[原创]k生素数群的数量公式

独舟星海 · 发表于 2021-11-18 06:29

mod(n,15) 120at^5 120bt^4 120ct^3 120dt^2 120et 6f 10周
1→→→ 17208 -31290 12960 -5790 6912 0 11836251
2→→→ 17436 -25710 1620 690 5964 0 12402072
3→→→ 17693 -21205 -5815 5245 4082 0 12933336
4→→→ 17763 -16830 -8715 5670 2112 0 13332276
5→→→ 17667 -12105 -8385 2745 78 0 13646169
6→→→ 17433 -6250 -6905 -2510 -1648 0 13946896
7→→→ 17280 630 -6240 -7830 -3120 0 14393715
8→→→ 17208 8160 -6780 -12300 -3768 0 14952936
9→→→ 17328 15110 -7080 -14750 -3888 0 15627551
10→→→ 17508 20820 -5640 -14880 -3408 0 16265316
11→→→ 17718 25260 -1230 -12300 -2808 0 16849266
12→→→ 17760 29550 6600 -7650 -2340 0 17310930
13→→→ 17622 34530 17790 -1770 -2652 0 17709054
14→→→ 17352 40680 31440 4680 -3432 0 18115614
15→→0同 17168 47610 46020 10950 -4628 0 18666406
一周汇总 262144 108960 59640 -49800 -12544 0 227987788
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 2021-11-18 07:21

组合186 1 2 3 4 6 10 11 13 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→→→ 2 0 200 202 204 206 208 210
4→→→ 5 -2 498 503 508 513 518 523
5→→→ 5 -1 499 504 509 514 519 524
6→→→ 5 -2 498 503 508 513 518 523
7→→→ 5 -1 499 504 509 514 519 524
8→→→ 5 -2 498 503 508 513 518 523
9→→→ 4 -2 398 402 406 410 414 418
10→→→ 2 0 200 202 204 206 208 210
11→→→ 3 -1 299 302 305 308 311 314
12→→→ 5 0 500 505 510 515 520 525
13→→→ 4 0 400 404 408 412 416 420
14→→→ 6 0 600 606 612 618 624 630
15→→0 4 0 400 404 408 412 416 420
一周汇总 64 -19 6381 6445 6509 6573 6637 6701

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 07:21

mod(n,15) 2at^2 2bt c 10周 11周 12周 13周 14周
1→→→ 33 -39 3 1458 1785 2145 2538 2964
2→→→ 36 -48 6 1566 1920 2310 2736 3198
3→→→ 39 -45 4 1729 2116 2542 3007 3511
4→→→ 33 -39 6 1461 1788 2148 2541 2967
5→→→ 33 -27 3 1518 1851 2217 2616 3048
6→→→ 31 -17 3 1468 1785 2133 2512 2922
7→→→ 33 -15 3 1578 1917 2289 2694 3132
8→→→ 36 -6 0 1770 2145 2556 3003 3486
9→→→ 35 -5 1 1726 2091 2491 2926 3396
10→→→ 39 -9 0 1905 2310 2754 3237 3759
11→→→ 33 -3 0 1635 1980 2358 2769 3213
12→→→ 34 -8 0 1660 2013 2400 2821 3276
13→→→ 30 6 0 1530 1848 2196 2574 2982
14→→→ 30 12 0 1560 1881 2232 2613 3024
15→→0同 37 17 0 1935 2332 2766 3237 3745
一周汇总 512 -226 29 24499 29762 35537 41824 48623
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 07:22

mod(n,15) 6at^3 6bt^2 6ct d 5周 6周 7周
1→→→ 273 -516 303 -10 3780 7025 11736
2→→→ 260 -408 220 -12 3888 7120 11776
3→→→ 272 -372 136 -6 4224 7690 12664
4→→→ 277 -297 50 -4 4571 8236 13464
5→→→ 278 -276 46 -4 4676 8394 13688
6→→→ 286 -246 20 0 4950 8840 14364
7→→→ 271 -174 29 -1 4944 8740 14104
8→→→ 269 -141 58 0 5065 8896 14294
9→→→ 265 -24 23 0 5440 9419 14980
10→→→ 269 9 58 0 5690 9796 15519
11→→→ 276 96 12 0 6160 10524 16576
12→→→ 273 147 6 0 6305 10716 16814
13→→→ 286 144 2 0 6560 11162 17528
14→→→ 277 201 2 0 6610 11180 17479
15→→0同 264 228 60 0 6500 10932 17024
一周汇总 4096 -1629 1025 -37 79363 138670 222010
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 07:22

mod(n,15) 24at^4 24bt^3 24ct^2 24dt 6e 6周 7周
1→→→ 2205 -4630 3195 -1010 60 81950 160660
2→→→ 2210 -4080 2230 -480 30 85850 167200
3→→→ 2165 -3450 1795 -630 30 88400 170770
4→→→ 2175 -2910 1305 -570 0 93075 178500
5→→→ 2164 -2108 596 -652 6 98616 187391
6→→→ 2165 -1530 355 -870 0 103455 195195
7→→→ 2200 -840 -460 -540 0 110415 206990
8→→→ 2200 -380 -340 -640 0 114710 213780
9→→→ 2215 50 -475 -230 0 119290 221270
10→→→ 2182 700 -238 -100 0 123746 227780
11→→→ 2175 1150 345 50 0 128330 234745
12→→→ 2175 1870 705 170 0 135380 245805
13→→→ 2150 2580 1330 60 0 141330 254695
14→→→ 2195 3150 1585 150 0 149295 267890
15→→0同 2192 3828 2080 -36 0 155931 278236
一周汇总 32768 -6600 14008 -5328 126 1729773 3210907
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 07:23

mod(n,15) 120at^5 120bt^4 120ct^3 120dt^2 120et 6f 10周
1→→→ 17388 -37170 30060 -18990 9432 -36 11627955
2→→→ 17457 -31620 20175 -14280 8268 0 12069414
3→→→ 17541 -25765 9645 -8435 7134 -6 12544356
4→→→ 17502 -20370 4350 -8430 6948 0 12917304
5→→→ 17547 -15105 -1185 -3255 1998 0 13351329
6→→→ 17463 -9150 -2555 -6510 872 0 13763356
7→→→ 17439 -3675 -2145 -7125 -3774 0 14202123
8→→→ 17421 3120 -2805 -9780 -5436 0 14745522
9→→→ 17414 9150 -270 -12750 -6824 0 15260723
10→→→ 17517 15030 975 -12330 -6792 0 15847284
11→→→ 17508 21060 4620 -11700 -4848 0 16373346
12→→→ 17547 25930 10665 -6070 -4152 0 16866804
13→→→ 17514 31860 18090 -900 -1044 0 17399913
14→→→ 17427 37230 29865 7230 -1032 0 17879814
15→→0同 17459 43275 41055 14925 406 0 18510013
一周汇总 262144 43800 160540 -98400 1156 -42 223359256
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 2021-11-18 07:25

针对素53 针对素53 针对素53 针对素53
统计4+24 统计4+25 统计4+26 统计4+27
638352691829 638352625268 638352641644 638352770289
626086838003 626056663849 626080821752 626061285738
626074689598 626082561350 626078867737 626092575360
626040437934 626069816643 626062681160 626071596400
626088040732 626084414242 626080982813 626085503040
626084808611 626073716094 626071086532 626098173638
626072924754 626066543932 626076845104 626089424749
626075081345 626095712008 626087247765 626072085200
626070913116 626076849101 626052849211 626062796874
626080141083 626080195274 626095891959 626096448352
626065773246 626073784622 626062630374 626043452716
626058252325 626074510274 626071140616 626099427026
626061673259 626056128410 626048487145 626050989549
626068561934 626073499239 626071853966 626079436081
626108799895 626108302623 626083096078 626088482757
626050085756 626043166985 626058546014 626072274540
626098563223 626080850969 626067136173 626076879118
626036276419 626043507793 626055095163 626045961187
626058588479 626073683747 626045914996 626080827943
626066226500 626103017446 626092909361 626066291081
626092926270 626110737343 626105826756 626093236451
626076896150 626083754551 626081498820 626086344922
626071631186 626045927965 626076195298 626038578009
626102657783 626057469924 626079787312 626102859252
626083643762 626074118384 626095401555 626072246371
626083499524 626098140250 626073148729 626115914773
626060183617 626080457700 626071904589 626061838274
626031193492 626060446147 626042816024 626052646710
626087716835 626065148869 626092567219 626049969570
626065111977 626075165252 626063494518 626086638468
626081420102 626067610588 626094064461 626070655567
626075507157 626078774156 626028871630 626066731375
626090347539 626073329201 626090766633 626085858179
626074207366 626059467364 626070192202 626082376047
626108192018 626079210643 626065584795 626092418893
626101790240 626114089964 626109254879 626074157051
626079567141 626078784676 626083799854 626092762147
626050093615 626090344621 626063263334 626053579038
626093746109 626105551022 626107011081 626093434429
626072051319 626087375341 626075004998 626069449321
626085787910 626063073690 626106612804 626099402176
626111441111 626103009549 626093459232 626091202967
626074931568 626059175464 626089588972 626060892490
626081760448 626081287948 626045793605 626065287709
626098509592 626084037356 626091663025 626090831677
626089881129 626082722514 626082345309 626072509170
626051017246 626056506775 626045694655 626060530521
626079928383 626074522696 626083843895 626071615820
626077558019 626076402103 626110467272 626083090175
626040460723 626047926074 626075823516 626071345171
626074580858 626065231416 626086226024 626077699388
626110163966 626098728230 626099803508 626086030896
626094421920 626104116471 626073692049 626093379471

独舟星海 · 发表于 2021-11-18 07:25

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+24 理论占比实际占比占比绝对误差相对误差
0 638352691829 1.923077% 1.92308% 0.000001% 0.00004%
1 626086838003 1.886095% 1.88612% -0.000030% -0.00159%
2 626074689598 1.886095% 1.88609% 0.000007% 0.00035%
3 626040437934 1.886095% 1.88598% 0.000110% 0.00583%
4 626088040732 1.886095% 1.88613% -0.000034% -0.00178%
5 626084808611 1.886095% 1.88612% -0.000024% -0.00126%
6 626072924754 1.886095% 1.88608% 0.000012% 0.00064%
7 626075081345 1.886095% 1.88609% 0.000006% 0.00029%
8 626070913116 1.886095% 1.88608% 0.000018% 0.00096%
9 626080141083 1.886095% 1.88610% -0.000010% -0.00052%
10 626065773246 1.886095% 1.88606% 0.000034% 0.00178%
11 626058252325 1.886095% 1.88604% 0.000056% 0.00298%
12 626061673259 1.886095% 1.88605% 0.000046% 0.00243%
13 626068561934 1.886095% 1.88607% 0.000025% 0.00133%
14 626108799895 1.886095% 1.88619% -0.000096% -0.00509%
15 626050085756 1.886095% 1.88601% 0.000081% 0.00428%
16 626098563223 1.886095% 1.88616% -0.000065% -0.00346%
17 626036276419 1.886095% 1.88597% 0.000122% 0.00649%
18 626058588479 1.886095% 1.88604% 0.000055% 0.00293%
19 626066226500 1.886095% 1.88606% 0.000032% 0.00171%
20 626092926270 1.886095% 1.88614% -0.000048% -0.00256%
21 626076896150 1.886095% 1.88609% 0.000000% 0.00000%
22 626071631186 1.886095% 1.88608% 0.000016% 0.00084%
23 626102657783 1.886095% 1.88617% -0.000078% -0.00411%
24 626083643762 1.886095% 1.88611% -0.000020% -0.00108%
25 626083499524 1.886095% 1.88611% -0.000020% -0.00105%
26 626060183617 1.886095% 1.88604% 0.000050% 0.00267%
27 626031193492 1.886095% 1.88596% 0.000138% 0.00730%
28 626087716835 1.886095% 1.88613% -0.000033% -0.00173%
29 626065111977 1.886095% 1.88606% 0.000036% 0.00188%
30 626081420102 1.886095% 1.88611% -0.000014% -0.00072%
31 626075507157 1.886095% 1.88609% 0.000004% 0.00022%
32 626090347539 1.886095% 1.88614% -0.000040% -0.00215%
33 626074207366 1.886095% 1.88609% 0.000008% 0.00043%
34 626108192018 1.886095% 1.88619% -0.000094% -0.00500%
35 626101790240 1.886095% 1.88617% -0.000075% -0.00397%
36 626079567141 1.886095% 1.88610% -0.000008% -0.00042%
37 626050093615 1.886095% 1.88601% 0.000081% 0.00428%
38 626093746109 1.886095% 1.88615% -0.000051% -0.00269%
39 626072051319 1.886095% 1.88608% 0.000015% 0.00078%
40 626085787910 1.886095% 1.88612% -0.000027% -0.00142%
41 626111441111 1.886095% 1.88620% -0.000104% -0.00552%
42 626074931568 1.886095% 1.88609% 0.000006% 0.00032%
43 626081760448 1.886095% 1.88611% -0.000015% -0.00077%
44 626098509592 1.886095% 1.88616% -0.000065% -0.00345%
45 626089881129 1.886095% 1.88613% -0.000039% -0.00207%
46 626051017246 1.886095% 1.88602% 0.000078% 0.00414%
47 626079928383 1.886095% 1.88610% -0.000009% -0.00048%
48 626077558019 1.886095% 1.88610% -0.000002% -0.00010%
49 626040460723 1.886095% 1.88598% 0.000110% 0.00582%
50 626074580858 1.886095% 1.88609% 0.000007% 0.00037%
51 626110163966 1.886095% 1.88619% -0.000100% -0.00531%
52 626094421920 1.886095% 1.88615% -0.000053% -0.00280%
合计 33194352194116 100.000000% 100.00000% 0.000000% 0.00000%

独舟星海 · 发表于 2021-11-18 07:25

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+25 理论占比实际占比占比绝对误差相对误差
0 638352625268 1.923077% 1.92308% 0.000001% 0.00005%
1 626056663849 1.886095% 1.88603% 0.000061% 0.00323%
2 626082561350 1.886095% 1.88611% -0.000017% -0.00090%
3 626069816643 1.886095% 1.88607% 0.000021% 0.00113%
4 626084414242 1.886095% 1.88612% -0.000023% -0.00120%
5 626073716094 1.886095% 1.88609% 0.000010% 0.00051%
6 626066543932 1.886095% 1.88606% 0.000031% 0.00166%
7 626095712008 1.886095% 1.88615% -0.000057% -0.00300%
8 626076849101 1.886095% 1.88609% 0.000000% 0.00001%
9 626080195274 1.886095% 1.88610% -0.000010% -0.00052%
10 626073784622 1.886095% 1.88609% 0.000009% 0.00050%
11 626074510274 1.886095% 1.88609% 0.000007% 0.00038%
12 626056128410 1.886095% 1.88603% 0.000063% 0.00332%
13 626073499239 1.886095% 1.88608% 0.000010% 0.00054%
14 626108302623 1.886095% 1.88619% -0.000095% -0.00501%
15 626043166985 1.886095% 1.88599% 0.000102% 0.00539%
16 626080850969 1.886095% 1.88611% -0.000012% -0.00063%
17 626043507793 1.886095% 1.88599% 0.000101% 0.00533%
18 626073683747 1.886095% 1.88608% 0.000010% 0.00052%
19 626103017446 1.886095% 1.88617% -0.000079% -0.00417%
20 626110737343 1.886095% 1.88620% -0.000102% -0.00540%
21 626083754551 1.886095% 1.88612% -0.000021% -0.00109%
22 626045927965 1.886095% 1.88600% 0.000093% 0.00495%
23 626057469924 1.886095% 1.88604% 0.000059% 0.00310%
24 626074118384 1.886095% 1.88609% 0.000008% 0.00045%
25 626098140250 1.886095% 1.88616% -0.000064% -0.00339%
26 626080457700 1.886095% 1.88611% -0.000011% -0.00057%
27 626060446147 1.886095% 1.88605% 0.000050% 0.00263%
28 626065148869 1.886095% 1.88606% 0.000035% 0.00188%
29 626075165252 1.886095% 1.88609% 0.000005% 0.00028%
30 626067610588 1.886095% 1.88607% 0.000028% 0.00149%
31 626078774156 1.886095% 1.88610% -0.000006% -0.00030%
32 626073329201 1.886095% 1.88608% 0.000011% 0.00057%
33 626059467364 1.886095% 1.88604% 0.000053% 0.00279%
34 626079210643 1.886095% 1.88610% -0.000007% -0.00037%
35 626114089964 1.886095% 1.88621% -0.000112% -0.00594%
36 626078784676 1.886095% 1.88610% -0.000006% -0.00030%
37 626090344621 1.886095% 1.88614% -0.000040% -0.00215%
38 626105551022 1.886095% 1.88618% -0.000086% -0.00457%
39 626087375341 1.886095% 1.88613% -0.000032% -0.00167%
40 626063073690 1.886095% 1.88605% 0.000042% 0.00221%
41 626103009549 1.886095% 1.88617% -0.000079% -0.00417%
42 626059175464 1.886095% 1.88604% 0.000053% 0.00283%
43 626081287948 1.886095% 1.88611% -0.000013% -0.00070%
44 626084037356 1.886095% 1.88612% -0.000021% -0.00114%
45 626082722514 1.886095% 1.88611% -0.000018% -0.00093%
46 626056506775 1.886095% 1.88603% 0.000061% 0.00326%
47 626074522696 1.886095% 1.88609% 0.000007% 0.00038%
48 626076402103 1.886095% 1.88609% 0.000002% 0.00008%
49 626047926074 1.886095% 1.88601% 0.000087% 0.00463%
50 626065231416 1.886095% 1.88606% 0.000035% 0.00187%
51 626098728230 1.886095% 1.88616% -0.000066% -0.00349%
52 626104116471 1.886095% 1.88618% -0.000082% -0.00435%
合计 33194352194116 100.000000% 100.00000% 0.000000% 0.00000%

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+26 理论占比实际占比占比绝对误差相对误差
0 638352641644 1.923077% 1.92308% 0.000001% 0.00004%
1 626080821752 1.886095% 1.88611% -0.000012% -0.00062%
2 626078867737 1.886095% 1.88610% -0.000006% -0.00031%
3 626062681160 1.886095% 1.88605% 0.000043% 0.00227%
4 626080982813 1.886095% 1.88611% -0.000012% -0.00065%
5 626071086532 1.886095% 1.88608% 0.000018% 0.00093%
6 626076845104 1.886095% 1.88609% 0.000000% 0.00001%
7 626087247765 1.886095% 1.88613% -0.000031% -0.00165%
8 626052849211 1.886095% 1.88602% 0.000072% 0.00384%
9 626095891959 1.886095% 1.88615% -0.000057% -0.00303%
10 626062630374 1.886095% 1.88605% 0.000043% 0.00228%
11 626071140616 1.886095% 1.88608% 0.000017% 0.00092%
12 626048487145 1.886095% 1.88601% 0.000086% 0.00454%
13 626071853966 1.886095% 1.88608% 0.000015% 0.00081%
14 626083096078 1.886095% 1.88611% -0.000019% -0.00099%
15 626058546014 1.886095% 1.88604% 0.000055% 0.00293%
16 626067136173 1.886095% 1.88607% 0.000029% 0.00156%
17 626055095163 1.886095% 1.88603% 0.000066% 0.00348%
18 626045914996 1.886095% 1.88600% 0.000093% 0.00495%
19 626092909361 1.886095% 1.88614% -0.000048% -0.00256%
20 626105826756 1.886095% 1.88618% -0.000087% -0.00462%
21 626081498820 1.886095% 1.88611% -0.000014% -0.00073%
22 626076195298 1.886095% 1.88609% 0.000002% 0.00011%
23 626079787312 1.886095% 1.88610% -0.000009% -0.00046%
24 626095401555 1.886095% 1.88615% -0.000056% -0.00295%
25 626073148729 1.886095% 1.88608% 0.000011% 0.00060%
26 626071904589 1.886095% 1.88608% 0.000015% 0.00080%
27 626042816024 1.886095% 1.88599% 0.000103% 0.00545%
28 626092567219 1.886095% 1.88614% -0.000047% -0.00250%
29 626063494518 1.886095% 1.88605% 0.000040% 0.00214%
30 626094064461 1.886095% 1.88615% -0.000052% -0.00274%
31 626028871630 1.886095% 1.88595% 0.000145% 0.00767%
32 626090766633 1.886095% 1.88614% -0.000042% -0.00221%
33 626070192202 1.886095% 1.88607% 0.000020% 0.00107%
34 626065584795 1.886095% 1.88606% 0.000034% 0.00181%
35 626109254879 1.886095% 1.88619% -0.000097% -0.00517%
36 626083799854 1.886095% 1.88612% -0.000021% -0.00110%
37 626063263334 1.886095% 1.88605% 0.000041% 0.00218%
38 626107011081 1.886095% 1.88619% -0.000091% -0.00481%
39 626075004998 1.886095% 1.88609% 0.000006% 0.00030%
40 626106612804 1.886095% 1.88618% -0.000089% -0.00474%
41 626093459232 1.886095% 1.88614% -0.000050% -0.00264%
42 626089588972 1.886095% 1.88613% -0.000038% -0.00203%
43 626045793605 1.886095% 1.88600% 0.000094% 0.00497%
44 626091663025 1.886095% 1.88614% -0.000044% -0.00236%
45 626082345309 1.886095% 1.88611% -0.000016% -0.00087%
46 626045694655 1.886095% 1.88600% 0.000094% 0.00499%
47 626083843895 1.886095% 1.88612% -0.000021% -0.00111%
48 626110467272 1.886095% 1.88620% -0.000101% -0.00536%
49 626075823516 1.886095% 1.88609% 0.000003% 0.00017%
50 626086226024 1.886095% 1.88612% -0.000028% -0.00149%
51 626099803508 1.886095% 1.88616% -0.000069% -0.00366%
52 626073692049 1.886095% 1.88608% 0.000010% 0.00051%
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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