[原创]k生素数群的数量公式

yangchuanju · 发表于 2021-5-10 23:05

本帖最后由 yangchuanju 于 2021-5-11 05:32 编辑

白新岭发表于 2021-5-10 20:54
如果yangchuanju先生能给出跨度为24的全部素数式，及跨度为30的全部素数式的话，我会把它们的公式贴出来 ...

跨距24的2-8生素数种类：
2生 1
3生 11
4生 39
5生 62
6生 46
7生 14
8生 2
合计 175

八生2种（间距式，仅显示中间6数，首0和尾24从略，下同）：
268121418 4610121622
附注：这两种八生的首素数分别为5和7，可能各只有唯一1组。

七生14种（间距式，仅显示中间5数）：
26121420 28121418 28121420 28141820
212141820 46101216 46101222 46101618
46101622 410121622 410121822 68141820
610121622 812141820

六生46种（间距式，仅显示中间4数）：
261214 261220 261420 281214
281218 281220 281418 281420
281820 2121418 2121420 2121820
2141820 461012 461016 461018
461022 461216 461222 461618
461622 4101216 4101218 4101222
4101618 4101622 4101822 4121622
4121822 681418 681420 681820
6101216 6101222 6101618 6101622
6121420 6121622 6141820 8121418
8121420 8121820 8141820 10121622
10121822 12141820

五生62种（间距式，仅显示中间3数）：
2612 2614 2620 2812
2814 2818 2820 21214
21218 21220 21418 21420
21820 4610 4612 4616
4618 4622 41012 41016
41018 41022 41216 41218
41222 41618 41622 41822
6814 6818 6820 61012
61016 61018 61022 61214
61216 61220 61222 61418
61420 61618 61622 61820
81214 81218 81220 81418
81420 81820 101216 101218
101222 101618 101622 101822
121418 121420 121622 121820
121822 141820

四生39种（间距式）：
02624 02824 021224 021424
021824 022024 04624 041024
041224 041624 041824 042224
06824 061024 061224 061424
061624 061824 062024 062224
081224 081424 081824 082024
0101224 0101624 0101824 0102224
0121424 0121624 0121824 0122024
0122224 0141824 0142024 0161824
0162224 0182024 0182224

三生11种（间距式）：
0224 0424 0624 0824
01024 01224 01424 01624
01824 02024 02224

二生1种：
0-24

yangchuanju · 发表于 2021-5-11 05:01

跨距26的共148种：
2生 1
3生 8
4生 28
5生 48
6生 42
7生 18
8生 3

八生3种：互素数式
序号 11-37 17-43 29-49
1 11 17 23
2 13 19 29
3 17 23 31
4 19 29 37
5 23 31 41
6 29 37 43
7 31 41 47
8 37 43 49

yangchuanju · 发表于 2021-5-11 05:02

七生18种：间距式，仅显示中间5数，首0和尾26略去，下同
2681218 2681220 2681820 26121420
26121424 26122024 26121820 26142024
28121820 212142024 68121820 68141820
68141824 68142024 68182024 612142024
614182024 814182024

六生42种：
26812 26818 26820 261214
261218 261220 261224 261420
261424 261820 262024 281218
281220 281820 2121420 2121424
2121820 2122024 2142024 681218
681220 681418 681420 681424
681820 681824 682024 6121420
6121424 6121820 6122024 6141820
6141824 6142024 6182024 8121820
8141820 8141824 8142024 8182024
12142024 14182024

五生48种：
268 2612 2614 2618
2620 2624 2812 2818
2820 21214 21218 21220
21224 21420 21424 21820
22024 6812 6814 6818
6820 6824 61214 61218
61220 61224 61418 61420
61424 61820 61824 62024
81218 81220 81418 81420
81424 81820 81824 82024
121420 121424 121820 122024
141820 141824 142024 182024

四生28种：
02626 02826 021226 021426
021826 022026 022426 06826
061226 061426 061826 062026
062426 081226 081426 081826
082026 082426 0121426 0121826
0122026 0122426 0141826 0142026
0142426 0182026 0182426 0202426

三生8种：
0226 0626 0826 01226
01426 01826 02026 02426

二生1种：
0 26

yangchuanju · 发表于 2021-5-11 05:16

跨距28的共147种：
2生 1
3生 8
4生 28
5生 48
6生 42
7生 18
8生 2

八生2种：互素数式
序号 13--41 19--47
1 13 19
2 17 23
3 19 29
4 23 31
5 29 37
6 31 41
7 37 43
8 41 47

yangchuanju · 发表于 2021-5-11 05:16

七生18种：间距式，仅显示中间5数，首0和尾28略去，下同
46101618 46101624 46101824 46161824
410121822 410121824 410122224 410161824
410182224 412182224 610121618 610121622
610121822 610161822 610161824 612161822
1012161822 1012182224

六生42种：
461016 461018 461024 461618
461624 461824 4101218 4101222
4101224 4101618 4101624 4101822
4101824 4102224 4121822 4121824
4122224 4161824 4182224 6101216
6101218 6101222 6101618 6101622
6101624 6101822 6101824 6121618
6121622 6121822 6161822 6161824
10121618 10121622 10121822 10121824
10122224 10161822 10161824 10182224
12161822 12182224

五生48种：
4610 4616 4618 4624
41012 41016 41018 41022
41024 41218 41222 41224
41618 41624 41822 41824
42224 61012 61016 61018
61022 61024 61216 61218
61222 61618 61622 61624
61822 61824 101216 101218
101222 101224 101618 101622
101624 101822 101824 102224
121618 121622 121822 121824
122224 161822 161824 182224

四生28种：
04628 041028 041228 041628
041828 042228 042428 061028
061228 061628 061828 062228
062428 0101228 0101628 0101828
0102228 0102428 0121628 0121828
0122228 0122428 0161828 0162228
0162428 0182228 0182428 0222428

三生8种：
0428 0628 01028 01228
01628 01828 02228 02428

二生1种：
0 28

yangchuanju · 发表于 2021-5-11 05:52

跨距24的4-5生素数的首素数（各4个）：
邻距首素1 首素2 首素3 首素4
2-4-18 5477 7877 12917 13757
2-6-16 4049 10859 32909 38669
2-10-12 1697 1877 2087 6089
2-12-10 617 1787 3557 7307
2-16-6 3389 5279 5879 19139
2-18-4 6449 7457 14009 16229
4-2-18 4153 21187 27103 30553
4-6-14 2347 4129 6043 10333
4-8-12 3037 8167 10627 12277
4-12-8 463 9157 9787 14827
4-14-6 313 3673 4969 7699
4-18-2 5479 10687 12979 13879
6-2-16 5273 17573 17783 22613
6-4-14 7717 8263 9127 15913
6-6-12 7817 8707 9467 12577
6-8-10 677 2903 8363 13463
6-10-8 6373 7213 9043 12697
6-12-6 2393 7103 8713 9203
6-14-4 947 2417 4133 5147
6-16-2 43627 46567 61357 65557
8-4-12 2609 10169 26489 46499
8-6-10 2003 4349 4943 6329
8-10-6 1163 2879 5693 5783
8-12-4 1193 7019 12413 15053
10-2-12 3547 7297 7549 11059
10-6-8 4273 8353 12253 15217
10-8-6 709 1723 3709 4339
10-12-2 787 1699 2089 2767
12-2-10 797 1709 3347 6287
12-4-8 15427 25747 36697 39607
12-6-6 1889 2399 10639 11789
12-8-4 467 26297 35129 40739
12-10-2 619 1459 3559 7309
14-4-6 113 953 1583 2423
14-6-4 1847 2357 3593 3677
16-2-6 2113 5623 7993 16633
16-6-2 6637 9907 10867 17167
18-2-4 1259 5483 12983 13883
18-4-2 1069 5209 6529 22549
2-4-6-12 1487 11777 20747 25577
2-4-8-10 8087 23057 81017 82007
2-4-14-4 107 857 16067 25997
2-6-4-12 16649 19379 28619 46679
2-6-6-10 4649 34259 78569 81929
2-6-10-6 569 29129 39839 83399
2-6-12-4 49409 54539 85619 146519
2-10-2-10 4217 4229 4259 6779
2-10-6-6 239 6299 52709 62189
2-10-8-4 2729 2999 10139 14867
2-12-4-6 659 7559 11069 15359
2-12-6-4 3167 5417 9719 9767
2-16-2-4 22619 65519 113759 150989
4-2-4-14 103 307 853 8287
4-2-6-12 1447 19207 52177 106657
4-2-10-8 2137 44617 104677 108187
4-2-12-6 3163 5413 8623 15643
4-2-16-2 18517 58147 70117 70177
4-6-2-12 3319 3919 4789 8419
4-6-6-8 967 1093 6967 8737
4-6-8-6 349 2833 3613 4933
4-6-12-2 499 5077 16879 20749
4-8-4-8 13147 14407 114757 132607
4-8-6-6 2269 2659 13159 17029
4-8-10-2 397 11677 81019 93889
4-12-2-6 1303 5503 28603 53593
4-12-6-2 11467 94327 114997 182107
4-14-4-2 859 8269 9319 21499
6-2-6-10 563 1613 3533 6263
6-2-10-6 233 22853 68483 237683
6-2-12-4 653 3323 3923 4793
6-4-2-12 607 1777 5407 22147
6-4-6-8 73 373 433 1543
6-4-8-6 733 18433 37483 72883
6-4-12-2 2287 7927 28597 66337
6-6-2-10 167 26687 60077 68477
6-6-4-8 727 5557 18427 200017
6-6-8-4 7517 10247 14747 38177
6-6-10-2 6067 15307 23887 127657
6-8-4-6 7523 12473 12893 31253
6-8-6-4 1973 2837 5393 6977
6-10-2-6 23893 74143 83383 111103
6-10-6-2 6337 9397 25147 28387
6-12-2-4 2063 19973 32303 77243
8-4-2-10 38699 39359 56519 107999
8-4-6-6 929 10589 12479 58049
8-4-8-4 479 1559 8669 14759
8-6-4-6 6029 7229 14723 21383
8-6-6-4 359 719 2273 2663
8-10-2-4 10313 20879 34739 39209
10-2-4-8 2647 53077 78877 82207
10-2-6-6 139 42169 81919 85819
10-2-10-2 409 1039 4219 6679
10-6-2-6 6343 6553 48463 121333
10-6-6-2 547 577 6247 10837
10-8-4-2 21169 23539 45319 48799
12-2-4-6 3989 4919 26669 44519
12-2-6-4 2777 5507 10079 19739
12-4-6-2 997 5827 50527 75967
12-6-2-4 8069 40829 69809 131759
12-6-4-2 5419 18289 27259 35509
14-4-2-4 293 839 863 1409

白新岭 · 发表于 2021-5-11 10:36

10的n次幂 2倍孪生素数对的数量 2倍最密3生素数的数量
2 2.1000000000000000E+01 9.0000000000000000E+00
3 8.5000000000000000E+01 3.2000000000000000E+01
4 4.2300000000000000E+02 1.2100000000000000E+02
5 2.4920000000000000E+03 5.4100000000000000E+02
6 1.6490000000000000E+04 2.8740000000000000E+03
7 1.1750300000000000E+05 1.7165000000000000E+04
8 8.8073000000000000E+05 1.1096400000000000E+05
9 6.8506110000000000E+06 7.5958700000000000E+05
10 5.4822832000000000E+07 5.4305680000000000E+06
11 4.4873775400000000E+08 4.0179298000000000E+07
12 3.7411199810000000E+09 3.0566117800000000E+08
13 3.1669198750000000E+10 2.3795266760000000E+09
14 2.7156054818900000E+11 1.8887784649000000E+10
15 2.3544171432900000E+12 1.5243559097300000E+11
16 2.0608386505751000E+13 1.2480506287530000E+12
17 1.8189767885037100E+14 1.0347375564011000E+13
18 1.6173519126057300E+15 8.6742790621883000E+13
19 1.4475037106575400E+16 7.3435144243092800E+14
20 1.3030853968928700E+17 6.2717676045617000E+15
21 1.1792599972705000E+18 5.3989323636700700E+16
22 1.0722887652785200E+19 4.6809009213857000E+17
23 9.7924485800636300E+19 4.0848059460748600E+18
24 8.9781050453224500E+20 3.5858141792381600E+19
25 8.2613094582510900E+21 3.1649246139431700E+20
26 7.6270767903820400E+22 2.8074304378051400E+21
27 7.0631936284605700E+23 2.5018277662466600E+22
28 6.5596248323867000E+24 2.2390302492026500E+23
29 6.1080633091541200E+25 2.0117963530272500E+24
30 5.7015847576925300E+26 1.8143066426284600E+25
31 5.3343803107348400E+27 1.6418482630450500E+26
32 5.0015476115657500E+28 1.4905769737953800E+27
33 4.6989261690599100E+29 1.3573359285840100E+28
34 4.4229665799111000E+30 1.2395164168541300E+29
35 4.1706258826518500E+31 1.1349499430194900E+30
36 3.9392832407946700E+32 1.0418239264187100E+31
37 3.7266715630228400E+33 9.5861536040255500E+31
38 3.5308217079207300E+34 8.8403823773421600E+32
39 3.3500166938770300E+35 8.1700160968233100E+33
40 3.1827539147557300E+36 7.5657591875054200E+34
41 3.0277138005171600E+37 7.0196581300247300E+35
42 2.8837336961940800E+38 6.5248807110289200E+36
43 2.7497859891721300E+39 6.0755358197402500E+37
44 2.6249597129980600E+40 5.6665256001894400E+38
45 2.5084450101809100E+41 5.2934235666942600E+39
46 2.3995199571837300E+42 4.9523736633245100E+40
47 2.2975393498647000E+43 4.6400063036036000E+41
48 2.2019251228968700E+44 4.3533682430660100E+42
49 2.1121581366146200E+45 4.0898637724329100E+43
50 2.0277711126784100E+46 3.8472052161064700E+44
51 1.9483425384984700E+47 3.6233711115886700E+45
52 1.8734913914988300E+48 3.4165707545144400E+46
53 1.8028725595721900E+49 3.2252140395871200E+47
54 1.7361728546693100E+50 3.0478857237807800E+48
55 1.6731075333175200E+51 2.8833233954271400E+49
56 1.6134172517073900E+52 2.7303985594716600E+50
57 1.5568653944035400E+53 2.5881003516417700E+51
58 1.5032357251853700E+54 2.4555214774809000E+52
59 1.4523303163731600E+55 2.3318460400440000E+53
60 1.4039677195364600E+56 2.2163389755682800E+54
61 1.3579813459523300E+57 2.1083368620304100E+55
62 1.3142180297695500E+58 2.0072399030808300E+56
63 1.2725367506950900E+59 1.9125049209211600E+57
64 1.2328074962778800E+60 1.8236392174712300E+58
65 1.1949102466208500E+61 1.7401951846269500E+59
66 1.1587340666927400E+62 1.6617655623189700E+60
67 1.1241762934009300E+63 1.5879792580751600E+61
68 1.0911418062852200E+64 1.5184976543769600E+62
69 1.0595423721440300E+65 1.4530113406966200E+63
70 1.0292960551498000E+66 1.3912372160469000E+64
71 1.0003266850795800E+67 1.3329159154445900E+65
72 9.7256337720805300E+67 1.2778095201111900E+66
73 9.4594009820525600E+68 1.2256995166961300E+67
74 9.2039527306896500E+69 1.1763849754636200E+68
75 8.9587142871761100E+70 1.1296809213624200E+69
76 8.7231487038733900E+71 1.0854168753045900E+70
77 8.4967538742725100E+72 1.0434355459023400E+71
78 8.2790598547962500E+73 1.0035916544265200E+72
79 8.0696264237495400E+74 9.6575087791654900E+72
80 7.8680408537186700E+75 9.2978889724242100E+73
81 7.6739158763513400E+76 8.9559053853756900E+74
82 7.4868878207608500E+77 8.6304899782433200E+75
83 7.3066149088300600E+78 8.3206513987169500E+76
84 7.1327756924815000E+79 8.0254686338466700E+77
85 6.9650676195606000E+80 7.7440852554803800E+78
86 6.8032057163753700E+81 7.4757041975330400E+79
87 6.6469213761719200E+82 7.2195830104235100E+80
88 6.4959612439212000E+83 6.9750295441872100E+81
89 6.3500861887650300E+84 6.7413980171872800E+82
90 6.2090703563340400E+85 6.5180854321037000E+83
91 6.0727002939199100E+86 6.3045283050648500E+84
92 5.9407741421707000E+87 6.1001996774741000E+85
93 5.8131008875898000E+88 5.9046063833381300E+86
94 5.6894996706671300E+89 5.7172865477794600E+87
95 5.5697991449601300E+90 5.5378072949603700E+88
96 5.4538368828812400E+91 5.3657626459002100E+89
97 5.3414588243420000E+92 5.2007715886686500E+90
98 5.2325187647571800E+93 5.0424763052146600E+91
99 5.1268778792300400E+94 4.8905405406722300E+92
100 5.0244042800259600E+95 4.7446481023913700E+93
101 4.9249726046990500E+96 4.6045014771989700E+94
102 4.8284636324689100E+97 4.4698205565144900E+95
103 4.7347639266545500E+98 4.3403414599476800E+96
104 4.6437655011622200E+99 4.2158154489013900E+97
105 4.5553655091952200E+100 4.0960079225062000E+98
106 4.4694659525097300E+101 3.9806974889330900E+99
107 4.3859734096810400E+102 3.8696751057772400E+100
108 4.3047987819729500E+103 3.7627432837868100E+101
109 4.2258570555188100E+104 3.6597153487332500E+102
110 4.1490670786287700E+105 3.5604147566903700E+103
111 4.0743513531333300E+106 3.4646744584135200E+104
112 4.0016358387613000E+107 3.3723363088930600E+105
113 3.9308497696298000E+108 3.2832505185020700E+106
114 3.8619254819966400E+109 3.1972751424705900E+107
115 3.7947982524922000E+110 3.1142756057016100E+108
116 3.7294061461082400E+111 3.0341242601999900E+109
117 3.6656898732769000E+112 2.9566999726176100E+110
118 3.6035926554240000E+113 2.8818877396287100E+111
119 3.5430600984269900E+114 2.8095783290405100E+112
120 3.4840400734510600E+115 2.7396679447179300E+113
121 3.4264826046756700E+116 2.6720579135594300E+114
122 3.3703397634599300E+117 2.6066543929045800E+115
123 3.3155655685282600E+118 2.5433680968853000E+116
124 3.2621158917880700E+119 2.4821140403519700E+117
125 3.2099483694191700E+120 2.4228112991147000E+118
126 3.1590223179004100E+121 2.3653827853396000E+119
127 3.1092986546626200E+122 2.3097550370307900E+120
128 3.0607398230788300E+123 2.2558580206121700E+121
129 3.0133097215230200E+124 2.2036249456987900E+122
130 2.9669736362469600E+125 2.1529920912178600E+123
131 2.9216981778422200E+126 2.1038986421026800E+124
132 2.8774512210701900E+127 2.0562865358418800E+125
133 2.8342018478573900E+128 2.0101003182199000E+126
134 2.7919202932674800E+129 1.9652870076337300E+127
135 2.7505778942734000E+130 1.9217959674168600E+128
136 2.7101470411651300E+131 1.8795787856425000E+129
137 2.6706011314392000E+132 1.8385891619168400E+130
138 2.6319145260261200E+133 1.7987828007083200E+131
139 2.5940625077212700E+134 1.7601173107914000E+132
140 2.5570212416933200E+135 1.7225521104134000E+133
141 2.5207677379524700E+136 1.6860483378204700E+134
142 2.4852798156680300E+137 1.6505687668044100E+135
143 2.4505360692319400E+138 1.6160777269556000E+136
144 2.4165158359713800E+139 1.5825410283290900E+137
145 2.3831991654193800E+140 1.5499258902508000E+138
146 2.3505667900581800E+141 1.5182008740099400E+139
147 2.3186000974551500E+142 1.4873358192002300E+140
148 2.2872811037162100E+143 1.4573017834892100E+141
149 2.2565924281857200E+144 1.4280709856091800E+142
150 2.2265172693267300E+145 1.3996167513771800E+143
151 2.1970393817188200E+146 1.3719134625642800E+144
152 2.1681430541149000E+147 1.3449365084459800E+145
153 2.1398130885015100E+148 1.3186622398765500E+146
154 2.1120347801106000E+149 1.2930679257405500E+147
155 2.0847938983335900E+150 1.2681317116437200E+148
156 2.0580766684915700E+151 1.2438325807147700E+149
157 2.0318697544179900E+152 1.2201503163972900E+150
158 2.0061602418127000E+153 1.1970654671189700E+151
159 1.9809356223284900E+154 1.1745593127321800E+152
160 1.9561837783537200E+155 1.1526138326265700E+153
161 1.9318929684561900E+156 1.1312116754206900E+154
162 1.9080518134558000E+157 1.1103361301450300E+155
163 1.8846492830951500E+158 1.0899710988346200E+156
164 1.8616746832787800E+159 1.0701010704539100E+157
165 1.8391176438535900E+160 1.0507110960816100E+158
166 1.8169681069044600E+161 1.0317867652873800E+159
167 1.7952163155401400E+162 1.0133141836364200E+160
168 1.7738528031463400E+163 9.9527995126163800E+160
169 1.7528683830837500E+164 9.7767114244674700E+161
170 1.7322541388101600E+165 9.6047528616706000E+162
171 1.7120014144066800E+166 9.4368034753760200E+163
172 1.6921018054895500E+167 9.2727471012130000E+164
173 1.6725471504894000E+168 9.1124715905262900E+165
174 1.6533295222813100E+169 8.9558686493467500E+166
175 1.6344412201495300E+170 8.8028336846996300E+167
176 1.6158747620716600E+171 8.6532656578765700E+168
177 1.5976228773079000E+172 8.5070669443182500E+169
178 1.5796784992816100E+173 8.3641431997745300E+170
179 1.5620347587381700E+174 8.2244032324275300E+171
180 1.5446849771698900E+175 8.0877588806802800E+172
181 1.5276226604949800E+176 7.9541248963302700E+173
182 1.5108414929796700E+177 7.8234188328623000E+174
183 1.4943353313926700E+178 7.6955609386097100E+175
184 1.4780981993820100E+179 7.5704740545465500E+176
185 1.4621242820644900E+180 7.4480835164861000E+177
186 1.4464079208187600E+181 7.3283170614732900E+178
187 1.4309436082732100E+182 7.2111047381694500E+179
188 1.4157259834804300E+183 7.0963788210392800E+180
189 1.4007498272703700E+184 6.9840737281592100E+181
190 1.3860100577745400E+185 6.8741259424761700E+182
191 1.3715017261143600E+186 6.7664739363547700E+183
192 1.3572200122464600E+187 6.6610580992591300E+184
193 1.3431602209588000E+188 6.5578206684235700E+185
194 1.3293177780110900E+189 6.4567056623739600E+186
195 1.3156882264137800E+190 6.3576588171685700E+187
196 1.3022672228398700E+191 6.2606275252338300E+188
197 1.2890505341642200E+192 6.1655607766767600E+189
198 1.2760340341250900E+193 6.0724091029620000E+190
199 1.2632137001031700E+194 5.9811245228465700E+191
200 1.2505856100132600E+195 5.8916604904712000E+192
201 1.2381459393041800E+196 5.8039718455118800E+193
202 1.2258909580625800E+197 5.7180147653001100E+194
203 1.2138170282166600E+198 5.6337467188248000E+195
204 1.2019206008357100E+199 5.5511264225330200E+196
205 1.1901982135219600E+200 5.4701137978508900E+197
206 1.1786464878908900E+201 5.3906699303496400E+198
207 1.1672621271368400E+202 5.3127570304854800E+199
208 1.1560419136804700E+203 5.2363383958453700E+200
209 1.1449827068949800E+204 5.1613783748340900E+201
210 1.1340814409081200E+205 5.0878423317408900E+202
211 1.1233351224770900E+206 5.0156966131271700E+203
212 1.1127408289336100E+207 4.9449085154790700E+204
213 1.1022957061964400E+208 4.8754462540718800E+205
214 1.0919969668490200E+209 4.8072789329952900E+206
215 1.0818418882794800E+210 4.7403765162910400E+207
216 1.0718278108811500E+211 4.6747098001567700E+208
217 1.0619521363109000E+212 4.6102503861720200E+209
218 1.0522123258034700E+213 4.5469706555041000E+210
219 1.0426058985397200E+214 4.4848437440538900E+211
220 1.0331304300666600E+215 4.4238435185030500E+212
221 1.0237835507676300E+216 4.3639445532261900E+213
222 1.0145629443806400E+217 4.3051221080327500E+214
223 1.0054663465631700E+218 4.2473521067055400E+215
224 9.9649154350194600E+218 4.1906111163037500E+216
225 9.8763637056578600E+219 4.1348763271999600E+217
226 9.7889871100028600E+220 4.0801255338221800E+218
227 9.7027649466268500E+221 4.0263371160727800E+219
228 9.6176769679558100E+222 3.9734900213977900E+220
229 9.5337033683812000E+223 3.9215637474811600E+221
230 9.4508247727335500E+224 3.8705383255393500E+222
231 9.3690222251052300E+225 3.8203943041931400E+223
232 9.2882771780103700E+226 3.7711127338942000E+224
233 9.2085714818704400E+227 3.7226751518850900E+225
234 9.1298873748141500E+228 3.6750635676722100E+226
235 9.0522074727812100E+229 3.6282604489920800E+227
236 8.9755147599195100E+230 3.5822487082522300E+228
237 8.8997925792658100E+231 3.5370116894287000E+229
238 8.8250246237005600E+232 3.4925331554028700E+230
239 8.7511949271674400E+233 3.4487972757212200E+231
240 8.6782878561490400E+234 3.4057886147621100E+232
241 8.6062881013900600E+235 3.3634921202944300E+233
242 8.5351806698597500E+236 3.3218931124136800E+234
243 8.4649508769459600E+237 3.2809772728412800E+235
244 8.3955843388730300E+238 3.2407306345741300E+236
245 8.3270669653362200E+239 3.2011395718711600E+237
246 8.2593849523456900E+240 3.1621907905649600E+238
247 8.1925247752733000E+241 3.1238713186863000E+239
248 8.1264731820955000E+242 3.0861684973905800E+240
249 8.0612171868262500E+243 3.0490699721750000E+241
250 7.9967440631337000E+244 3.0125636843762300E+242
251 7.9330413381348300E+245 2.9766378629384100E+243
252 7.8700967863625300E+246 2.9412810164419500E+244
253 7.8078984238994100E+247 2.9064819253837800E+245
254 7.7464345026733600E+248 2.8722296347002000E+246
255 7.6856935049095700E+249 2.8385134465238500E+247
256 7.6256641377343100E+250 2.8053229131664300E+248

白新岭 · 发表于 2021-5-11 10:40

二生相邻素数（P，P+6）的数量公式：
2*1.32032372118072*\(∫_1^n\)\(1\over{ln^2(n)}\)\(d_n\)-2*2.85824917688516*\(∫_1^n\)\(1\over{ln^3(n)}\)\(d_n\)

白新岭 · 发表于 2021-5-11 10:49

10的n次幂二生相邻素数(0,6)的数量实际数据实际-理论误差/实际
2 1.2000000000000000E+01 7 -5 -71.43%
3 5.3000000000000000E+01 44 -9 -20.45%
4 3.0200000000000000E+02 299 -3 -1.00%
5 1.9510000000000000E+03 1940 -11 -0.57%
6 1.3616000000000000E+04 13549 -67 -0.49%
7 1.0033800000000000E+05 99987 -351 -0.35%
8 7.6976600000000000E+05 768752 -1014 -0.13%
9 6.0910240000000000E+06
10 4.9392264000000000E+07
11 4.0855845600000000E+08
12 3.4354588030000000E+09
13 2.9289672074000000E+10
14 2.5267276354000000E+11
15 2.2019815523170000E+12
16 1.9360335876998000E+13
17 1.7155030328636000E+14
18 1.5306091219838500E+15
19 1.3740685664144500E+16
20 1.2403677208472500E+17
21 1.1252706736338000E+18
22 1.0254797560646600E+19
23 9.3839679854561400E+19
24 8.6195236273986300E+20
25 7.9448169968567700E+21
26 7.3463337466015300E+22
27 6.8130108518359000E+23
28 6.3357218074664300E+24
29 5.9068836738513900E+25
30 5.5201540934296800E+26
31 5.1701954844303400E+27
32 4.8524899141862100E+28
33 4.5631925762015100E+29
34 4.2990149382256900E+30
35 4.0571308883499000E+31
36 3.8351008481528000E+32
37 3.6308100269825800E+33
38 3.4424178841473100E+34
39 3.2683165329088000E+35
40 3.1070963228806800E+36
41 2.9575172192169100E+37
42 2.8184848890837900E+38
43 2.6890306309747300E+39
44 2.5682944569961700E+40
45 2.4555107745139700E+41
46 2.3499962205504900E+42
47 2.2511392868286600E+43
48 2.1583914404662100E+44
49 2.0712594988902900E+45
50 1.9892990605173500E+46
51 1.9121088273825800E+47
52 1.8393256839536900E+48
53 1.7706204191763200E+49
54 1.7056939974315000E+50
55 1.6442742993632500E+51
56 1.5861132661126700E+52
57 1.5309843908871200E+53
58 1.4786805104105600E+54
59 1.4290118559727200E+55
60 1.3818043297807800E+56
61 1.3368979773320300E+57
62 1.2941456307387400E+58
63 1.2534117014858800E+59
64 1.2145711041031700E+60
65 1.1775082947745800E+61
66 1.1421164110695500E+62
67 1.1082965008201800E+63
68 1.0759568297414500E+64
69 1.0450122587370600E+65
70 1.0153836829893300E+66
71 9.8699752592513400E+66
72 9.5978528200694100E+67
73 9.3368310303829500E+68
74 9.0863142331432900E+69
75 8.8457461950398700E+70
76 8.6146070163429300E+71
77 8.3924103196822700E+72
78 8.1787006893536000E+73
79 7.9730513359578900E+74
80 7.7750619639944300E+75
81 7.5843568224975800E+76
82 7.4005829209784200E+77
83 7.2234083948428900E+78
84 7.0525210061430300E+79
85 6.8876267670058000E+80
86 6.7284486744000400E+81
87 6.5747255460676800E+82
88 6.4262109484793300E+83
89 6.2826722085931600E+84
90 6.1438895020130000E+85
91 6.0096550108692600E+86
92 5.8797721453959600E+87
93 5.7540548237564200E+88
94 5.6323268051893400E+89
95 5.5144210720105300E+90
96 5.4001792564222400E+91
97 5.2894511084553100E+92
98 5.1820940017050300E+93
99 5.0779724738233200E+94
100 4.9769577990020500E+95
101 4.8789275899270600E+96
102 4.7837654269037700E+97
103 4.6913605120550700E+98
104 4.6016073466732100E+99
105 4.5144054299701600E+100
106 4.4296589776204000E+101
107 4.3472766586232700E+102
108 4.2671713491350800E+103
109 4.1892599020314800E+104
110 4.1134629310618700E+105
111 4.0397046085492000E+106
112 3.9679124756723700E+107
113 3.8980172644447800E+108
114 3.8299527305719300E+109
115 3.7636554964351800E+110
116 3.6990649035062400E+111
117 3.6361228735507200E+112
118 3.5747737780277100E+113
119 3.5149643151365800E+114
120 3.4566433940038800E+115
121 3.3997620255400800E+116
122 3.3442732195308800E+117
123 3.2901318875594100E+118
124 3.2372947513845500E+119
125 3.1857202564280200E+120
126 3.1353684900470100E+121
127 3.0862011042923100E+122
128 3.0381812428727100E+123
129 2.9912734720660300E+124
130 2.9454437153347800E+125
131 2.9006591914211900E+126
132 2.8568883557117700E+127
133 2.8141008446751900E+128
134 2.7722674231911400E+129
135 2.7313599345992300E+130
136 2.6913512533087000E+131
137 2.6522152398200300E+132
138 2.6139266980190400E+133
139 2.5764613346133600E+134
140 2.5397957205891900E+135
141 2.5039072545742700E+136
142 2.4687741279999900E+137
143 2.4343752919623800E+138
144 2.4006904256880900E+139
145 2.3676999065168700E+140
146 2.3353847813180800E+141
147 2.3037267392631500E+142
148 2.2727080858813200E+143
149 2.2423117183296300E+144
150 2.2125211018129600E+145
151 2.1833202470931800E+146
152 2.1546936890304400E+147
153 2.1266264661027400E+148
154 2.0991041008531900E+149
155 2.0721125812171500E+150
156 2.0456383426844200E+151
157 2.0196682512540200E+152
158 1.9941895871415100E+153
159 1.9691900292011700E+154
160 1.9446576400274500E+155
161 1.9205808517019800E+156
162 1.8969484521543500E+157
163 1.8737495721068000E+158
164 1.8509736725742400E+159
165 1.8286105328927700E+160
166 1.8066502392515900E+161
167 1.7850831737037800E+162
168 1.7639000036337200E+163
169 1.7430916716592800E+164
170 1.7226493859484900E+165
171 1.7025646109313000E+166
172 1.6828290583883400E+167
173 1.6634346788988700E+168
174 1.6443736536319600E+169
175 1.6256383864648300E+170
176 1.6072214964137800E+171
177 1.5891158103635800E+172
178 1.5713143560818400E+173
179 1.5538103555057400E+174
180 1.5365972182892100E+175
181 1.5196685355986500E+176
182 1.5030180741468100E+177
183 1.4866397704540600E+178
184 1.4705277253274600E+179
185 1.4546761985480000E+180
186 1.4390796037572900E+181
187 1.4237325035350400E+182
188 1.4086296046593900E+183
189 1.3937657535422100E+184
190 1.3791359318320600E+185
191 1.3647352521780100E+186
192 1.3505589541472000E+187
193 1.3366024002903800E+188
194 1.3228610723487200E+189
195 1.3093305675966100E+190
196 1.2960065953146400E+191
197 1.2828849733875400E+192
198 1.2699616250221300E+193
199 1.2572325755803200E+194
200 1.2446939495227900E+195
201 1.2323419674586700E+196
202 1.2201729432972800E+197
203 1.2081832814978400E+198
204 1.1963694744131800E+199
205 1.1847280997241100E+200
206 1.1732558179605400E+201
207 1.1619493701063500E+202
208 1.1508055752846200E+203
209 1.1398213285201500E+204
210 1.1289935985763800E+205
211 1.1183194258639600E+206
212 1.1077959204181300E+207
213 1.0974202599423700E+208
214 1.0871896879160200E+209
215 1.0771015117631900E+210
216 1.0671531010809900E+211
217 1.0573418859247300E+212
218 1.0476653551479700E+213
219 1.0381210547956700E+214
220 1.0287065865481600E+215
221 1.0194196062144000E+216
222 1.0102578222726100E+217
223 1.0012189944564600E+218
224 9.9230093238564200E+218
225 9.8350149423858600E+219
226 9.7481858546646400E+220
227 9.6625015754661200E+221
228 9.5779420677418300E+222
229 9.4944877309063900E+223
230 9.4121193894781600E+224
231 9.3308182820633000E+225
232 9.2505660506714300E+226
233 9.1713447303515900E+227
234 9.0931367391374300E+228
235 9.0159248682912900E+229
236 8.9396922728369900E+230
237 8.8644224623715200E+231
238 8.7900992921465300E+232
239 8.7167069544102300E+233
240 8.6442299700014200E+234
241 8.5726531801871200E+235
242 8.5019617387356100E+236
243 8.4321411042175500E+237
244 8.3631770325272900E+238
245 8.2950555696175100E+239
246 8.2277630444400400E+240
247 8.1612860620864400E+241
248 8.0956114971215900E+242
249 8.0307264871045000E+243
250 7.9666184262899400E+244
251 7.9032749595054500E+245
252 7.8406839761981100E+246
253 7.7788336046455700E+247
254 7.7177122063263600E+248
255 7.6573083704443300E+249
256 7.5976109086026500E+250
理论值大于实际的（不知道大范围时，会不会翻转）。

yangchuanju · 发表于 2021-5-11 11:05

跨距30的2-9生素数共665种：
2生 1
3生 14
4生 66
5生 164
6生 220
7生 150
8生 46
9生 4
合计 665

跨距等于30的九生素数有4种，11-41,13-43,17-47,19-49，跨距式：
11-41 0 2 6 8 12 18 20 26 30
13-43 0 4 6 10 16 18 24 28 30
17-47 0 2 6 12 14 20 24 26 30
19-49 0 4 10 12 18 22 24 28 30

		自动登录	找回密码
密码			注册

[原创]k生素数群的数量公式

点评

点评