[原创]k生素数群的数量公式

yangchuanju · 发表于 2021-11-9 17:08

快马加鞭，让您的两个副手也都成为论坛元老！

独木星空谁 · 发表于 2021-11-9 20:36

组合158 1 2 3 4 6 8 10 14 mod(n,15)
mod(n,15) at b 100周 101周 102周 103周 104周 105周
1→→→ 5 -5 495 500 505 510 515 520
2→→→ 3 -2 298 301 304 307 310 313
3→→→ 6 -4 596 602 608 614 620 626
4→→→ 3 0 300 303 306 309 312 315
5→→→ 7 -3 697 704 711 718 725 732
6→→→ 3 0 300 303 306 309 312 315
7→→→ 6 -2 598 604 610 616 622 628
8→→→ 3 0 300 303 306 309 312 315
9→→→ 6 -2 598 604 610 616 622 628
10→→→ 4 0 400 404 408 412 416 420
11→→→ 4 0 400 404 408 412 416 420
12→→→ 5 0 500 505 510 515 520 525
13→→→ 3 -1 299 302 305 308 311 314
14→→→ 4 0 400 404 408 412 416 420
15→→0 2 0 200 202 204 206 208 210
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

独木星空谁 · 发表于 2021-11-9 20:37

mod(n,15) 2at^2 2bt c 10周 11周 12周 13周 14周
1→→→ 27 -33 3 1188 1455 1749 2070 2418
2→→→ 36 -54 9 1539 1890 2277 2700 3159
3→→→ 29 -27 0 1315 1606 1926 2275 2653
4→→→ 36 -42 6 1596 1953 2346 2775 3240
5→→→ 33 -21 0 1545 1881 2250 2652 3087
6→→→ 34 -20 3 1603 1950 2331 2746 3195
7→→→ 36 -12 0 1740 2112 2520 2964 3444
8→→→ 33 -9 3 1608 1950 2325 2733 3174
9→→→ 38 -6 0 1870 2266 2700 3172 3682
10→→→ 30 6 0 1530 1848 2196 2574 2982
11→→→ 42 0 0 2100 2541 3024 3549 4116
12→→→ 29 13 1 1516 1827 2167 2536 2934
13→→→ 42 12 0 2160 2607 3096 3627 4200
14→→→ 27 21 0 1455 1749 2070 2418 2793
15→→0同 40 14 0 2070 2497 2964 3471 4018
一周汇总 512 -158 25 24835 30132 35941 42262 49095
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 2021-11-9 20:37

mod(n,15) 6at^3 6bt^2 6ct d 5周 6周 7周
1→→→ 271 -432 257 -16 4044 7405 12248
2→→→ 281 -387 106 0 4330 7900 13027
3→→→ 258 -324 126 -10 4120 7460 12240
4→→→ 287 -327 46 0 4655 8416 13790
5→→→ 248 -192 -8 -4 4356 7764 12596
6→→→ 294 -234 0 0 5150 9180 14896
7→→→ 248 -72 -32 -4 4836 8460 13548
8→→→ 295 -111 2 0 5685 9956 15960
9→→→ 249 60 -45 0 5400 9279 14672
10→→→ 295 3 38 0 6190 10676 16933
11→→→ 255 162 -3 -1 5984 10148 15896
12→→→ 291 141 66 0 6705 11388 17864
13→→→ 264 276 36 0 6680 11196 17388
14→→→ 286 270 140 0 7200 12056 18718
15→→0同 274 372 122 0 7360 12218 18844
一周汇总 4096 -795 851 -35 82695 143502 228620
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 2021-11-9 20:38

mod(n,15) 24at^4 24bt^3 24ct^2 24dt 6e 6周 7周
1→→→ 2280 -4120 2640 -800 0 89800 174370
2→→→ 2105 -2710 955 -710 90 90550 173615
3→→→ 2280 -2980 1500 -800 0 98350 188335
4→→→ 2100 -1580 -360 -280 30 98575 186695
5→→→ 2263 -1858 521 -902 0 106036 200641
6→→→ 2115 -590 -1035 -490 30 107230 200905
7→→→ 2230 -640 -130 -1100 0 114190 213360
8→→→ 2145 470 -1245 -530 0 118060 218610
9→→→ 2195 610 -35 -1210 0 123665 227885
10→→→ 2183 1534 -635 -562 6 130596 238855
11→→→ 2155 1910 545 -890 0 134155 243740
12→→→ 2220 2640 360 -180 0 144135 260505
13→→→ 2130 3180 1710 -420 0 146100 261905
14→→→ 2255 3790 1945 290 0 158870 283815
15→→0同 2112 4508 3360 364 0 159751 282681
一周汇总 32768 4164 10096 -8220 156 1820063 3355917
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 2021-11-9 20:38

mod(n,15) 120at^5 120bt^4 120ct^3 120dt^2 120et 6f 10周
1→→→ 17265 -27135 5745 -3105 9750 -126 12172329
2→→→ 17637 -24870 12375 -19230 14088 0 12713274
3→→→ 17400 -15910 -4780 70 3940 -36 13134714
4→→→ 17520 -12300 2460 -17760 10080 0 13581540
5→→→ 17538 -5040 -8730 -3600 552 -36 14119290
6→→→ 17375 90 -2755 -19230 4640 0 14448070
7→→→ 17658 5760 -8430 -9000 -5268 0 15116811
8→→→ 17250 12090 -2130 -23430 -1260 0 15345120
9→→→ 17751 16695 -2085 -15375 -10146 -6 16152716
10→→→ 17157 24030 4875 -24030 -7632 0 16319964
11→→→ 17796 27960 10560 -15000 -14676 0 17234277
12→→→ 17128 35700 19540 -18000 -10448 0 17395296
13→→→ 17781 39435 29985 -6675 -14286 0 18346872
14→→→ 17160 47430 40740 -2430 -8580 0 18589260
15→→0同 17728 51210 55920 12750 -9688 0 19516651
一周汇总 262144 175145 153290 -164045 -38934 -204 234186184
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 2021-11-9 22:28

截止2021年11月08日周一23:30分浏览量74432,回复6289热度146度。参照浏览量72664，差距 1768
截止2021年11月09日周二22:26分浏览量74846,回复6314热度148度。参照浏览量72738，差距 2108
                                                浏览量 ↑ 414, 回复↑ 25热度↑ 2。  参照浏览量↑ 74,  差距 ↑340
晚安!

独木星空谁 · 发表于 2021-11-10 07:51

针对素53 针对素53 针对素53 针对素53
统计4+8 统计4+9 统计4+10 统计4+11
638352677045 638352653403 638352709569 638352742800
626051316256 626082492574 626081662701 626072337453
626085387124 626101724630 626074949268 626098648665
626062766774 626079004871 626059213989 626066232378
626086743082 626076009629 626082966469 626095433468
626077588865 626099715358 626089620566 626088089704
626062018911 626084365203 626059710944 626075920643
626080080707 626089664070 626085297799 626051984475
626062431327 626050975093 626078816920 626032315333
626066736322 626088031504 626063143316 626080326891
626076362581 626065713449 626073528687 626059457102
626085689167 626094392735 626058138741 626083249002
626049228189 626062268523 626046767392 626072026276
626056716539 626053999437 626060236113 626069160153
626098754116 626085045811 626112106388 626104779505
626065738282 626048074726 626049496221 626058183795
626068347598 626073979792 626056099682 626087457611
626066709993 626042446211 626042471779 626050558100
626076101618 626050476127 626071408321 626069250492
626096600609 626093827348 626094229879 626069779216
626085242767 626082225257 626074150910 626112129166
626073282020 626051175065 626089797298 626092331044
626071250004 626082079746 626066725742 626050758712
626097544814 626075692516 626105129084 626075520941
626058705061 626058790869 626095136309 626075974602
626098792046 626065860808 626088913045 626108546743
626057208460 626089559987 626070303933 626086951689
626065356414 626027604778 626055338429 626055420464
626089356962 626080281339 626068299552 626050054117
626092382092 626076368223 626073580698 626090318954
626053724781 626057173032 626053537810 626094807917
626051699133 626065448865 626066096297 626060606219
626091376317 626074544504 626093339609 626089357241
626064586810 626074195463 626070760498 626046054305
626058138156 626088919182 626078439561 626078969912
626099375593 626098508905 626113439606 626101843987
626076065463 626093981594 626103375354 626078541704
626074349706 626087788636 626080393922 626086278238
626101434138 626093203203 626078880430 626098064224
626058428029 626099683230 626086069879 626091946114
626107081087 626087215190 626101265364 626087706728
626086290828 626096146740 626070021060 626101059620
626071607461 626072074324 626083296137 626062979186
626091028749 626091476264 626066120198 626067448100
626071134451 626073164634 626084699789 626088839367
626072159175 626093863186 626070078552 626071269884
626062516623 626058091809 626049970946 626063144177
626071681040 626044086716 626081541911 626043550348
626098858269 626098383065 626108980494 626085484390
626084068725 626063555064 626078240715 626058200119
626100848001 626093342994 626096955571 626090400468
626105336997 626096671989 626072460534 626082487738
626083288839 626086176445 626084280135 626087214636

独木星空谁 · 发表于 2021-11-10 07:51

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+8 理论占比实际占比占比绝对误差相对误差
0 638352677045 1.923077% 1.92308% 0.000001% 0.00004%
1 626051316256 1.886095% 1.88602% 0.000077% 0.00409%
2 626085387124 1.886095% 1.88612% -0.000026% -0.00135%
3 626062766774 1.886095% 1.88605% 0.000043% 0.00226%
4 626086743082 1.886095% 1.88612% -0.000030% -0.00157%
5 626077588865 1.886095% 1.88610% -0.000002% -0.00011%
6 626062018911 1.886095% 1.88605% 0.000045% 0.00238%
7 626080080707 1.886095% 1.88610% -0.000010% -0.00051%
8 626062431327 1.886095% 1.88605% 0.000044% 0.00231%
9 626066736322 1.886095% 1.88606% 0.000031% 0.00162%
10 626076362581 1.886095% 1.88609% 0.000002% 0.00009%
11 626085689167 1.886095% 1.88612% -0.000026% -0.00140%
12 626049228189 1.886095% 1.88601% 0.000083% 0.00442%
13 626056716539 1.886095% 1.88603% 0.000061% 0.00323%
14 626098754116 1.886095% 1.88616% -0.000066% -0.00349%
15 626065738282 1.886095% 1.88606% 0.000034% 0.00178%
16 626068347598 1.886095% 1.88607% 0.000026% 0.00137%
17 626066709993 1.886095% 1.88606% 0.000031% 0.00163%
18 626076101618 1.886095% 1.88609% 0.000002% 0.00013%
19 626096600609 1.886095% 1.88615% -0.000059% -0.00315%
20 626085242767 1.886095% 1.88612% -0.000025% -0.00133%
21 626073282020 1.886095% 1.88608% 0.000011% 0.00058%
22 626071250004 1.886095% 1.88608% 0.000017% 0.00090%
23 626097544814 1.886095% 1.88616% -0.000062% -0.00330%
24 626058705061 1.886095% 1.88604% 0.000055% 0.00291%
25 626098792046 1.886095% 1.88616% -0.000066% -0.00350%
26 626057208460 1.886095% 1.88604% 0.000059% 0.00315%
27 626065356414 1.886095% 1.88606% 0.000035% 0.00185%
28 626089356962 1.886095% 1.88613% -0.000038% -0.00199%
29 626092382092 1.886095% 1.88614% -0.000047% -0.00247%
30 626053724781 1.886095% 1.88602% 0.000070% 0.00370%
31 626051699133 1.886095% 1.88602% 0.000076% 0.00403%
32 626091376317 1.886095% 1.88614% -0.000044% -0.00231%
33 626064586810 1.886095% 1.88606% 0.000037% 0.00197%
34 626058138156 1.886095% 1.88604% 0.000057% 0.00300%
35 626099375593 1.886095% 1.88616% -0.000068% -0.00359%
36 626076065463 1.886095% 1.88609% 0.000003% 0.00013%
37 626074349706 1.886095% 1.88609% 0.000008% 0.00041%
38 626101434138 1.886095% 1.88617% -0.000074% -0.00392%
39 626058428029 1.886095% 1.88604% 0.000056% 0.00295%
40 626107081087 1.886095% 1.88619% -0.000091% -0.00482%
41 626086290828 1.886095% 1.88612% -0.000028% -0.00150%
42 626071607461 1.886095% 1.88608% 0.000016% 0.00085%
43 626091028749 1.886095% 1.88614% -0.000043% -0.00226%
44 626071134451 1.886095% 1.88608% 0.000017% 0.00092%
45 626072159175 1.886095% 1.88608% 0.000014% 0.00076%
46 626062516623 1.886095% 1.88605% 0.000043% 0.00230%
47 626071681040 1.886095% 1.88608% 0.000016% 0.00084%
48 626098858269 1.886095% 1.88616% -0.000066% -0.00351%
49 626084068725 1.886095% 1.88612% -0.000022% -0.00114%
50 626100848001 1.886095% 1.88617% -0.000072% -0.00382%
51 626105336997 1.886095% 1.88618% -0.000086% -0.00454%
52 626083288839 1.886095% 1.88611% -0.000019% -0.00102%
合计 33194352194116 100.000000% 100.00000% 0.000000% 0.00000%

独木星空谁 · 发表于 2021-11-10 07:51

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+9 理论占比实际占比占比绝对误差相对误差
0 638352653403 1.923077% 1.92308% 0.000001% 0.00004%
1 626082492574 1.886095% 1.88611% -0.000017% -0.00089%
2 626101724630 1.886095% 1.88617% -0.000075% -0.00396%
3 626079004871 1.886095% 1.88610% -0.000006% -0.00033%
4 626076009629 1.886095% 1.88609% 0.000003% 0.00014%
5 626099715358 1.886095% 1.88616% -0.000069% -0.00364%
6 626084365203 1.886095% 1.88612% -0.000022% -0.00119%
7 626089664070 1.886095% 1.88613% -0.000038% -0.00204%
8 626050975093 1.886095% 1.88602% 0.000078% 0.00414%
9 626088031504 1.886095% 1.88613% -0.000034% -0.00178%
10 626065713449 1.886095% 1.88606% 0.000034% 0.00179%
11 626094392735 1.886095% 1.88615% -0.000053% -0.00279%
12 626062268523 1.886095% 1.88605% 0.000044% 0.00234%
13 626053999437 1.886095% 1.88603% 0.000069% 0.00366%
14 626085045811 1.886095% 1.88612% -0.000025% -0.00130%
15 626048074726 1.886095% 1.88601% 0.000087% 0.00461%
16 626073979792 1.886095% 1.88609% 0.000009% 0.00047%
17 626042446211 1.886095% 1.88599% 0.000104% 0.00550%
18 626050476127 1.886095% 1.88602% 0.000080% 0.00422%
19 626093827348 1.886095% 1.88615% -0.000051% -0.00270%
20 626082225257 1.886095% 1.88611% -0.000016% -0.00085%
21 626051175065 1.886095% 1.88602% 0.000078% 0.00411%
22 626082079746 1.886095% 1.88611% -0.000016% -0.00083%
23 626075692516 1.886095% 1.88609% 0.000004% 0.00019%
24 626058790869 1.886095% 1.88604% 0.000055% 0.00289%
25 626065860808 1.886095% 1.88606% 0.000033% 0.00176%
26 626089559987 1.886095% 1.88613% -0.000038% -0.00202%
27 626027604778 1.886095% 1.88595% 0.000149% 0.00788%
28 626080281339 1.886095% 1.88610% -0.000010% -0.00054%
29 626076368223 1.886095% 1.88609% 0.000002% 0.00009%
30 626057173032 1.886095% 1.88604% 0.000059% 0.00315%
31 626065448865 1.886095% 1.88606% 0.000035% 0.00183%
32 626074544504 1.886095% 1.88609% 0.000007% 0.00038%
33 626074195463 1.886095% 1.88609% 0.000008% 0.00043%
34 626088919182 1.886095% 1.88613% -0.000036% -0.00192%
35 626098508905 1.886095% 1.88616% -0.000065% -0.00345%
36 626093981594 1.886095% 1.88615% -0.000051% -0.00273%
37 626087788636 1.886095% 1.88613% -0.000033% -0.00174%
38 626093203203 1.886095% 1.88614% -0.000049% -0.00260%
39 626099683230 1.886095% 1.88616% -0.000069% -0.00364%
40 626087215190 1.886095% 1.88613% -0.000031% -0.00165%
41 626096146740 1.886095% 1.88615% -0.000058% -0.00307%
42 626072074324 1.886095% 1.88608% 0.000015% 0.00077%
43 626091476264 1.886095% 1.88614% -0.000044% -0.00233%
44 626073164634 1.886095% 1.88608% 0.000011% 0.00060%
45 626093863186 1.886095% 1.88615% -0.000051% -0.00271%
46 626058091809 1.886095% 1.88604% 0.000057% 0.00301%
47 626044086716 1.886095% 1.88600% 0.000099% 0.00524%
48 626098383065 1.886095% 1.88616% -0.000065% -0.00343%
49 626063555064 1.886095% 1.88605% 0.000040% 0.00213%
50 626093342994 1.886095% 1.88614% -0.000050% -0.00262%
51 626096671989 1.886095% 1.88615% -0.000060% -0.00316%
52 626086176445 1.886095% 1.88612% -0.000028% -0.00148%
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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