[原创]k生素数群的数量公式

独木星空谁 · 发表于 2021-10-21 17:29

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

独木星空谁 · 发表于 2021-10-21 20:02

组合100 1 2 3 4 5 9 14 15 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→→→ 7 -5 695 702 709 716 723 730
4→→→ 7 -4 696 703 710 717 724 731
5→→→ 6 -2 598 604 610 616 622 628
6→→→ 5 0 500 505 510 515 520 525
7→→→ 4 0 400 404 408 412 416 420
8→→→ 5 -2 498 503 508 513 518 523
9→→→ 4 -2 398 402 406 410 414 418
10→→→ 3 0 300 303 306 309 312 315
11→→→ 2 0 200 202 204 206 208 210
12→→→ 2 0 200 202 204 206 208 210
13→→→ 3 -1 299 302 305 308 311 314
14→→→ 4 -2 398 402 406 410 414 418
15→→0 3 -1 299 302 305 308 311 314
一周汇总 64 -27 6373 6437 6501 6565 6629 6693

x+y=N 正整数解组数系数及 a,b值

独木星空谁 · 发表于 2021-10-21 20:02

mod(n,15) 2at^2 2bt c 10周 11周 12周 13周 14周
1→→→ 27 -51 12 1107 1365 1650 1962 2301
2→→→ 33 -63 15 1350 1665 2013 2394 2808
3→→→ 37 -65 15 1540 1896 2289 2719 3186
4→→→ 39 -51 9 1704 2088 2511 2973 3474
5→→→ 39 -33 3 1788 2181 2613 3084 3594
6→→→ 40 -20 0 1900 2310 2760 3250 3780
7→→→ 42 -18 3 2013 2445 2919 3435 3993
8→→→ 42 -18 6 2016 2448 2922 3438 3996
9→→→ 37 -5 3 1828 2214 2637 3097 3594
10→→→ 33 3 0 1665 2013 2394 2808 3255
11→→→ 30 6 0 1530 1848 2196 2574 2982
12→→→ 30 0 1 1501 1816 2161 2536 2941
13→→→ 30 -6 3 1473 1785 2127 2499 2901
14→→→ 27 -3 3 1338 1620 1929 2265 2628
15→→0同 26 4 1 1321 1596 1897 2224 2577
一周汇总 512 -320 74 24074 29290 35018 41258 48010
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 2021-10-21 20:03

mod(n,15) 6at^3 6bt^2 6ct d 5周 6周 7周
1→→→ 245 -564 547 -38 3172 5945 10000
2→→→ 252 -600 612 -44 3216 6040 10176
3→→→ 256 -564 512 -34 3376 6310 10592
4→→→ 261 -489 330 -16 3659 6776 11296
5→→→ 271 -408 185 -4 4096 7489 12372
6→→→ 287 -357 154 -4 4616 8340 13667
7→→→ 302 -300 190 -12 5188 9250 15024
8→→→ 303 -183 162 -12 5673 9960 16004
9→→→ 298 -48 86 -4 6076 10522 16740
10→→→ 290 42 76 0 6280 10768 17010
11→→→ 287 78 121 -1 6404 10920 17184
12→→→ 281 87 190 -4 6371 10824 16992
13→→→ 268 120 200 -6 6244 10562 16528
14→→→ 252 168 156 -4 6076 10232 15956
15→→0同 243 186 129 -1 5944 9992 15560
一周汇总 4096 -2832 3650 -184 76391 133930 215101
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 2021-10-21 20:04

mod(n,15) 24at^4 24bt^3 24ct^2 24dt 6e 6周 7周 8周
1→→→ 2130 -5360 8070 -7480 660 77125 150890 268310
2→→→ 2100 -5020 7560 -7160 630 77875 151795 269185
3→→→ 2075 -4550 6145 -5230 390 79075 153645 271775
4→→→ 2070 -4100 4710 -3280 150 81150 157175 277305
5→→→ 2102 -3772 3850 -2396 60 84746 163551 287750
6→→→ 2155 -3430 3485 -2570 120 90105 172955 303070
7→→→ 2200 -2800 2780 -2540 180 97165 185040 322330
8→→→ 2230 -1860 1670 -1680 120 105785 199450 344820
9→→→ 2255 -890 1045 -850 30 115120 214765 368375
10→→→ 2283 -62 1365 -706 6 124596 230091 391715
11→→→ 2300 620 2260 -860 30 132960 243325 411505
12→→→ 2285 1350 2995 -750 60 139855 253795 426520
13→→→ 2240 2100 3280 -60 60 144775 260795 435830
14→→→ 2190 2700 3510 720 30 148010 265060 440965
15→→0同 2153 3014 4075 1078 6 149771 267100 442971
一周汇总 32768 -22060 56800 -33764 2532 1648113 3069432 5262426
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 2021-10-21 20:05

mod(n,15) 120at^5 120bt^4 120ct^3 120dt^2 120et 6f 10周 11周
1→→→ 17598 -48240 95370 -133200 101592 -1656 11336940 18664986
2→→→ 17403 -42390 83445 -113850 81312 -1296 11577060 19002471
3→→→ 17213 -37015 71045 -88625 50702 -666 11781885 19288466
4→→→ 17103 -32670 62205 -71910 30312 -252 11990934 19587966
5→→→ 17085 -29085 56745 -65955 25530 -216 12233754 19946220
6→→→ 17117 -25010 49715 -60430 25928 -360 12546034 20413960
7→→→ 17172 -19710 38640 -46530 18348 -360 12952194 21024900
8→→→ 17277 -13560 27615 -31080 5868 -180 13472184 21808350
9→→→ 17448 -7210 22320 -24710 -288 -42 14104544 22759752
10→→→ 17655 -720 23625 -26460 1740 -36 14827464 23842296
11→→→ 17808 6480 28200 -26280 5112 -90 15593511 24977322
12→→→ 17868 14430 33200 -16830 4852 -120 16355526 26092772
13→→→ 17853 22305 40125 -705 2142 -90 17070201 27126282
14→→→ 17808 29130 51060 14790 2772 -36 17705550 28035573
15→→0同 17736 34740 65220 26820 8724 -6 18241576 28793148
一周汇总 262144 -148525 748530 -664955 364646 -5406 211789357 341364464
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 2021-10-21 22:59

针对素29 针对素29 针对素29
统计9+10 统计9+11 统计9+12
1185512156492 1185512156492 1185512224657
1143222886382 1143187194164 1143163330760
1143123590123 1143135442067 1143119030269
1143137105814 1143177461971 1143178053273
1143172985375 1143204113243 1143157243182
1143148844614 1143181919885 1143169155182
1143216202098 1143187691743 1143174227038
1143134207814 1143115339942 1143163907408
1143164673516 1143170414295 1143183714770
1143146022754 1143152187302 1143159168198
1143152187302 1143182211696 1143220965505
1143115339942 1143146022754 1143174196490
1143181919885 1143148205912 1143158851383
1143177461971 1143164673516 1143197327651
1143187194164 1143228096056 1143194313589
1143211985229 1143134207814 1143174236636
1143170069021 1143194236966 1143189657158
1143197761314 1143216202098 1143166224821
1143237649625 1143167055359 1143215552900
1143124483344 1143148844614 1143095005326
1143167055359 1143124483344 1143163371574
1143194236966 1143172985375 1143152913392
1143228096056 1143237649625 1143157249939
1143148205912 1143137105814 1143141461159
1143182211696 1143197761314 1143198863052
1143170414295 1143123590123 1143174615431
1143187691743 1143170069021 1143162457279
1143204113243 1143222886382 1143224178550
1143135442067 1143211985229 1143210697544

独舟星海 · 发表于 2021-10-21 22:59

素数29 统计9+10 理论占比实际占比占比绝对误差相对误差
0 1185512156492 3.57% 3.57143% 0.000001% 0.00004%
1 1143222886382 3.44% 3.44403% -0.000151% -0.00438%
2 1143123590123 3.44% 3.44373% 0.000148% 0.00431%
3 1143137105814 3.44% 3.44377% 0.000108% 0.00313%
4 1143172985375 3.44% 3.44388% 0.000000% -0.00001%
5 1143148844614 3.44% 3.44381% 0.000072% 0.00210%
6 1143216202098 3.44% 3.44401% -0.000131% -0.00379%
7 1143134207814 3.44% 3.44376% 0.000116% 0.00338%
8 1143164673516 3.44% 3.44385% 0.000025% 0.00071%
9 1143146022754 3.44% 3.44380% 0.000081% 0.00235%
10 1143152187302 3.44% 3.44382% 0.000062% 0.00181%
11 1143115339942 3.44% 3.44370% 0.000173% 0.00503%
12 1143181919885 3.44% 3.44390% -0.000027% -0.00079%
13 1143177461971 3.44% 3.44389% -0.000014% -0.00040%
14 1143187194164 3.44% 3.44392% -0.000043% -0.00126%
15 1143211985229 3.44% 3.44400% -0.000118% -0.00342%
16 1143170069021 3.44% 3.44387% 0.000008% 0.00024%
17 1143197761314 3.44% 3.44395% -0.000075% -0.00218%
18 1143237649625 3.44% 3.44407% -0.000195% -0.00567%
19 1143124483344 3.44% 3.44373% 0.000146% 0.00423%
20 1143167055359 3.44% 3.44386% 0.000017% 0.00051%
21 1143194236966 3.44% 3.44394% -0.000064% -0.00187%
22 1143228096056 3.44% 3.44404% -0.000166% -0.00483%
23 1143148205912 3.44% 3.44380% 0.000074% 0.00216%
24 1143182211696 3.44% 3.44391% -0.000028% -0.00082%
25 1143170414295 3.44% 3.44387% 0.000007% 0.00021%
26 1143187691743 3.44% 3.44392% -0.000045% -0.00130%
27 1143204113243 3.44% 3.44397% -0.000094% -0.00274%
28 1143135442067 3.44% 3.44376% 0.000113% 0.00327%
合计 33194352194116 100.00% 100.00000% 0.000000% 0.00000%

独舟星海 · 发表于 2021-10-21 22:59

素数29 统计9+11 理论占比实际占比占比绝对误差相对误差
0 1185512156492 3.57% 3.57143% 0.000001% 0.00004%
1 1143187194164 3.44% 3.44392% -0.000043% -0.00126%
2 1143135442067 3.44% 3.44376% 0.000113% 0.00327%
3 1143177461971 3.44% 3.44389% -0.000014% -0.00040%
4 1143204113243 3.44% 3.44397% -0.000094% -0.00274%
5 1143181919885 3.44% 3.44390% -0.000027% -0.00079%
6 1143187691743 3.44% 3.44392% -0.000045% -0.00130%
7 1143115339942 3.44% 3.44370% 0.000173% 0.00503%
8 1143170414295 3.44% 3.44387% 0.000007% 0.00021%
9 1143152187302 3.44% 3.44382% 0.000062% 0.00181%
10 1143182211696 3.44% 3.44391% -0.000028% -0.00082%
11 1143146022754 3.44% 3.44380% 0.000081% 0.00235%
12 1143148205912 3.44% 3.44380% 0.000074% 0.00216%
13 1143164673516 3.44% 3.44385% 0.000025% 0.00071%
14 1143228096056 3.44% 3.44404% -0.000166% -0.00483%
15 1143134207814 3.44% 3.44376% 0.000116% 0.00338%
16 1143194236966 3.44% 3.44394% -0.000064% -0.00187%
17 1143216202098 3.44% 3.44401% -0.000131% -0.00379%
18 1143167055359 3.44% 3.44386% 0.000017% 0.00051%
19 1143148844614 3.44% 3.44381% 0.000072% 0.00210%
20 1143124483344 3.44% 3.44373% 0.000146% 0.00423%
21 1143172985375 3.44% 3.44388% 0.000000% -0.00001%
22 1143237649625 3.44% 3.44407% -0.000195% -0.00567%
23 1143137105814 3.44% 3.44377% 0.000108% 0.00313%
24 1143197761314 3.44% 3.44395% -0.000075% -0.00218%
25 1143123590123 3.44% 3.44373% 0.000148% 0.00431%
26 1143170069021 3.44% 3.44387% 0.000008% 0.00024%
27 1143222886382 3.44% 3.44403% -0.000151% -0.00438%
28 1143211985229 3.44% 3.44400% -0.000118% -0.00342%
合计 33194352194116 100.00% 100.00000% 0.000000% 0.00000%

独舟星海 · 发表于 2021-10-21 23:00

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

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