[原创]k生素数群的数量公式

白新岭 · 发表于 2021-8-18 19:42

余数统计组合10
0 0 无份
1 6 其余
2 6 均分
3 6
4 6
5 6
余数统计组合11
0 6 独拥
1 0 其余
2 0 都
3 0 无份
4 0
5 0
这是6的11种拆分法中，其和模6的余数各自占的组合方法数的分析结果，共有462种组合，分别分配在6类余数上。

白新岭 · 发表于 2021-8-18 19:48

截止2021年8月18日周日19:44分浏览量50266,回复3451,热度126度。
截止2021年8月18日周日19:44分浏览量50266,回复3451,热度126度。
浏览量↑ ，回复↑ ，热度↑ °
先做个模板。

独舟星海 · 发表于 2021-8-18 22:02

有二生素数（P，P+2k）（2k不是3的倍数）的中项差合成的6n类偶数，其合成数的数量公式：2.38128218320321×\((2C_2)^2\)×\((∏{{P_k-1}\over{P_k-2}})^2\)×∏\({P_i-2}\over{P_i-4}\)×∏\({P_j-3}\over{P_j-4}\)×\(d_{(N-6n)}\over{{LN}^4(N-6n)}\)。所对应条件不写了，以后补上，用手机编写太难了。
\(C_2\)是孪生素数常数，2\(C_2\)是常数的2倍之意，C2 被称为孪生素数常数(twin prime constant），\(C_2\)=0.660....，0≡2k|\(P_k\),0≡6n|\(P_i\)，±2k≡6n|\(P_j\)。一定注意\(P_k\)是相对于2k而言。而\(P_i\)和\(P_j\)是相对于6n而言，没有一个是相对于范围（N-6n）而言。当0≡2k|3时，变得多少比这复杂点，以后给出。
加法合成与此公式类似。

独舟星海 · 发表于 2021-8-18 22:05

二生素数(P,P+10)的系数 1.7604315089249800
上边系数的平方值 3.0991190976159000
二生素数L10的四生素数系数 12.4535425906871000
二生L10差6的四生素数系数 12.4535425906871000 ∏(Pi-2)/(Pi-4)∏(Pj-3)/(Pj-4)
二生L10差12的四生素数系数 14.2326201036424000 ∏(Pi-2)/(Pi-4)∏(Pj-3)/(Pj-4) 12%11≡-10
二生L10差18的四生素数系数 16.6047234542495000 ∏(Pi-2)/(Pi-4)∏(Pj-3)/(Pj-4) 18%7≡-10
二生L10差24的四生素数系数 17.8820098738071000 ∏(Pi-2)/(Pi-4)∏(Pj-3)/(Pj-4) 24%7≡10 24%17≡-10
二生L10差30的四生素数系数 16.6047234542495000 ∏(Pi-2)/(Pi-4)∏(Pj-3)/(Pj-4) 30%5≡0 与18档次相同
二生L10差36的四生素数系数 14.5655468896925000 ∏(Pi-2)/(Pi-4)∏(Pj-3)/(Pj-4) 36%13≡10 36%23≡-10
二生L10差42的四生素数系数 23.0621159086798000 ∏(Pi-2)/(Pi-4)∏(Pj-3)/(Pj-4) 42%7≡0 42%13≡-10
二生L10差48的四生素数系数 13.8151299139356000 ∏(Pi-2)/(Pi-4)∏(Pj-3)/(Pj-4) 48%19≡10 48%29≡-10
二生L10差54的四生素数系数 14.2326201036424000 ∏(Pi-2)/(Pi-4)∏(Pj-3)/(Pj-4) 54%11≡10
二生L10差60的四生素数系数 22.1396312723326000 ∏(Pi-2)/(Pi-4)∏(Pj-3)/(Pj-4) 60%5≡0 60%7≡-10
二生L10差66的四生素数系数 22.7721921658278000 ∏(Pi-2)/(Pi-4)∏(Pj-3)/(Pj-4) 66%7≡10 66%11≡0 66%19≡-10
二生L10差72的四生素数系数 13.2638331496407000 ∏(Pi-2)/(Pi-4)∏(Pj-3)/(Pj-4) 72%31≡10 72%41≡-10
二生L10差78的四生素数系数 18.7335341535122000 ∏(Pi-2)/(Pi-4)∏(Pj-3)/(Pj-4) 78%11≡-10 78%13≡0 78%17≡10
二生L10差84的四生素数系数 21.8821936993985000 ∏(Pi-2)/(Pi-4)∏(Pj-3)/(Pj-4) 84%7≡0 84%37≡10 84%47≡-10
二生L10差90的四生素数系数 16.6047234542495000 ∏(Pi-2)/(Pi-4)∏(Pj-3)/(Pj-4) 90%5≡0
二生L10差96的四生素数系数 13.0335348934454000 ∏(Pi-2)/(Pi-4)∏(Pj-3)/(Pj-4) 96%43≡10 96%53≡-10
二生L10差102的四生素数系数 20.1676803088050000 ∏(Pi-2)/(Pi-4)∏(Pj-3)/(Pj-4) 102%7≡-10 102%17≡0 102%23≡10

独舟星海 · 发表于 2021-8-18 22:07

10^n 二生L10差等于6的数量实际数量理论-实际误差/实际
2 2 5 -3 -6.000000000000E-01
3 10 10 0 0.000000000000E+00
4 35 36 -1 -2.777777777778E-02
5 120 126 -6 -4.761904761905E-02
6 512 513 -1 -1.949317738791E-03
7 2551 2542 9 3.540519276161E-03
8 14166 14270 -104 -7.288016818500E-03
9 85152 85239 -87 -1.020659557245E-03
10 543187
11 3629831
12 25183696
13 180226277
14 1323872159
15 9943650832
16 76138323974
17 5.9286723838600000E+11
18 4.6853154060480000E+12
19 3.7516787543951000E+13
20 3.0395679721331500E+14
21 2.4887632555309400E+15
22 2.0573169208820100E+16
23 1.7154798633720800E+17
24 1.4418088110829200E+18
25 1.2206175989883400E+19
26 1.0402758626664300E+20
27 8.9205321812887400E+20
28 7.6932126933904600E+21
29 6.6699444252100100E+22
30 5.8113278086198800E+23
31 5.0865619939665300E+24
32 4.4713649771801100E+25
33 3.9464430922588700E+26
34 3.4963532341027500E+27
35 3.1086489417112200E+28
36 2.7732337751190000E+29
37 2.4818675409490200E+30
38 2.2277862489369400E+31
39 2.0054074193564700E+32
40 1.8100999617388800E+33
41 1.6380032779725200E+34
42 1.4858841620546300E+35
43 1.3510229208784400E+36
44 1.2311222332364900E+37
45 1.1242338119523400E+38
46 1.0286990872428600E+39
47 9.4310099475266500E+39
48 8.6622460544389700E+40
49 7.9702483160192100E+41
50 7.3459982350651900E+42
51 6.7816896397419100E+43
52 6.2705459446457200E+44
53 5.8066678267053500E+45
54 5.3849057934074300E+46
55 5.0007532041719300E+47
56 4.6502561612677800E+48
57 4.3299373654379500E+49
58 4.0367315723000700E+50
59 3.7679307184404400E+51
60 3.5211371339234300E+52
61 3.2942235385070600E+53
62 3.0852987460450100E+54
63 2.8926781861965700E+55
64 2.7148585031586500E+56
65 2.5504956143769000E+57
66 2.3983857133866900E+58

独舟星海 · 发表于 2021-8-18 22:07

10^n 二生L10差等于12的数量实际数量理论-实际误差/实际
2 3 4 -1 -2.500000000000E-01
3 12 11 1 9.090909090909E-02
4 40 42 -2 -4.761904761905E-02
5 138 134 4 2.985074626866E-02
6 586 564 22 3.900709219858E-02
7 2916 2980 -64 -2.147651006711E-02
8 16190 16285 -95 -5.833589192508E-03
9 97317 98107 -790 -8.052432548136E-03
10 620785
11 4148378
12 28781367
13 205972888
14 1512996754
15 11364172380
16 87015227399
17 6.7756255815600000E+11
18 5.3546461783400000E+12
19 4.2876328621658000E+13
20 3.4737919681521700E+14
21 2.8443008634639300E+15
22 2.3512193381508600E+16
23 1.9605484152823800E+17
24 1.6477814983804800E+18
25 1.3949915417009500E+19
26 1.1888867001902000E+20
27 1.0194893921472800E+21
28 8.7922430781605200E+21
29 7.6227936288114300E+22
30 6.6415174955655800E+23
31 5.8132137073903200E+24
32 5.1101314024915500E+25
33 4.5102206768672800E+26
34 3.9958322675460000E+27
35 3.5527416476699700E+28
36 3.1694100287074300E+29
37 2.8364200467988800E+30
38 2.5460414273565000E+31
39 2.2918941935502500E+32
40 2.0686856705587300E+33
41 1.8720037462543100E+34
42 1.6981533280624300E+35
43 1.5440261952896400E+36
44 1.4069968379845600E+37
45 1.2848386422312500E+38
46 1.1756560997061300E+39
47 1.0778297082887600E+40
48 9.8997097765016900E+40
49 9.1088552183076600E+41
50 8.3954265543602200E+42
51 7.7505024454193300E+43
52 7.1663382224522500E+44
53 6.6361918019489700E+45
54 6.1541780496084900E+46
55 5.7151465190536400E+47
56 5.3145784700203200E+48
57 4.9484998462147900E+49
58 4.6134075112000900E+50
59 4.3062065353605000E+51
60 4.0241567244839200E+52
61 3.7648269011509200E+53
62 3.5260557097657300E+54
63 3.3059179270817900E+55
64 3.1026954321813200E+56
65 2.9148521307164600E+57
66 2.7410122438705000E+58

独舟星海 · 发表于 2021-8-18 22:08

10^n 二生L10差等于18的数量实际数量理论-实际误差/实际
2 3 5 -2 -4.000000000000E-01
3 14 15 -1 -6.666666666667E-02
4 47 42 5 1.190476190476E-01
5 161 151 10 6.622516556291E-02
6 683 666 17 2.552552552553E-02
7 3402 3361 41 1.219875037191E-02
8 18888 18934 -46 -2.429491919299E-03
9 113536 114101 -565 -4.951753271225E-03
10 724250
11 4839775
12 33578261
13 240301702
14 1765162879
15 13258201110
16 1.0151776529800000E+11
17 7.9048965118200000E+11
18 6.2470872080640000E+12
19 5.0022383391934000E+13
20 4.0527572961775300E+14
21 3.3183510073745800E+15
22 2.7430892278426700E+16
23 2.2873064844961100E+17
24 1.9224117481105600E+18
25 1.6274901319844500E+19
26 1.3870344835552300E+20
27 1.1894042908385000E+21
28 1.0257616924520600E+22
29 8.8932592336133400E+22
30 7.7484370781598400E+23
31 6.7820826586220400E+24
32 5.9618199695734700E+25
33 5.2619241230118300E+26
34 4.6618043121370000E+27
35 4.1448652556149600E+28
36 3.6976450334920000E+29
37 3.3091567212653600E+30
38 2.9703816652492500E+31
39 2.6738765591419600E+32
40 2.4134666156518500E+33
41 2.1840043706300300E+34
42 1.9811788827395100E+35
43 1.8013638945045800E+36
44 1.6414963109819800E+37
45 1.4989784159364600E+38
46 1.3715987829904800E+39
47 1.2574679930035500E+40
48 1.1549661405918600E+41
49 1.0626997754692300E+42
50 9.7946643134202500E+42
51 9.0422528529892100E+43
52 8.3607279261942900E+44
53 7.7422237689404600E+45
54 7.1798743912099000E+46
55 6.6676709388959100E+47
56 6.2003415483570400E+48
57 5.7732498205839200E+49
58 5.3823087630667600E+50
59 5.0239076245872500E+51
60 4.6948495118979000E+52
61 4.3922980513427400E+53
62 4.1137316613933500E+54
63 3.8569042482620900E+55
64 3.6198113375448700E+56
65 3.4006608191692000E+57
66 3.1978476178489200E+58

独舟星海 · 发表于 2021-8-18 22:08

10^n 二生L10差等于24的数量实际数量理论-实际误差/实际
2 3 6 -3 -5.000000000000E-01
3 15 18 -3 -1.666666666667E-01
4 50 45 5 1.111111111111E-01
5 173 149 24 1.610738255034E-01
6 736 703 33 4.694167852063E-02
7 3664 3606 58 1.608430393788E-02
8 20341 20176 165 8.178033306899E-03
9 122270 121837 433 3.553928609536E-03
10 779961
11 5212065
12 36161205
13 258786449
14 1900944639
15 14278062733
16 1.0932682416800000E+11
17 8.5129654742700000E+11
18 6.7276323779150000E+12
19 5.3870259037468000E+13
20 4.3645078574219600E+14
21 3.5736087771726300E+15
22 2.9540960915228800E+16
23 2.4632531371496500E+17
24 2.0702895748883000E+18
25 1.7526816805986300E+19
26 1.4937294438287100E+20
27 1.2808969285953100E+21
28 1.1046664380253000E+22
29 9.5773560977374400E+22
30 8.3444706995567500E+23
31 7.3037813246698900E+24
32 6.4204215056945100E+25
33 5.6666875170896600E+26
34 5.0204046438398400E+27
35 4.4637010445084200E+28
36 3.9820792668375400E+29
37 3.5637072382857800E+30
38 3.1988725625761200E+31
39 2.8795593713836500E+32
40 2.5991178937789100E+33
41 2.3520047068323400E+34
42 2.1335772583348500E+35
43 1.9399303479280100E+36
44 1.7677652579806000E+37
45 1.6142844479315700E+38
46 1.4771063816820600E+39
47 1.3541963001576700E+40
48 1.2438096898681600E+41
49 1.1444459120437800E+42
50 1.0548100029837200E+43
51 9.7378107647576100E+43
52 9.0038608435938500E+44
53 8.3377794434743400E+45
54 7.7321724213029700E+46
55 7.1805687034263600E+47
56 6.6772908982306600E+48
57 6.2173459606288400E+49
58 5.7963325140719000E+50
59 5.4103620572478100E+51
60 5.0559917820438900E+52
61 4.7301671322152600E+53
62 4.4301725584236100E+54
63 4.1535891904361000E+55
64 3.8982583635098600E+56
65 3.6622501129514500E+57
66 3.4438358961449900E+58

独舟星海 · 发表于 2021-8-18 22:08

10^n 二生L10差等于30的数量实际数量理论-实际误差/实际
2 3 5 -2 -4.000000000000E-01
3 14 16 -2 -1.250000000000E-01
4 47 47 0 0.000000000000E+00
5 161 180 -19 -1.055555555556E-01
6 683 718 -35 -4.874651810585E-02
7 3402 3454 -52 -1.505500868558E-02
8 18888 18770 118 6.286627597230E-03
9 113536 113349 187 1.649771943290E-03
10 724250
11 4839775
12 33578261
13 240301702
14 1765162879
15 13258201110
16 1.0151776529800000E+11
17 7.9048965118200000E+11
18 6.2470872080640000E+12
19 5.0022383391934000E+13
20 4.0527572961775300E+14
21 3.3183510073745800E+15
22 2.7430892278426700E+16
23 2.2873064844961100E+17
24 1.9224117481105600E+18
25 1.6274901319844500E+19
26 1.3870344835552300E+20
27 1.1894042908385000E+21
28 1.0257616924520600E+22
29 8.8932592336133400E+22
30 7.7484370781598400E+23
31 6.7820826586220400E+24
32 5.9618199695734700E+25
33 5.2619241230118300E+26
34 4.6618043121370000E+27
35 4.1448652556149600E+28
36 3.6976450334920000E+29
37 3.3091567212653600E+30
38 2.9703816652492500E+31
39 2.6738765591419600E+32
40 2.4134666156518500E+33
41 2.1840043706300300E+34
42 1.9811788827395100E+35
43 1.8013638945045800E+36
44 1.6414963109819800E+37
45 1.4989784159364600E+38
46 1.3715987829904800E+39
47 1.2574679930035500E+40
48 1.1549661405918600E+41
49 1.0626997754692300E+42
50 9.7946643134202500E+42
51 9.0422528529892100E+43
52 8.3607279261942900E+44
53 7.7422237689404600E+45
54 7.1798743912099000E+46
55 6.6676709388959100E+47
56 6.2003415483570400E+48
57 5.7732498205839200E+49
58 5.3823087630667600E+50
59 5.0239076245872500E+51
60 4.6948495118979000E+52
61 4.3922980513427400E+53
62 4.1137316613933500E+54
63 3.8569042482620900E+55
64 3.6198113375448700E+56
65 3.4006608191692000E+57
66 3.1978476178489200E+58

独舟星海 · 发表于 2021-8-18 22:09

10^n 二生L10差等于36的数量实际数量理论-实际误差/实际
2 3 4 -1 -2.500000000000E-01
3 12 13 -1 -7.692307692308E-02
4 41 37 4 1.081081081081E-01
5 141 135 6 4.444444444444E-02
6 599 577 22 3.812824956672E-02
7 2984 2959 25 8.448800270362E-03
8 16568 16523 45 2.723476366277E-03
9 99593 99658 -65 -6.522306287503E-04
10 635307
11 4245416
12 29454615
13 210790967
14 1548388490
15 11630000973
16 89050671314
17 6.9341197472100000E+11
18 5.4799010597050000E+12
19 4.3879283677135000E+13
20 3.5550502598048500E+14
21 2.9108342169952500E+15
22 2.4062186209146300E+16
23 2.0064091969264100E+17
24 1.6863260948338300E+18
25 1.4276229227933700E+19
26 1.2166969153993300E+20
27 1.0433370972267500E+21
28 8.9979095829128100E+21
29 7.8011045908888900E+22
30 6.7968746299647700E+23
31 5.9491953145807400E+24
32 5.2296666399767300E+25
33 4.6157229149226600E+26
34 4.0893020281903500E+27
35 3.6358467154517200E+28
36 3.2435482749929800E+29
37 2.9027690537415500E+30
38 2.6055979519730300E+31
39 2.3455057536333000E+32
40 2.1170759786419700E+33
41 1.9157933075702000E+34
42 1.7378762129293900E+35
43 1.5801437671092800E+36
44 1.4399090447210400E+37
45 1.3148933473126800E+38
46 1.2031568271846400E+39
47 1.1030420991259200E+40
48 1.0131281935016300E+41
49 9.3219278549932200E+41
50 8.5918108012458400E+42
51 7.9318007482361500E+43
52 7.3339718650827100E+44
53 6.7914243587197000E+45
54 6.2981354308858800E+46
55 5.8488341569262400E+47
56 5.4388960950500400E+48
57 5.0642542285823900E+49
58 4.7213234763743600E+50
59 4.4069365127958400E+51
60 4.1182890455244700E+52
61 3.8528930274936400E+53
62 3.6085365450818900E+54
63 3.3832493405807800E+55
64 3.1752731031095300E+56
65 2.9830358062887800E+57
66 2.8051294893411600E+58

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