
18 1143199790034 3.44% 3.44396% -0.000081% -0.00236%
19 1143184277436 3.44% 3.44391% -0.000034% -0.00100%
20 1143180229396 3.44% 3.44390% -0.000022% -0.00065%
21 1143221686363 3.44% 3.44402% -0.000147% -0.00427%
22 1143131358172 3.44% 3.44375% 0.000125% 0.00363%
23 1143152369135 3.44% 3.44382% 0.000062% 0.00179%
24 1143140582864 3.44% 3.44378% 0.000097% 0.00282%
25 1143177340382 3.44% 3.44389% -0.000014% -0.00039%
26 1143191113458 3.44% 3.44393% -0.000055% -0.00160%
27 1143184680699 3.44% 3.44391% -0.000036% -0.00104%
28 1143168190329 3.44% 3.44386% 0.000014% 0.00041%
合计 33194352194116 100.00% 100.00000% 0.000000% 0.00000%

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