[原创]k生素数群的数量公式

独木星空谁 · 发表于 2021-8-22 16:19

2生d26z 二kd 系数 Excel计算比较
4 6 10.14733099981910 10.14733099981910 0.00000000000000
4 12 7.21587982209360 7.21587982209360 0.00000000000000
4 18 5.79847485703950 5.79847485703950 0.00000000000000
4 24 10.14733099981910 10.14733099981910 0.00000000000000
4 30 20.29466199963820 20.29466199963820 0.00000000000000
4 36 10.52315807388650 10.52315807388650 0.00000000000000
4 42 9.10657910240178 9.10657910240177 0.00000000000000
4 48 5.97418621634372 5.97418621634372 0.00000000000000
4 54 13.52977466642550 13.52977466642550 0.00000000000000
4 60 16.81214603520330 16.81214603520330 0.00000000000000
4 66 13.73322992456720 13.73322992456720 0.00000000000000
4 72 7.12093403496078 7.12093403496079 0.00000000000000

独木星空谁 · 发表于 2021-8-22 16:50

SELECT 1
USE D:\VFP温习\L6二生素数表.DBF ALIAS 二生素数表
SELECT 2
USE D:\VFP温习\L6二生素数四.DBF ALIAS 二生素数四
SELECT 3
USE D:\vfp温习\L6四生素数统计表.DBF ALIAS 四生统计
kssj=SECONDS()
FOR m=81 TO 90
@ 15,22 say m
SELECT 2
DELETE ALL
PACK
SELECT  1
GO 1
For i=1 TO  6852730-m
   @ 5,12 say i
SELECT  1    &&打开盛放素数式的表
jl=recno()
PUBLIC A
A=二生6中
count next m+1 for 2*m=二生6中-A to js1
      IF js1=1
      SELECT 2
      APPEND BLANK    &&增加一条空记录
      REPLACE 二6四 WITH A+m &&将N值付给素数式
      else
   ENDIF
   SELECT 1
   GO jl+1
   ENDFOR

   SELECT 2
   For j=1 to 9
   @ 3,6 say j
   fw=10^j
         SELECT 2
         GO 1
         COUNT ALL FOR fw>二6四 TO tj
            SELECT  3  &&打开盛放素数式的表
            APPEND BLANK    &&增加一条空记录
            REPLACE 范围 WITH fw
            REPLACE 跨度 WITH 2*m
            REPLACE 统计 WITH tj
            REPLACE k生 WITH 4
ENDFOR
endfor
=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")

独木星空谁 · 发表于 2021-8-22 17:21

10^n 二生L6差等于162的数量实际数量理论-实际误差/实际
2 2 2 0 0.000000000000E+00
3 10 8 2 2.500000000000E-01
4 34 27 7 2.592592592593E-01
5 119 116 3 2.586206896552E-02
6 506 500 6 1.200000000000E-02
7 2520 2479 41 1.653892698669E-02
8 13991 13893 98 7.053912042036E-03
9 84101 84073 28 3.330439023230E-04
10 536481
11 3585018
12 24872786
13 178001261
14 1307528059
15 9820889711
16 75198344665
17 5.8554788976400000E+11
18 4.6274720059730000E+12
19 3.7053617327359000E+13
20 3.0020424416129900E+14
21 2.4580377832404300E+15
22 2.0319179465501300E+16
23 1.6943010996267500E+17
24 1.4240087023041200E+18
25 1.2055482459144100E+19
26 1.0274329507816600E+20
27 8.8104021543592600E+20
28 7.5982347589041600E+21
29 6.5875994323061800E+22
30 5.7395830208591400E+23
31 5.0237649323126300E+24
32 4.4161629404248000E+25
33 3.8977215726013600E+26
34 3.4531883793607400E+27
35 3.0702705597147900E+28
36 2.7389963211051900E+29
37 2.4512272009373100E+30
38 2.2002827149994500E+31
39 1.9806493030681200E+32
40 1.7877530486310000E+33
41 1.6177810152815000E+34
42 1.4675399131403800E+35
43 1.3343436255589500E+36
44 1.2159231933199900E+37
45 1.1103543821751600E+38
46 1.0159990985114700E+39
47 9.3145777259522500E+39
48 8.5553047451249200E+40
49 7.8718501886609500E+41
50 7.2553068988298200E+42
51 6.6979650762883100E+43
52 6.1931317971809600E+44
53 5.7349805695855300E+45
54 5.3184254749703000E+46
55 4.9390155102932700E+47
56 4.5928455913755900E+48
57 4.2764813485806900E+49
58 3.9868953800494600E+50
59 3.7214130552498200E+51
60 3.4776663051095600E+52
61 3.2535541121057400E+53
62 3.0472086380691500E+54
63 2.8569661098237700E+55
64 2.6813417315147200E+56
65 2.5190080141994100E+57
66 2.3687760132214200E+58

独木星空谁 · 发表于 2021-8-22 17:22

10^n 二生L6差等于164的数量实际数量理论-实际误差/实际
2 2 0 2 #DIV/0!
3 8 5 3 6.000000000000E-01
4 27 26 1 3.846153846154E-02
5 92 94 -2 -2.127659574468E-02
6 393 385 8 2.077922077922E-02
7 1956 1993 -37 -1.856497742097E-02
8 10863 10968 -105 -9.573304157549E-03
9 65299 65184 115 1.764236622484E-03
10 416541
11 2783524
12 19312038
13 138205952
14 1015207191
15 7625257287
16 58386433663
17 4.5463837235500000E+11
18 3.5929193456110000E+12
19 2.8769630231902000E+13
20 2.3308831152069700E+14
21 1.9085002550521900E+15
22 1.5776469937430300E+16
23 1.3155103240561400E+17
24 1.1056465405349400E+18
25 9.3602675698997400E+18
26 7.9773226513663300E+19
27 6.8406819754171000E+20
28 5.8995158960486100E+21
29 5.1148258511160000E+22
30 4.4563984060335500E+23
31 3.9006140263642500E+24
32 3.4288521338519900E+25
33 3.0263174415592400E+26
34 2.6811674530344700E+27
35 2.3838576389050400E+28
36 2.1266455760191800E+29
37 1.9032122980683000E+30
38 1.7083708604460600E+31
39 1.5378403561767800E+32
40 1.3880694481370600E+33
41 1.2560976488380300E+34
42 1.1394455844512600E+35
43 1.0360276668934500E+36
44 9.4408220264045000E+36
45 8.6211515381426600E+37
46 7.8885465140642000E+38
47 7.2321402408420600E+39
48 6.6426160734580700E+40
49 6.1119597897257200E+41
50 5.6332555835022500E+42
51 5.2005173165300200E+43
52 4.8085483856598500E+44
53 4.4528249135960300E+45
54 4.1293980282418100E+46
55 3.8348118264785100E+47
56 3.5660342742983200E+48
57 3.3203988157304300E+49
58 3.0955548777854300E+50
59 2.8894257905734300E+51
60 2.7001729084645200E+52
61 2.5261649333128000E+53
62 2.3659516149851500E+54
63 2.2182411460275000E+55
64 2.0818806827825600E+56
65 1.9558395197816400E+57
66 1.8391945218331100E+58

独木星空谁 · 发表于 2021-8-22 17:23

10^n 二生L6差等于166的数量实际数量理论-实际误差/实际
2 1 1 0 0.000000000000E+00
3 7 5 2 4.000000000000E-01
4 24 20 4 2.000000000000E-01
5 84 74 10 1.351351351351E-01
6 359 336 23 6.845238095238E-02
7 1788 1748 40 2.288329519451E-02
8 9931 9986 -55 -5.507710795113E-03
9 59698 60077 -379 -6.308570667643E-03
10 380813
11 2544769
12 17655561
13 126351430
14 928128485
15 6971206036
16 53378377080
17 4.1564207559700000E+11
18 3.2847391356910000E+12
19 2.6301934792254000E+13
20 2.1309532034429100E+14
21 1.7447999454549900E+15
22 1.4423253973077400E+16
23 1.2026733219356400E+17
24 1.0108104615187000E+18
25 8.5573969938812200E+18
26 7.2930732338834200E+19
27 6.2539271378071100E+20
28 5.3934889379173600E+21
29 4.6761051471774200E+22
30 4.0741538677763500E+23
31 3.5660415147574500E+24
32 3.1347446772830400E+25
33 2.7667371240763300E+26
34 2.4511921407536300E+27
35 2.1793838734489600E+28
36 1.9442340000834300E+29
37 1.7399655593800400E+30
38 1.5618365133735100E+31
39 1.4059331469685100E+32
40 1.2690087365647500E+33
41 1.1483567284714900E+34
42 1.0417104154618600E+35
43 9.4716309935002500E+35
44 8.6310419467407200E+36
45 7.8816781363747600E+37
46 7.2119118092975900E+38
47 6.6118083371170300E+39
48 6.0728502036962700E+40
49 5.5877106012987600E+41
50 5.1500669223436600E+42
51 4.7544464855055300E+43
52 4.3960984227311800E+44
53 4.0708868892189400E+45
54 3.7752017246868100E+46
55 3.5058834537524800E+47
56 3.2601601130601800E+48
57 3.0355938686614600E+49
58 2.8300357663642200E+50
59 2.6415872612240700E+51
60 2.4685674161878000E+52
61 2.3094848565969700E+53
62 2.1630137265359400E+54
63 2.0279730224552400E+55
64 1.9033087850771500E+56
65 1.7880787169925700E+57
66 1.6814388643022600E+58

独木星空谁 · 发表于 2021-8-22 17:25

10^n 二生L6差等于168的数量实际数量理论-实际误差/实际
2 3 1 2 2.000000000000E+00
3 12 8 4 5.000000000000E-01
4 40 30 10 3.333333333333E-01
5 139 118 21 1.779661016949E-01
6 592 555 37 6.666666666667E-02
7 2948 2996 -48 -1.602136181575E-02
8 16370 16281 89 5.466494687059E-03
9 98398 98274 124 1.261778293343E-03
10 627683
11 4194471
12 29101160
13 208261475
14 1529807829
15 11490440962
16 87982063259
17 6.8509103102400000E+11
18 5.4141422469890000E+12
19 4.3352732273010000E+13
20 3.5123896566872000E+14
21 2.8759042063913100E+15
22 2.3773439974636500E+16
23 1.9823322865632900E+17
24 1.6660901816958200E+18
25 1.4104914477198600E+19
26 1.2020965524145400E+20
27 1.0308170520600300E+21
28 8.8899346679178700E+21
29 7.7074913357982300E+22
30 6.7153121344052000E+23
31 5.8778049708057800E+24
32 5.1669106402970100E+25
33 4.5603342399435900E+26
34 4.0402304038520700E+27
35 3.5922165548663000E+28
36 3.2046256956930700E+29
37 2.8679358250966500E+30
38 2.5743307765493600E+31
39 2.3173596845897000E+32
40 2.0916710668982700E+33
41 1.8928037878793600E+34
42 1.7170216983742400E+35
43 1.5611820419039700E+36
44 1.4226301361843900E+37
45 1.2991146271449300E+38
46 1.1887189452584200E+39
47 1.0898055939364100E+40
48 1.0009706551796200E+41
49 9.2100647207333100E+41
50 8.4887090716308900E+42
51 7.8366191392573300E+43
52 7.2459642027017300E+44
53 6.7099272664150700E+45
54 6.2225578057152500E+46
55 5.7786481470431300E+47
56 5.3736293419094400E+48
57 5.0034831778394100E+49
58 4.6646675946578700E+50
59 4.3540532746422900E+51
60 4.0688695769781900E+52
61 3.8066583111637200E+53
62 3.5652341065409100E+54
63 3.3426503484938200E+55
64 3.1371698258722200E+56
65 2.9472393766133100E+57
66 2.7714679354690700E+58

独木星空谁 · 发表于 2021-8-22 17:26

10^n 二生L6差等于170的数量实际数量理论-实际误差/实际
2 3 0 3 #DIV/0!
3 14 10 4 4.000000000000E-01
4 47 41 6 1.463414634146E-01
5 163 166 -3 -1.807228915663E-02
6 694 721 -27 -3.744798890430E-02
7 3455 3500 -45 -1.285714285714E-02
8 19185 19194 -9 -4.688965301657E-04
9 115324 115118 206 1.789468197849E-03
10 735650
11 4915958
12 34106817
13 244084295
14 1792948336
15 13466898662
16 1.0311575804000000E+11
17 8.0293276122400000E+11
18 6.3454227061410000E+12
19 5.0809786516310000E+13
20 4.1165518125711800E+14
21 3.3705852228158800E+15
22 2.7862682385571600E+16
23 2.3233110118730900E+17
24 1.9526724616982900E+18
25 1.6531084797703600E+19
26 1.4088678151942100E+20
27 1.2081267225030200E+21
28 1.0419082233994800E+22
29 9.0332481671985900E+22
30 7.8704053481754200E+23
31 6.8888395285082800E+24
32 6.0556650715596300E+25
33 5.3447521534601900E+26
34 4.7351858471958800E+27
35 4.2101096448479900E+28
36 3.7558497221688900E+29
37 3.3612462093042900E+30
38 3.0171384897987700E+31
39 2.7159660921489500E+32
40 2.4514570316392400E+33
41 2.2183828178065600E+34
42 2.0123646507184800E+35
43 1.8297191919232800E+36
44 1.6673351302519700E+37
45 1.5225738587771600E+38
46 1.3931891410239000E+39
47 1.2772618164752500E+40
48 1.1731464807912600E+41
49 1.0794277493628600E+42
50 9.9488422785557700E+42
51 9.1845870974823700E+43
52 8.4923342760868700E+44
53 7.8640942351578200E+45
54 7.2928929070204600E+46
55 6.7726268521009900E+47
56 6.2979412222694100E+48
57 5.8641266368865600E+49
58 5.4670317700292100E+50
59 5.1029890335872900E+51
60 4.7687512119663900E+52
61 4.4614372841081700E+53
62 4.1784859762296600E+54
63 3.9176158387455800E+55
64 3.6767908447886700E+56
65 3.4541906746536000E+57
66 3.2481849875388500E+58

独木星空谁 · 发表于 2021-8-22 17:27

10^n 二生L6差等于172的数量实际数量理论-实际误差/实际
2 0 0 0 #DIV/0!
3 3 3 0 0.000000000000E+00
4 12 9 3 3.333333333333E-01
5 43 41 2 4.878048780488E-02
6 184 179 5 2.793296089385E-02
7 916 890 26 2.921348314607E-02
8 5086 5168 -82 -1.586687306502E-02
9 30573 30678 -105 -3.422648151770E-03
10 195025
11 1303247
12 9041903
13 64708082
14 475320412
15 3570148509
16 27336551573
17 2.1286186761800000E+11
18 1.6822062734120000E+12
19 1.3469952371457000E+13
20 1.0913204060043100E+14
21 8.9356058208777000E+14
22 7.3865495292768000E+15
23 6.1592245942557000E+16
24 5.1766415211545900E+17
25 4.3824810167647300E+18
26 3.7349856532567800E+19
27 3.2028100345545200E+20
28 2.7621557000866600E+21
29 2.3947635074724100E+22
30 2.0864875145649100E+23
31 1.8262690459019300E+24
32 1.6053899393028300E+25
33 1.4169230355109900E+26
34 1.2553236729553100E+27
35 1.1161230991693600E+28
36 9.9569630853945800E+28
37 8.9108475851474400E+29
38 7.9985991955773600E+30
39 7.2001746931168700E+31
40 6.4989467031623900E+32
41 5.8810542114603600E+33
42 5.3348887798381000E+34
43 4.8506856765551000E+35
44 4.4201966454913300E+36
45 4.0364265953315100E+37
46 3.6934206302953200E+38
47 3.3860909508605200E+39
48 3.1100755001064700E+40
49 2.8616220160028200E+41
50 2.6374925153498600E+42
51 2.4348842858231700E+43
52 2.2513642757516500E+44
53 2.0848144039776300E+45
54 1.9333858070073600E+46
55 1.7954604296196400E+47
56 1.6696186722803500E+48
57 1.5546120524183500E+49
58 1.4493400308206600E+50
59 1.3528303098149700E+51
60 1.2642220347826000E+52
61 1.1827514312797200E+53
62 1.1077394916144900E+54
63 1.0385813910206500E+55
64 9.7473736763718600E+55
65 9.1572484475175200E+56
66 8.6111161009873000E+57

独木星空谁 · 发表于 2021-8-22 17:28

10^n 二生L6差等于174的数量实际数量理论-实际误差/实际
2 5 0 5 #DIV/0!
3 20 13 7 5.384615384615E-01
4 67 53 14 2.641509433962E-01
5 232 211 21 9.952606635071E-02
6 984 954 30 3.144654088050E-02
7 4899 4924 -25 -5.077173030057E-03
8 27199 27092 107 3.949505389045E-03
9 163493 163008 485 2.975314095014E-03
10 1042920
11 6969276
12 48352697
13 346034452
14 2541834546
15 19091809598
16 1.4618558203000000E+11
17 1.1383050977020000E+12
18 8.9958055796120000E+12
19 7.2032232084386000E+13
20 5.8359705064956500E+14
21 4.7784254506194000E+15
22 3.9500484880934500E+16
23 3.2937213376743900E+17
24 2.7682729172792100E+18
25 2.3435857900576000E+19
26 1.9973296563195400E+20
27 1.7127421788074400E+21
28 1.4770968371309700E+22
29 1.2806293296403200E+23
30 1.1157749392550200E+24
31 9.7661990284157500E+24
32 8.5850207561858100E+25
33 7.5771707371370400E+26
34 6.7129982094772800E+27
35 5.9686059680855500E+28
36 5.3246088482284800E+29
37 4.7651856786221300E+30
38 4.2773495979589300E+31
39 3.8503822451644200E+32
40 3.4753919265386600E+33
41 3.1449662937072400E+34
42 2.8528975911448900E+35
43 2.5939640080866000E+36
44 2.3637546878140600E+37
45 2.1585289189485000E+38
46 1.9751022475063000E+39
47 1.8107539099251200E+40
48 1.6631512424522800E+41
49 1.5302876766756900E+42
50 1.4104316611325200E+43
51 1.3020844108304500E+44
52 1.2039448213719800E+45
53 1.1148802227274300E+46
54 1.0339019123342300E+47
55 9.6014461520101100E+47
56 8.9284918296341500E+48
57 8.3134797416408600E+49
58 7.7505246188161500E+50
59 7.2344269794056500E+51
60 6.7605832971329800E+52
61 6.3249091939335600E+53
62 5.9237735924064300E+54
63 5.5539421174974100E+55
64 5.2125283260646200E+56
65 4.8969515796036600E+57
66 4.6049005697024500E+58

独木星空谁 · 发表于 2021-8-22 17:29

10^n 二生L6差等于176的数量实际数量理论-实际误差/实际
2 3 0 3 #DIV/0!
3 14 10 4 4.000000000000E-01
4 48 43 5 1.162790697674E-01
5 165 171 -6 -3.508771929825E-02
6 701 740 -39 -5.270270270270E-02
7 3489 3558 -69 -1.939291736931E-02
8 19372 19476 -104 -5.339905524748E-03
9 116448 116606 -158 -1.354990309247E-03
10 742820
11 4963871
12 34439242
13 246463284
14 1810423466
15 13598154984
16 1.0412078492100000E+11
17 8.1075861659700000E+11
18 6.4072689313480000E+12
19 5.1305008607112000E+13
20 4.1566741499256800E+14
21 3.4034369306406000E+15
22 2.8134248490694100E+16
23 2.3459553687139600E+17
24 1.9717043570364800E+18
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