[原创]k生素数群的数量公式

独舟星海 · 发表于 2021-10-9 07:46

mod(n,15) 120at^5 120bt^4 120ct^3 120dt^2 120et 6f 10周 11周
1→→→ 17625 -4425 -38835 4425 21210 0 14000580 22690140
2→→→ 17310 3120 -39330 -4380 23280 0 14355540 23173755
3→→→ 17557 7175 -34415 -7175 16858 0 14937384 24051104
4→→→ 17280 15120 -32280 -15480 15360 0 15379380 24663870
5→→→ 17517 19425 -23715 -19425 6198 0 16002954 25597374
6→→→ 17361 27410 -19305 -27410 2064 0 16568122 26402728
7→→→ 17550 31890 -8430 -31530 -8760 0 17185245 27318456
8→→→ 17493 39390 -2265 -38130 -13968 0 17808186 28218267
9→→→ 17540 43890 10320 -40530 -24500 0 18324350 28966586
10→→→ 17553 50640 18435 -43080 -28428 0 18962856 29894667
11→→→ 17445 55335 33405 -40575 -36090 0 19390305 30490416
12→→→ 17571 61550 44605 -35630 -36256 0 20110662 31546999
13→→→ 17373 66735 63045 -24975 -38658 0 20540091 32128932
14→→→ 17616 72600 78180 -9780 -32976 0 21370602 33354354
15→→0同 17353 78235 100545 10925 -28738 0 21825001 33958232
一周汇总 262144 568090 149960 -322750 -163404 0 266761258 422455880
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 2021-10-9 08:23

10^n 两组三生差等于1014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 5 -3 -6.000000000000E-01
5 7 11 -4 -3.636363636364E-01
6 20 21 -1 -4.761904761905E-02
7 69 71 -2 -2.816901408451E-02
8 281 274 7 2.554744525547E-02
9 1290 1292 -2 -1.547987616099E-03
10 6514 6496 18 2.770935960591E-03
11 35388
12 203768
13 1230527
14 7732804
15 50267289
16 336438191
17 2309760077
18 16215885870
19 1.1612522073100000E+11
20 8.4645345056000000E+11
21 6.2688869276430000E+12
22 4.7100175189415000E+13
23 3.5853016480302900E+14
24 2.7618642365497100E+15
25 2.1508880833027600E+16
26 1.6919610381427100E+17
27 1.3433299112048000E+18
28 1.0757103685661400E+19
29 8.6828297791910700E+19
30 7.0605941087085700E+20
31 5.7812278664481500E+21
32 4.7643495859393300E+22
33 3.9501716326593200E+23
34 3.2938007036400700E+24
35 2.7612265482306000E+25
36 2.3264677422924500E+26

独木星空谁 · 发表于 2021-10-9 08:24

10^n 两组三生差等于1020的数量实际数量理论-实际误差/实际
2 0 0 0 #DIV/0!
3 1 1 0 0.000000000000E+00
4 4 1 3 3.000000000000E+00
5 11 10 1 1.000000000000E-01
6 32 23 9 3.913043478261E-01
7 110 106 4 3.773584905660E-02
8 446 417 29 6.954436450839E-02
9 2050 2024 26 1.284584980237E-02
10 10351 10272 79 7.690809968847E-03
11 56233
12 323794
13 1955350
14 12287686
15 79876417
16 534611625
17 3670286604
18 25767589145
19 1.8452688932300000E+11
20 1.3450430595970000E+12
21 9.9614725982190000E+12
22 7.4843765717287000E+13
23 5.6971651483642000E+14
24 4.3886953505373700E+15
25 3.4178336522832100E+16
26 2.6885831110452100E+17
27 2.1345965009877700E+18
28 1.7093400285847300E+19
29 1.3797309142555100E+20
30 1.1219521990563700E+21
31 9.1865659151929900E+21
32 7.5707120572543900E+22
33 6.2769558505648600E+23
34 5.2339603237415400E+24
35 4.3876820423073200E+25
36 3.6968356476961300E+26

独木星空谁 · 发表于 2021-10-9 08:24

10^n 两组三生差等于1026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 2 0 0.000000000000E+00
5 5 8 -3 -3.750000000000E-01
6 14 14 0 0.000000000000E+00
7 49 44 5 1.136363636364E-01
8 197 179 18 1.005586592179E-01
9 906 861 45 5.226480836237E-02
10 4574 4512 62 1.374113475177E-02
11 24850
12 143093
13 864119
14 5430244
15 35299439
16 236258604
17 1621993893
18 11387359286
19 81547170550
20 5.9440906515800000E+11
21 4.4022305252340000E+12
22 3.3075381859007000E+13
23 2.5177235670872700E+14
24 1.9394771654086400E+15
25 1.5104284518078500E+16
26 1.1881539124234300E+17
27 9.4333300453858900E+17
28 7.5540124993025800E+18
29 6.0973851882411600E+19
30 4.9581948550687000E+20
31 4.0597793644656800E+21
32 3.3456920538197900E+22
33 2.7739479658705500E+23
34 2.3130214612204900E+24
35 1.9390293584827200E+25
36 1.6337265976088700E+26

独木星空谁 · 发表于 2021-10-9 08:24

10^n 两组三生差等于1044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 0 1 #DIV/0!
5 4 2 2 1.000000000000E+00
6 13 12 1 8.333333333333E-02
7 45 43 2 4.651162790698E-02
8 182 169 13 7.692307692308E-02
9 839 786 53 6.743002544529E-02
10 4238 4113 125 3.039144177000E-02
11 23022
12 132564
13 800541
14 5030712
15 32702275
16 218875822
17 1502655313
18 10549531658
19 75547318370
20 5.5067527891500000E+11
21 4.0783353828630000E+12
22 3.0641852888910000E+13
23 2.3324814657165500E+14
24 1.7967796785290700E+15
25 1.3992983245609200E+16
26 1.1007352099231400E+17
27 8.7392705769938000E+17
28 6.9982242597023300E+18
29 5.6487686443514000E+19
30 4.5933945068632800E+20
31 3.7610801464871400E+21
32 3.0995319770382500E+22
33 2.5698540943239800E+23
34 2.1428403652522200E+24
35 1.7963648191026500E+25
36 1.5135247803949100E+26

独木星空谁 · 发表于 2021-10-9 08:25

10^n 两组三生差等于1050的数量实际数量理论-实际误差/实际
2 0 0 0 #DIV/0!
3 1 2 -1 -5.000000000000E-01
4 8 6 2 3.333333333333E-01
5 20 17 3 1.764705882353E-01
6 57 48 9 1.875000000000E-01
7 198 191 7 3.664921465969E-02
8 801 815 -14 -1.717791411043E-02
9 3677 3710 -33 -8.894878706199E-03
10 18566 18501 65 3.513323604130E-03
11 100858
12 580749
13 3507069
14 22038898
15 143264422
16 958866563
17 6582937852
18 46216128660
19 3.30963E+11
20 2.41244E+12
21 1.78667E+13
22 1.34238E+14
23 1.02183E+15
24 7.87146E+15
25 6.13014E+16
26 4.82218E+17
27 3.82856E+18
28 3.06583E+19
29 2.47465E+20
30 2.01231E+21
31 1.64768E+22
32 1.35786E+23
33 1.12582E+24
34 9.38751E+24
35 7.86964E+25
36 6.63056E+26

独木星空谁 · 发表于 2021-10-9 08:25

10^n 两组三生差等于1056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 7 5 2 4.000000000000E-01
6 20 22 -2 -9.090909090909E-02
7 69 89 -20 -2.247191011236E-01
8 279 309 -30 -9.708737864078E-02
9 1281 1322 -41 -3.101361573374E-02
10 6469 6451 18 2.790265075182E-03
11 35147
12 202380
13 1222150
14 7680161
15 49925083
16 334147809
17 2294035843
18 16105492420
19 1.1533467103200000E+11
20 8.4069102000100000E+11
21 6.2262100083370000E+12
22 4.6779529690614000E+13
23 3.5608938654549400E+14
24 2.7430621974450300E+15
25 2.1362454077806100E+16
26 1.6804426162080800E+17
27 1.3341848775037500E+18
28 1.0683872177220700E+19
29 8.6237193772795000E+19
30 7.0125274569241000E+20
31 5.7418708006736900E+21
32 4.7319151577593600E+22
33 3.9232799120147700E+23
34 3.2713773821700000E+24
35 2.7424288503388400E+25
36 2.3106297670265100E+26

独木星空谁 · 发表于 2021-10-9 08:25

10^n 两组三生差等于1074的数量实际数量理论-实际误差/实际
2 0 0 0 #DIV/0!
3 0 2 -2 -1.000000000000E+00
4 1 2 -1 -5.000000000000E-01
5 4 5 -1 -2.000000000000E-01
6 12 15 -3 -2.000000000000E-01
7 43 52 -9 -1.730769230769E-01
8 177 174 3 1.724137931034E-02
9 812 767 45 5.867014341591E-02
10 4102 4089 13 3.179261433113E-03
11 22285
12 128319
13 774906
14 4869617
15 31655072
16 211866911
17 1454536807
18 10211711206
19 73128118154
20 5.3304138028500000E+11
21 3.9477376322940000E+12
22 2.9660629746406000E+13
23 2.2577900036199100E+14
24 1.7392426291559200E+15
25 1.3544895493114600E+16
26 1.0654871175293400E+17
27 8.4594188797142600E+17
28 6.7741249004061200E+18
29 5.4678819812444500E+19
30 4.4463033694857300E+20
31 3.6406416438311400E+21
32 3.0002777799168300E+22
33 2.4875614105443300E+23
34 2.0742216506888300E+24
35 1.7388410544897900E+25
36 1.4650582093079400E+26

独木星空谁 · 发表于 2021-10-9 08:25

10^n 两组三生差等于1080的数量实际数量理论-实际误差/实际
2 0 0 0 #DIV/0!
3 0 2 -2 -1.000000000000E+00
4 3 3 0 0.000000000000E+00
5 8 10 -2 -2.000000000000E-01
6 24 30 -6 -2.000000000000E-01
7 84 94 -10 -1.063829787234E-01
8 340 346 -6 -1.734104046243E-02
9 1564 1553 11 7.083065035415E-03
10 7897 7730 167 2.160413971539E-02
11 42900
12 247024
13 1491747
14 9374345
15 60938173
16 407858253
17 2800082550
18 19658240486
19 1.4077661461200000E+11
20 1.0261410092150000E+12
21 7.5996641685720000E+12
22 5.7098735046900000E+13
23 4.3463997329271300E+14
24 3.3481606733747300E+15
25 2.6074847554205800E+16
26 2.0511353649550600E+17
27 1.6284958255886800E+18
28 1.3040652412639900E+19
29 1.0526045710564100E+20
30 8.5594372136741600E+20
31 7.0084834475575500E+21
32 5.7757393382157100E+22
33 4.7887253611252400E+23
34 3.9930181346056200E+24
35 3.3473876147559700E+25
36 2.8203369664359200E+26

独木星空谁 · 发表于 2021-10-9 08:26

10^n 两组三生差等于1086的数量实际数量理论-实际误差/实际
2 0 0 0 #DIV/0!
3 0 2 -2 -1.000000000000E+00
4 1 2 -1 -5.000000000000E-01
5 4 4 0 0.000000000000E+00
6 12 12 0 0.000000000000E+00
7 44 42 2 4.761904761905E-02
8 179 177 2 1.129943502825E-02
9 821 870 -49 -5.632183908046E-02
10 4149 4114 35 8.507535245503E-03
11 22541
12 129796
13 783820
14 4925636
15 32019225
16 214304182
17 1471269482
18 10329184511
19 73969368126
20 5.3917337243300000E+11
21 3.9931515477260000E+12
22 3.0001839182398000E+13
23 2.2837631289483500E+14
24 1.7592504982275400E+15
25 1.3700713026029100E+16
26 1.0777442496785000E+17
27 8.5567341953177100E+17
28 6.8520529604766500E+18
29 5.5307833067673100E+19
30 4.4974526767635400E+20
31 3.6825227937784600E+21
32 3.0347923231971900E+22
33 2.5161777761827100E+23
34 2.0980830455953200E+24
35 1.7588443039337500E+25
36 1.4819119204249200E+26

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