[原创]k生素数群的数量公式

独木星空谁 · 发表于 2021-10-6 12:14

mod(n,15) 120at^5 120bt^4 120ct^3 120dt^2 120et 6f 10周 11周
1→→→ 17211 -8535 -14685 -7305 14034 -36 13503951 21888432
2→→→ 17427 -1620 -14475 -10080 8748 0 14259204 23021064
3→→→ 17631 5515 -12085 -15955 5614 -36 15038541 24185672
4→→→ 17829 12510 -8625 -20610 -1104 0 15810858 25337928
5→→→ 17922 19530 -4950 -24930 -7572 0 16499844 26355054
6→→→ 18014 25420 1090 -31060 -13344 0 17112088 27257439
7→→→ 17922 31290 5790 -34530 -19752 0 17560329 27898200
8→→→ 17829 36120 11415 -37560 -25284 0 17929218 28421514
9→→→ 17631 40475 17355 -39155 -29466 -6 18174956 28751018
10→→→ 17427 44490 24165 -38730 -32232 0 18396414 29042805
11→→→ 17211 48645 31635 -33885 -33366 0 18628857 29347494
12→→→ 17074 52730 42870 -26630 -31324 0 18954948 29794149
13→→→ 16971 57795 56235 -12435 -27126 0 19414752 30436824
14→→→ 16971 63510 74145 7590 -19296 0 20057592 31353663
15→→0同 17074 70030 96570 34970 -7924 0 20897398 32564774
一周汇总 262144 497905 306450 -290305 -219394 -78 262238950 415656030
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

独木星空谁 · 发表于 2021-10-6 15:57

序15 1 2 3 4 5 6 8 15 mod(n,15)
mod(n,15) at b 100周 101周 102周 103周 104周 105周
1→→→ 3 -3 297 300 303 306 309 312
2→→→ 3 -2 298 301 304 307 310 313
3→→→ 4 -2 398 402 406 410 414 418
4→→→ 5 -2 498 503 508 513 518 523
5→→→ 6 -2 598 604 610 616 622 628
6→→→ 7 -2 698 705 712 719 726 733
7→→→ 6 0 600 606 612 618 624 630
8→→→ 7 -2 698 705 712 719 726 733
9→→→ 6 0 600 606 612 618 624 630
10→→→ 5 0 500 505 510 515 520 525
11→→→ 4 0 400 404 408 412 416 420
12→→→ 3 0 300 303 306 309 312 315
13→→→ 2 0 200 202 204 206 208 210
14→→→ 2 0 200 202 204 206 208 210
15→→0 1 -1 99 100 101 102 103 104
一周汇总 64 -16 6384 6448 6512 6576 6640 6704

x+y=N 正整数解组数系数及 a,b值

独木星空谁 · 发表于 2021-10-6 15:58

mod(n,15) 2at^2 2bt c 10周 11周 12周 13周 14周
1→→→ 27 -39 6 1161 1425 1716 2034 2379
2→→→ 24 -30 3 1053 1290 1551 1836 2145
3→→→ 23 -27 3 1018 1246 1497 1771 2068
4→→→ 24 -24 3 1083 1323 1587 1875 2187
5→→→ 27 -21 3 1248 1521 1821 2148 2502
6→→→ 31 -17 3 1468 1785 2133 2512 2922
7→→→ 36 -6 0 1770 2145 2556 3003 3486
8→→→ 39 -3 3 1938 2346 2793 3279 3804
9→→→ 44 6 0 2230 2695 3204 3757 4354
10→→→ 45 15 0 2325 2805 3330 3900 4515
11→→→ 45 21 0 2355 2838 3366 3939 4557
12→→→ 43 25 0 2275 2739 3246 3796 4389
13→→→ 39 27 0 2085 2508 2970 3471 4011
14→→→ 36 24 0 1920 2310 2736 3198 3696
15→→0同 29 25 1 1576 1893 2239 2614 3018
一周汇总 512 -24 25 25505 30869 36745 43133 50033
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 2021-10-6 15:59

mod(n,15) 6at^3 6bt^2 6ct d 5周 6周 7周
1→→→ 303 -312 69 -10 5060 9095 14844
2→→→ 287 -261 -2 -4 4886 8760 14269
3→→→ 266 -216 -26 -4 4616 8250 13408
4→→→ 247 -183 -34 -4 4351 7756 12582
5→→→ 233 -156 -29 -4 4176 7419 12008
6→→→ 224 -120 -20 -4 4146 7320 11798
7→→→ 228 -84 -24 0 4380 7680 12320
8→→→ 233 -9 10 -4 4821 8340 13254
9→→→ 251 48 37 0 5460 9361 14784
10→→→ 270 150 60 0 6300 10680 16730
11→→→ 290 252 106 0 7180 12058 18760
12→→→ 307 357 158 0 8015 13352 20650
13→→→ 318 456 210 0 8700 14394 22148
14→→→ 322 522 272 0 9110 14996 22988
15→→0同 317 594 295 -1 9324 15270 23316
一周汇总 4096 1038 1082 -35 90525 154731 243859
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 2021-10-6 15:59

mod(n,15) 24at^4 24bt^3 24ct^2 24dt 6e 6周 7周 8周
1→→→ 2360 -2040 700 -1380 90 109800 207985 360675
2→→→ 2395 -1370 125 -1270 30 116875 219910 379435
3→→→ 2390 -700 -410 -1400 30 121800 227855 391405
4→→→ 2350 -140 -730 -1600 30 124150 231145 395605
5→→→ 2282 308 -890 -1796 30 124221 230361 393065
6→→→ 2195 690 -995 -1890 30 122780 226875 386055
7→→→ 2110 940 -850 -1840 0 120665 222250 377280
8→→→ 2035 1290 -835 -1770 30 119810 219805 372015
9→→→ 1985 1590 -305 -1590 0 120645 220220 371350
10→→→ 1973 2046 139 -1134 0 124881 226576 380366
11→→→ 1995 2650 945 -670 0 132830 239190 399310
12→→→ 2050 3420 2030 -60 0 144510 258090 428220
13→→→ 2130 4340 3390 700 0 159340 282240 465380
14→→→ 2215 5350 5105 1490 0 175790 308910 506270
15→→0同 2303 6398 6745 2554 6 192701 336351 548375
一周汇总 32768 24772 14164 -11656 276 2010798 3657763 6154806
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 2021-10-6 16:01

mod(n,15) 120at^5 120bt^4 120ct^3 120dt^2 120et 6f 10周 11周
1→→→ 17061 -13335 165 -16905 15534 -126 13094811 21256632
2→→→ 17433 -6360 -765 -18480 8892 -36 13976460 22594401
3→→→ 17816 1040 -1260 -19880 3004 -36 14906511 24003842
4→→→ 18138 8490 -90 -23430 -2388 -36 15802020 25353861
5→→→ 18345 15645 2385 -27885 -7770 -36 16587234 26527110
6→→→ 18405 22230 5475 -31710 -13560 -36 17208064 27440946
7→→→ 18297 27915 10065 -36555 -19002 0 17625579 28035150
8→→→ 18060 32730 13800 -37410 -23940 -36 17859324 28344651
9→→→ 17707 36765 19215 -40005 -26962 0 17944124 28420370
10→→→ 17325 40140 24795 -37080 -30060 0 17955720 28384026
11→→→ 16965 43455 31725 -31935 -29970 0 17994015 28387392
12→→→ 16693 47090 40935 -22430 -27568 0 18155136 28577802
13→→→ 16560 51480 53400 -7560 -22440 0 18526830 29088642
14→→→ 16578 57090 70110 12570 -13428 0 19166106 30003732
15→→0同 16761 63805 91445 41315 -2486 -6 20080846 31335248
一周汇总 262144 428180 361400 -297380 -192144 -348 256882780 407753805
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 2021-10-6 19:19

10^n 两组三生差等于576的数量实际数量理论-实际误差/实际
2 0 0 0 #DIV/0!
3 0 0 0 #DIV/0!
4 2 1 1 1.000000000000E+00
5 6 4 2 5.000000000000E-01
6 17 14 3 2.142857142857E-01
7 60 57 3 5.263157894737E-02
8 243 243 0 0.000000000000E+00
9 1115 1082 33 3.049907578558E-02
10 5633 5500 133 2.418181818182E-02
11 30604
12 176224
13 1064197
14 6687560
15 43472659
16 290961840
17 1997549797
18 14023984508
19 1.0042857415200000E+11
20 7.3203833406000000E+11
21 5.4215214550620000E+12
22 4.0733644309421000E+13
23 3.1006764090692300E+14
24 2.3885430359887400E+15
25 1.8601525319658900E+16
26 1.4632586574453500E+17
27 1.1617520014133500E+18
28 9.3030659348750200E+18
29 7.5091716411344200E+19
30 6.1062135731071100E+20
31 4.9997792712358100E+21
32 4.1203524322135500E+22
33 3.4162269163294000E+23
34 2.8485776485678100E+24
35 2.3879915440024200E+25
36 2.0119990877057200E+26

独舟星海 · 发表于 2021-10-6 19:20

10^n 两组三生差等于594的数量实际数量理论-实际误差/实际
2 0 0 0 #DIV/0!
3 0 1 -1 -1.000000000000E+00
4 2 5 -3 -6.000000000000E-01
5 7 10 -3 -3.000000000000E-01
6 20 23 -3 -1.304347826087E-01
7 70 69 1 1.449275362319E-02
8 285 287 -2 -6.968641114983E-03
9 1308 1344 -36 -2.678571428571E-02
10 6607 6560 47 7.164634146341E-03
11 35896
12 206692
13 1248186
14 7843775
15 50988662
16 341266330
17 2342906855
18 16448595914
19 1.1779170417200000E+11
20 8.5860068826100000E+11
21 6.3588501259470000E+12
22 4.7776097797309000E+13
23 3.6367533980562100E+14
24 2.8014990461849200E+15
25 2.1817549299059300E+16
26 1.7162419397053300E+17
27 1.3626076963338700E+18
28 1.0911476138573800E+19
29 8.8074348560224700E+19
30 7.1619188949550300E+20
31 5.8641927938736600E+21
32 4.8327215523724800E+22
33 4.0068595388260800E+23
34 3.3410691979192100E+24
35 2.8008522065633000E+25
36 2.3598542878249700E+26

独舟星海 · 发表于 2021-10-6 19:20

10^n 两组三生差等于600的数量实际数量理论-实际误差/实际
2 0 0 0 #DIV/0!
3 0 1 -1 -1.000000000000E+00
4 4 6 -2 -3.333333333333E-01
5 10 9 1 1.111111111111E-01
6 30 24 6 2.500000000000E-01
7 105 108 -3 -2.777777777778E-02
8 425 406 19 4.679802955665E-02
9 1950 1917 33 1.721439749609E-02
10 9848 9642 206 2.136486206181E-02
11 53499
12 308051
13 1860283
14 11690271
15 75992907
16 508619352
17 3491841010
18 24514795220
19 1.7555538001500000E+11
20 1.2796484367730000E+12
21 9.4771559522330000E+12
22 7.1204938101416000E+13
23 5.4201747848333600E+14
24 4.1753214551149200E+15
25 3.2516620632244500E+16
26 2.5578669401220000E+17
27 2.0308145944776500E+18
28 1.6262336583838500E+19
29 1.3126498032885700E+20
30 1.0674040265200500E+21
31 8.7399244424282500E+21
32 7.2026317523454900E+22
33 5.9717766539578900E+23
34 4.9794905067316800E+24
35 4.1743574128983600E+25
36 3.5170992659514100E+26

独舟星海 · 发表于 2021-10-6 19:20

10^n 两组三生差等于606的数量实际数量理论-实际误差/实际
2 0 0 0 #DIV/0!
3 0 0 0 #DIV/0!
4 1 3 -2 -6.666666666667E-01
5 4 6 -2 -3.333333333333E-01
6 12 19 -7 -3.684210526316E-01
7 44 46 -2 -4.347826086957E-02
8 177 189 -12 -6.349206349206E-02
9 814 866 -52 -6.004618937644E-02
10 4112 4100 12 2.926829268293E-03
11 22338
12 128624
13 776746
14 4881179
15 31730232
16 212369956
17 1457990380
18 10235957339
19 73301749589
20 5.3430700480800000E+11
21 3.9571109262710000E+12
22 2.9731054335891000E+13
23 2.2631507776664200E+14
24 1.7433721924598700E+15
25 1.3577055757845000E+16
26 1.0680169523135300E+17
27 8.4795044647803000E+17
28 6.7902090149144200E+18
29 5.4808646234598200E+19
30 4.4568604308899600E+20
31 3.6492857857600200E+21
32 3.0074014766420000E+22
33 2.4934677413489500E+23
34 2.0791465700010300E+24
35 1.7429696643166400E+25
36 1.4685367640063400E+26

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