[原创]k生素数群的数量公式

独木星空谁 · 发表于 2021-8-29 19:20

10^n 二生L14差等于210的数量实际数量理论-实际误差/实际
2 5 0 5 #DIV/0!
3 21 17 4 2.352941176471E-01
4 70 53 17 3.207547169811E-01
5 241 237 4 1.687763713080E-02
6 1025 1022 3 2.935420743640E-03
7 5103 5091 12 2.357100766058E-03
8 28332 28214 118 4.182320833629E-03
9 170305 170281 24 1.409434992747E-04
10 1086375
11 7259662
12 50367392
13 360452554
14 2647744319
15 19887301665
16 1.5227664794800000E+11
17 1.1857344767730000E+12
18 9.3706308120960000E+12
19 7.5033575087902000E+13
20 6.0791359442663100E+14
21 4.9775265110618800E+15
22 4.1146338417640100E+16
23 3.4309597267441600E+17
24 2.8836176221658500E+18
25 2.4412351979766700E+19
26 2.0805517253328500E+20
27 1.7841064362577500E+21
28 1.5386425386780900E+22
29 1.3339888850420000E+23
30 1.1622655617239800E+24
31 1.0173123987933100E+25
32 8.9427299543602200E+25
33 7.8928861845177500E+26
34 6.9927064682055000E+27
35 6.2172978834224400E+28
36 5.5464675502380000E+29
37 4.9637350818980500E+30
38 4.4555724978738900E+31
39 4.0108148387129400E+32
40 3.6201999234777700E+33
41 3.2760065559450500E+34
42 2.9717683241092600E+35
43 2.7020458417568800E+36
44 2.4622444664729800E+37
45 2.2484676239046900E+38
46 2.0573981744857300E+39
47 1.8862019895053300E+40
48 1.7324492108878000E+41
49 1.5940496632038400E+42
50 1.4691996470130400E+43
51 1.3563379279483800E+44
52 1.2541091889291400E+45
53 1.1613335653410700E+46
54 1.0769811586814900E+47
55 1.0001506408343900E+48
56 9.3005123225355700E+48
57 8.6598747308759000E+49
58 8.0734631446001500E+50
59 7.5358614368808800E+51
60 7.0422742678468600E+52
61 6.5884470770141200E+53
62 6.1705974920900300E+54
63 5.7853563723931400E+55
64 5.4297170063173100E+56
65 5.1009912287538100E+57
66 4.7967714267733800E+58

白新岭 · 发表于 2021-8-29 19:29

10^n 二生L14差等于216的数量实际数量理论-实际误差/实际
2 3 0 3 #DIV/0!
3 12 11 1 9.090909090909E-02
4 41 32 9 2.812500000000E-01
5 142 135 7 5.185185185185E-02
6 606 603 3 4.975124378109E-03
7 3015 2985 30 1.005025125628E-02
8 16739 16782 -43 -2.562269097843E-03
9 100620 101112 -492 -4.865891288868E-03
10 641856
11 4289183
12 29758271
13 212964070
14 1564351258
15 11749897890
16 89968719472
17 7.0056055178000000E+11
18 5.5363948850630000E+12
19 4.4331647426384000E+13
20 3.5917002624832600E+14
21 2.9408428171704600E+15
22 2.4310249984498300E+16
23 2.0270938278225600E+17
24 1.7037108999352100E+18
25 1.4423406848840300E+19
26 1.2292401825684000E+20
27 1.0540931497754800E+21
28 9.0906715373758400E+21
29 7.8815283495578600E+22
30 6.8669455024386400E+23
31 6.0105272250403400E+24
32 5.2835807290486600E+25
33 4.6633076872414500E+26
34 4.1314597810582900E+27
35 3.6733296712811200E+28
36 3.2769869170032200E+29
37 2.9326945079038300E+30
38 2.6324597865294600E+31
39 2.3696862253202400E+32
40 2.1389015041949800E+33
41 1.9355437540400000E+34
42 1.7557924625472200E+35
43 1.5964339090382500E+36
44 1.4547534678624900E+37
45 1.3284489488313700E+38
46 1.2155605058154100E+39
47 1.1144136671581500E+40
48 1.0235728140532000E+41
49 9.4180302040137800E+41
50 8.6803861703308500E+42
51 8.0135718899705500E+43
52 7.4095798224547000E+44
53 6.8614390428302200E+45
54 6.3630646621321300E+46
55 5.9091314162759900E+47
56 5.4949671888134400E+48
57 5.1164630350626200E+49
58 4.7699969142751200E+50
59 4.4523688479793000E+51
60 4.1607456336226700E+52
61 3.8926135741688300E+53
62 3.6457379527631500E+54
63 3.4181281997620300E+55
64 3.2080078773684000E+56
65 3.0137887527453600E+57
66 2.8340483500560200E+58

白新岭 · 发表于 2021-8-29 19:29

10^n 二生L14差等于222的数量实际数量理论-实际误差/实际
2 1 0 1 #DIV/0!
3 7 8 -1 -1.250000000000E-01
4 23 25 -2 -8.000000000000E-02
5 80 91 -11 -1.208791208791E-01
6 341 348 -7 -2.011494252874E-02
7 1700 1707 -7 -4.100761570006E-03
8 9443 9501 -58 -6.104620566256E-03
9 56762 56965 -203 -3.563591679101E-03
10 362088
11 2419640
12 16787417
13 120138592
14 882491389
15 6628424185
16 50753703700
17 3.9520449860100000E+11
18 3.1232249076130000E+12
19 2.5008639793947000E+13
20 2.0261718958545000E+14
21 1.6590062173385800E+15
22 1.3714046746688200E+16
23 1.1435365548445000E+17
24 9.6110780183060600E+17
25 8.1366203925352500E+18
26 6.9344648193252300E+19
27 5.9464146771846200E+20
28 5.1282851678554200E+21
29 4.4461759253857200E+22
30 3.8738232509930800E+23
31 3.3906953399906200E+24
32 2.9806058413335400E+25
33 2.6306936233810800E+26
34 2.3306643331773600E+27
35 2.0722211766670100E+28
36 1.8486338806357300E+29
37 1.6544095433323400E+30
38 1.4850392980023800E+31
39 1.3368018712167700E+32
40 1.2066101843377300E+33
41 1.0918907678897200E+34
42 9.9048837112780200E+34
43 9.0059005030838300E+35
44 8.2066441422423500E+36
45 7.4941273728075200E+37
46 6.8572941910553800E+38
47 6.2866984651743900E+39
48 5.7742414946435400E+40
49 5.3129567389034000E+41
50 4.8968324799264600E+42
51 4.5206651341339900E+43
52 4.1799374388686900E+44
53 3.8707169133566300E+45
54 3.5895709128587400E+46
55 3.3334953168646000E+47
56 3.0998544624986800E+48
57 2.8863303867831100E+49
58 2.6908798019617600E+50
59 2.5116975166286700E+51
60 2.3471852472502500E+52
61 2.1959249516967100E+53
62 2.0566559678428200E+54
63 1.9282553633796800E+55
64 1.8097210033639300E+56
65 1.7001569241841800E+57
66 1.5987606700805800E+58

白新岭 · 发表于 2021-8-29 19:33

SELECT 1
USE D:\素数式系数\素数表十亿.dbf ALIAS 素数表
SELECT 2
USE D:\素数式系数\第n组常数.dbf ALIAS 系数表
kssj=SECONDS()  &&取出开始时间
s=1.0000000000000000
  SELECT 1
  GO 8
   FOR i=1 TO 50876320
   @ 5,12 say i
   P=素数
   s=s*(1-1/(P-16)^2)
      SELECT 1
      SKIP
      ENDFOR

         SELECT 2
         APPEND BLANK    &&增加一条空记录
         REPLACE n值 WITH 16 &&将B值付给素数式
         REPLACE 常数 WITH s &&将B值付给素数式
=MESSAGEBOX("运行时间："+LTRIM(STR(INT((SECONDS()-kssj)/60)))+"分"+LTRIM(STR(MOD(SECONDS()-kssj,60),5,2))+"秒",64,"运行时间提示")

白新岭 · 发表于 2021-8-29 19:34

n值常数
2 0.819802446761417000
3 0.670891137176445000
4 0.840258827690047000
6 0.913696498927949000
7 0.882170421101332000
8 0.821858222440805000
9 0.672805875835215000
10 0.843012489389695000
11 0.702195167944529000
12 0.917771869584323000
13 0.886849848018845000
14 0.827125013235018000
15 0.678113173806174000

白新岭 · 发表于 2021-8-29 19:39

截止2021年8月28日周六22:23分浏览量53225,回复3808,热度127度。参照浏览量67751，差距14526
截止2021年8月29日周日19:36分浏览量53754,回复3844,热度127度。参照浏览量67862，差距14108
浏览量↑\({23}^2\),回复↑\(6^2\), 热度 ° 参照浏览量↑111, 差距↓418度

白新岭 · 发表于 2021-8-29 20:54

2对三生素数的中项差合成数中，合成方法与余数类目数的关系恒等式：
\((P-3)^2=1*(P-3)+6*(P-5)+(P-7)*(P-6)\)，能理解此恒等式者，他素数有关问题上会有大作为。

白新岭 · 发表于 2021-8-29 21:01

2对三生素数的中项差合成数的数量公式，前公共系数（即最小系数，其他系数可在此基础上调整）：
\({105}\over 4^2\)∏\({P(P-6)}\over(P-3)^2\),P≥11，是素数，趋于∞。

独木星空谁 · 发表于 2021-8-29 21:34

10^n 二生L14差等于228的数量实际数量理论-实际误差/实际
2 2 0 2 #DIV/0!
3 7 5 2 4.000000000000E-01
4 25 24 1 4.166666666667E-02
5 87 82 5 6.097560975610E-02
6 372 357 15 4.201680672269E-02
7 1853 1833 20 1.091107474086E-02
8 10292 10168 124 1.219512195122E-02
9 61868 61493 375 6.098255085945E-03
10 394660
11 2637300
12 18297539
13 130945726
14 961876397
15 7224687798
16 55319281568
17 4.3075534081900000E+11
18 3.4041763550180000E+12
19 2.7258306006146000E+13
20 2.2084373245929700E+14
21 1.8082430516376200E+15
22 1.4947701509711400E+16
23 1.2464040266879700E+17
24 1.0475647929294100E+18
25 8.8685546412344100E+18
26 7.5582584895227500E+19
27 6.4813277429572100E+20
28 5.5896029349830300E+21
29 4.8461341732249600E+22
30 4.2222951931535200E+23
31 3.6957072400813000E+24
32 3.2487279106814300E+25
33 2.8673391430066000E+26
34 2.5403205498099000E+27
35 2.2586289942756200E+28
36 2.0149287776895900E+29
37 1.8032328812443100E+30
38 1.6186268405488300E+31
39 1.4570546329366600E+32
40 1.3151514798805600E+33
41 1.1901124140156900E+34
42 1.0795883078081200E+35
43 9.8160313314350600E+35
44 8.9448774166008600E+36
45 8.1682658017434400E+37
46 7.4741459341259900E+38
47 6.8522219498544700E+39
48 6.2936666252624900E+40
49 5.7908867407292200E+41
50 5.3373297907619100E+42
51 4.9273241005039100E+43
52 4.5559460544033000E+44
53 4.2189094231736000E+45
54 3.9124727765939600E+46
55 3.6333617568093600E+47
56 3.3787036084127800E+48
57 3.1459718547672600E+49
58 2.9329394030211300E+50
59 2.7376386747635300E+51
60 2.5583276119696400E+52
61 2.3934606117349300E+53
62 2.2416636083659900E+54
63 2.1017126555485800E+55
64 1.9725154707287200E+56
65 1.8530954933860900E+57
66 1.7425780824031100E+58

独木星空谁 · 发表于 2021-8-29 21:34

10^n 二生L14差等于234的数量实际数量理论-实际误差/实际
2 4 0 4 #DIV/0!
3 17 13 4 3.076923076923E-01
4 56 46 10 2.173913043478E-01
5 194 187 7 3.743315508021E-02
6 825 820 5 6.097560975610E-03
7 4107 4096 11 2.685546875000E-03
8 22801 22911 -110 -4.801187202654E-03
9 137054 137397 -343 -2.496415496699E-03
10 874266
11 5842252
12 40533429
13 290076129
14 2130786466
15 16004412862
16 1.2254545056600000E+11
17 9.5422619072700000E+11
18 7.5410654912160000E+12
19 6.0383672681622000E+13
20 4.8922173122582100E+14
21 4.0056912023177400E+15
22 3.3112736906742900E+16
23 2.7610832734658100E+17
24 2.3206067741252400E+18
25 1.9645971414901400E+19
26 1.6743351790515900E+20
27 1.4357692399696600E+21
28 1.2382308495992000E+22
29 1.0735347223017500E+23
30 9.3533945525111900E+23
31 8.1868761859909500E+24
32 7.1967099769885600E+25
33 6.3518425627577700E+26
34 5.6274180996989900E+27
35 5.0034038750907600E+28
36 4.4635495603195600E+29
37 3.9945924756015400E+30
38 3.5856459059250300E+31
39 3.2277247901850800E+32
40 2.9133753385097800E+33
41 2.6363838767550400E+34
42 2.3915465251176500E+35
43 2.1744859083182900E+36
44 1.9815044631881300E+37
45 1.8094664005817300E+38
46 1.6557022346112900E+39
47 1.5179311849700000E+40
48 1.3941978103166500E+41
49 1.2828200307447500E+42
50 1.1823463094389300E+43
51 1.0915202346543900E+44
52 1.0092511076887500E+45
53 9.3458942615467900E+45
54 8.6670637369886400E+46
55 8.0487660167742200E+47
56 7.4846372600194800E+48
57 6.9690807162055700E+49
58 6.4971628415620800E+50
59 6.0645249789256300E+51
60 5.6673080527711300E+52
61 5.3020881826908300E+53
62 4.9658214842608400E+54
63 4.6557966234165200E+55
64 4.3695939328388000E+56
65 4.1050500972138600E+57
66 3.8602275771015800E+58

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