[原创]k生素数群的数量公式

独舟星海 · 发表于 2021-8-29 18:00

10^n 二生L14差等于186的数量实际数量理论-实际误差/实际
2 3 0 3 #DIV/0!
3 13 10 3 3.000000000000E-01
4 43 37 6 1.621621621622E-01
5 148 150 -2 -1.333333333333E-02
6 627 604 23 3.807947019868E-02
7 3123 3093 30 9.699321047527E-03
8 17339 17263 76 4.402479290969E-03
9 104228 104024 204 1.961085903253E-03
10 664870
11 4442971
12 30825248
13 220599853
14 1620440756
15 12171188103
16 93194529714
17 7.2567900868200000E+11
18 5.7349012039840000E+12
19 4.5921149679205000E+13
20 3.7204799490075500E+14
21 3.0462861416227600E+15
22 2.5181889081176800E+16
23 2.0997748670587900E+17
24 1.7647971096931400E+18
25 1.4940555184409300E+19
26 1.2733143407123100E+20
27 1.0918874464804200E+21
28 9.4166157268470300E+21
29 8.1641189545674900E+22
30 7.1131584446544900E+23
31 6.2260334631224800E+24
32 5.4730224475350000E+25
33 4.8305096412580900E+26
34 4.2795924359598900E+27
35 3.8050361637491000E+28
36 3.3944826201730900E+29
37 3.0378456763753000E+30
38 2.7268460997856400E+31
39 2.4546508456827100E+32
40 2.2155913850555100E+33
41 2.0049422838958800E+34
42 1.8187460461996100E+35
43 1.6536737239833200E+36
44 1.5069133592427200E+37
45 1.3760802172256200E+38
46 1.2591441819159200E+39
47 1.1543707438145900E+40
48 1.0602728102932600E+41
49 9.7557117722721100E+41
50 8.9916196609429400E+42
51 8.3008968894171400E+43
52 7.6752488084721300E+44
53 7.1074545520504400E+45
54 6.5912110587238800E+46
55 6.1210021281412300E+47
56 5.6919881260637700E+48
57 5.2999127824290600E+49
58 4.9410241889501800E+50
59 4.6120076325745600E+51
60 4.3099283268451800E+52
61 4.0321824466267700E+53
62 3.7764551497438200E+54
63 3.5406844950807400E+55
64 3.3230303510225200E+56
65 3.1218475389650800E+57
66 2.9356625804880900E+58

独舟星海 · 发表于 2021-8-29 18:00

10^n 二生L14差等于192的数量实际数量理论-实际误差/实际
2 1 0 1 #DIV/0!
3 6 7 -1 -1.428571428571E-01
4 20 20 0 0.000000000000E+00
5 68 70 -2 -2.857142857143E-02
6 291 302 -11 -3.642384105960E-02
7 1448 1407 41 2.914001421464E-02
8 8043 7964 79 9.919638372677E-03
9 48347 48243 104 2.155753166262E-03
10 308405
11 2060906
12 14298527
13 102326928
14 751653830
15 5645698630
16 43228994928
17 3.3661175481100000E+11
18 2.6601777574440000E+12
19 2.1300876271075000E+13
20 1.7257730613550600E+14
21 1.4130431106863500E+15
22 1.1680811724820300E+16
23 9.7399662144318300E+16
24 8.1861462832991000E+17
25 6.9302907184919100E+18
26 5.9063658935309100E+19
27 5.0648033775059900E+20
28 4.3679691795839400E+21
29 3.7869889784647800E+22
30 3.2994929130607400E+23
31 2.8879932097519100E+24
32 2.5387032946292300E+25
33 2.2406688184740400E+26
34 1.9851216619319800E+27
35 1.7649951078574300E+28
36 1.5745567086567300E+29
37 1.4091279363677000E+30
38 1.2648684056815000E+31
39 1.1386085565765900E+32
40 1.0277189985445600E+33
41 9.3000780290246900E+33
42 8.4363925488016300E+34
43 7.6706919651116200E+35
44 6.9899327958234700E+36
45 6.3830532665149300E+37
46 5.8406365288761000E+38
47 5.3546369280206800E+39
48 4.9181564711279600E+40
49 4.5252614720911900E+41
50 4.1708315060118000E+42
51 3.8504344689892700E+43
52 3.5602228245826400E+44
53 3.2968471188793800E+45
54 3.0573836286594000E+46
55 2.8392736222274100E+47
56 2.6402721982506700E+48
57 2.4584050533284700E+49
58 2.2919318361246900E+50
59 2.1393149916543100E+51
60 1.9991931967875800E+52
61 1.8703586473335100E+53
62 1.7517375860558000E+54
63 1.6423735658077800E+55
64 1.5414130274750400E+56
65 1.4480928423873600E+57
66 1.3617295263171300E+58

独舟星海 · 发表于 2021-8-29 19:08

n值常数
2 0.8198024467614170
3 0.6708911371764450
4 0.8402588276900470
6 0.9136964989279490
7 0.8821704211013320
8 0.8218582224408050
9 0.6728058758352150
10 0.8430124893896950
11 0.7021951679445290
12 0.9177718695843230
13 0.8868498480188450
14 0.8271250132350180

独木星空谁 · 发表于 2021-8-29 19:20

10^n 二生L14差等于198的数量实际数量理论-实际误差/实际
2 2 0 2 #DIV/0!
3 8 6 2 3.333333333333E-01
4 27 27 0 0.000000000000E+00
5 92 94 -2 -2.127659574468E-02
6 393 387 6 1.550387596899E-02
7 1957 2020 -63 -3.118811881188E-02
8 10868 10973 -105 -9.568941948419E-03
9 65331 65516 -185 -2.823737712925E-03
10 416746
11 2784894
12 19321540
13 138273958
14 1015706736
15 7629009385
16 58415163398
17 4.5486208254300000E+11
18 3.5946872840630000E+12
19 2.8783786668675000E+13
20 2.3320300538078500E+14
21 1.9094393551718100E+15
22 1.5784232936028900E+16
23 1.3161576364677600E+17
24 1.1061905869901200E+18
25 9.3648734002480900E+18
26 7.9812479873133900E+19
27 6.8440480138781200E+20
28 5.9024188226104500E+21
29 5.1173426616618100E+22
30 4.4585912295687300E+23
31 3.9025333696229400E+24
32 3.4305393410926100E+25
33 3.0278065768443100E+26
34 2.6824867531860900E+27
35 2.3850306442467600E+28
36 2.1276920171236800E+29
37 1.9041487961861500E+30
38 1.7092114845304200E+31
39 1.5385970687098900E+32
40 1.3887524641237400E+33
41 1.2567157265402200E+34
42 1.1400062621257000E+35
43 1.0365374565585700E+36
44 9.4454674945257700E+36
45 8.6253936777071100E+37
46 7.8924281666630700E+38
47 7.2356989009718100E+39
48 6.6458846512497900E+40
49 6.1149672518177200E+41
50 5.6360274935286100E+42
51 5.2030762925747400E+43
52 4.8109144887568900E+44
53 4.4550159787520000E+45
54 4.1314299473741200E+46
55 3.8366987909866000E+47
56 3.5677889836334100E+48
57 3.3220326572333500E+49
58 3.0970780821697700E+50
59 2.8908475667028100E+51
60 2.7015015604752400E+52
61 2.5274079626416000E+53
62 2.3671158094560500E+54
63 2.2193326578153800E+55
64 2.0829050967919700E+56
65 1.9568019137462800E+57
66 1.8400995192471200E+58

独木星空谁 · 发表于 2021-8-29 19:20

10^n 二生L14差等于204的数量实际数量理论-实际误差/实际
2 3 0 3 #DIV/0!
3 15 14 1 7.142857142857E-02
4 48 38 10 2.631578947368E-01
5 166 163 3 1.840490797546E-02
6 708 724 -16 -2.209944751381E-02
7 3522 3600 -78 -2.166666666667E-02
8 19557 19609 -52 -2.651843541231E-03
9 117557 117437 120 1.021824467587E-03
10 749895
11 5011146
12 34767235
13 248810554
14 1827665594
15 13727661222
16 1.0511241144400000E+11
17 8.1848012723100000E+11
18 6.4682905402180000E+12
19 5.1793627736704000E+13
20 4.1962615227821100E+14
21 3.4358506156943200E+15
22 2.8402193714415000E+16
23 2.3682978007969500E+17
24 1.9904824937701600E+18
25 1.6851179876957400E+19
26 1.4361480366970000E+20
27 1.2315199494884600E+21
28 1.0620829245413300E+22
29 9.2081609647180900E+22
30 8.0228017610250900E+23
31 7.0222296636282000E+24
32 6.1729222639784000E+25
33 5.4482437806032100E+26
34 4.8268743060954500E+27
35 4.2916309362167100E+28
36 3.8285750774129600E+29
37 3.4263307687827000E+30
38 3.0755600148124200E+31
39 2.7685559489040100E+32
40 2.4989251405039900E+33
41 2.2613378587231600E+34
42 2.0513305159500600E+35
43 1.8651484524296600E+36
44 1.6996201119813500E+37
45 1.5520557957437300E+38
46 1.4201657728643900E+39
47 1.3019937216935500E+40
48 1.1958623775603200E+41
49 1.1003289494479900E+42
50 1.0141483928913800E+43
51 9.3624303044381700E+43
52 8.6567732373782200E+44
53 8.0163684445195600E+45
54 7.4341068177606900E+46
55 6.9037667352670800E+47
56 6.4198896617909400E+48
57 5.9776750279061900E+49
58 5.5728911246405600E+50
59 5.2017993475579900E+51
60 4.8610896045047900E+52
61 4.5478250885697800E+53
62 4.2593949314549000E+54
63 3.9934735073580700E+55
64 3.7479853653700300E+56
65 3.5210749385292900E+57
66 3.3110803173820300E+58

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

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