[原创]k生素数群的数量公式

白新岭 · 发表于 2021-5-30 06:48

截止2021年5月29日星期六四月初十八22：06分，浏览量33497人次，回复2345，热度96°。
截止2021年5月30日星期日四月初十九06：45分，浏览量33541人次，回复2348，热度97°。
浏览量 ↑ 44人次，回复 ↑ 3，热度↑1°
大早起，温度又上升了。

白新岭 · 发表于 2021-5-30 09:23

k生统计
2 1
3 20
4 141
5 518
6 1150
7 1666
8 1550
9 874
10 276
11 42
12 2
合计 6240
跨度42的k生素数式种类分布情况。

白新岭 · 发表于 2021-5-30 09:38

k生 7 11 13 17 19 23 29
2 36 324 3564 53460 908820 19085220 515300940
3 314 2542 25580 359720 5777920 115558400 3004518400
4 1218 8800 80546 1058278 16006998 304132962 7603324050
5 2760 17626 145764 1782620 25293628 455285304 10926847296
6 4032 22486 166696 1889606 25040302 425685134 9790758082
7 3948 18926 124590 1303074 16042408 256678528 5646927616
8 2604 10502 60680 582674 6621546 99323190 2085786990
9 1128 3710 18536 162618 1691666 23683324 473666480
10 300 766 3244 25916 243872 3170336 60236384
11 42 76 266 1944 16210 194520 3501360
12 2 2 6 42 294 3234 54978
合计 16384 85760 629472 7219952 97643664 1702800152 40110922576
2邻 0 0 0 0 0 0 272
跨度42的相关数据。

白新岭 · 发表于 2021-5-30 11:10

范围跨度统计
10 42 0
100 42 0
1000 42 0
10000 42 0
100000 42 19
1000000 42 476
10000000 42 7180
100000000 42 86637
1000000000 42 954456
这是跨度42的统计数据。

白新岭 · 发表于 2021-5-30 11:24

综合单一
比值至29 29 29 分母分子
2.40 515300940 214708725 12 5
40.30 3004518400 74547200 2257 56
434.32 7603324050 17506125 762238 1755
1568.31 10926847296 6967296 6323407 4032
5003.06 9790758082 1956955 3577186 715
5570.28 5646927616 1013760 2005301 360
3715.79 2085786990 561330 1103591 297
1409.72 473666480 336000 845833 600
387.10 60236384 155610 121936 315
72.37 3501360 48384 8105 112
2.00 54978 27489 2 1

白新岭 · 发表于 2021-5-30 12:21

二生相邻素数（P，P+42）的数量公式：
\({12}\over {5}\)*1.32032372118072*\(∫_1^n\)\(1\over{ln^2(n)}\)\(d_n\)-\({2257}\over {56}\)*2.85824917688516*\(∫_1^n\)\(1\over{ln^3(n)}\)\(d_n\)+\({762238}\over{1756}\)*4.15118255134627*\(∫_1^n\)\(1\over{ln^4(n)}\)\(d_n\)-\({6323407}\over{4032}\)*10.1318018169296*\(∫_1^n\)\(1\over{ln^5(n)}\)\(d_n\)+\({3577186}\over{715}\)*17.2986298980835*\(∫_1^n\)\(1\over{ln^6(n)}\)\(d_n\)-\({2005301}\over{360}\)*53.9720251184226*\(∫_1^n\)\(1\over{ln^7(n)}\)\(d_n\)+\({1103591}\over {297}\)*178.26229268981*\(∫_1^n\)\(1\over{ln^8(n)}\)\(d_n\)-\({845833}\over{600}\)*630.065899972291*\(∫_1^n\)\(1\over{ln^9(n)}\)\(d_n\)+\({121936}\over{315}\)*1704.74613953383*\(∫_1^n\)\(1\over{ln^{10}(n)}\)\(d_n\)-\({8105}\over {112}\)*3062.09074084973*\(∫_1^n\)\(1\over{ln^{11}(n)}\)\(d_n\)+2*9931.36007094338*\(∫_1^n\)\(1\over{ln^{12}(n)}\)\(d_n\)
这次先贴出公式，后贴出数据，实际数据已经统计完成（且发表）。
再就是本次没有验证素数式是否正确，因为需在至29的素数式中验证，但是vfp容量不允许。

白新岭 · 发表于 2021-5-30 14:52

10的n次幂 12/5倍孪生素数对的数量 2257/56倍最密三生素数的数量
2 2.5000000000000000E+01 1.9400000000000000E+02
3 1.0200000000000000E+02 6.5200000000000000E+02
4 5.0800000000000000E+02 2.4540000000000000E+03
5 2.9900000000000000E+03 1.0905000000000000E+04
6 1.9788000000000000E+04 5.7921000000000000E+04
7 1.4100300000000000E+05 3.4591900000000000E+05
8 1.0568760000000000E+06 2.2361310000000000E+06
9 8.2207330000000000E+06 1.5307051000000000E+07
10 6.5787398000000000E+07 1.0943564400000000E+08
11 5.3848530500000000E+08 8.0968461800000000E+08
12 4.4893439780000000E+09 6.1596185640000000E+09
13 3.8003038501000000E+10 4.7951711684000000E+10
14 3.2587265782700000E+11 3.8062258888100000E+11
15 2.8253005719480000E+12 3.0718493645270000E+12
16 2.4730063806901000E+13 2.5150448831211000E+13
17 2.1827721462044500E+14 2.0851809507119000E+14
18 1.9408222951268800E+15 1.7480221288713500E+15
19 1.7370044527890500E+16 1.4798492906844700E+16
20 1.5637024762714400E+17 1.2638731681692600E+17
21 1.4151119967246000E+18 1.0879812807860100E+18
22 1.2867465183342300E+19 9.4328512317567100E+18
23 1.1750938296076400E+20 8.2316134109740700E+19
24 1.0773726054386900E+21 7.2260558951254800E+20
25 9.9135713499013100E+21 6.3778882622051200E+21
26 9.1524921484584500E+22 5.6574736590412600E+22
27 8.4758323541526900E+23 5.0416297039452800E+23
28 7.8715497988640500E+24 4.5120457789735600E+24
29 7.3296759709849400E+25 4.0541289006986600E+25
30 6.8419017092310300E+26 3.6561518682253900E+26
31 6.4012563728818000E+27 3.3086174372256000E+27
32 6.0018571338788900E+28 3.0037787766573000E+28
33 5.6387114028718900E+29 2.7352742775126000E+29
34 5.3075598958933200E+30 2.4978469221783800E+30
35 5.0047510591822200E+31 2.2871268048169600E+31
36 4.7271398889536000E+32 2.0994612517205600E+32
37 4.4720058756274100E+33 1.9317811325255100E+33
38 4.2369860495048700E+34 1.7814949130054700E+34
39 4.0200200326524300E+35 1.6464041366544800E+35
40 3.8193046977068800E+36 1.5246355791249800E+36
41 3.6332565606205900E+37 1.4145864642380200E+37
42 3.4604804354328900E+38 1.3148799789993100E+38
43 3.2997431870065500E+39 1.2243289593887300E+39
44 3.1499516555976700E+40 1.1419060963953200E+40
45 3.0101340122170900E+41 1.0667193741097300E+41
46 2.8794239486204700E+42 9.9799172840387700E+41
47 2.7570472198376400E+43 9.3504412743154600E+42
48 2.6423101474762400E+44 8.7728143969642700E+43
49 2.5345897639375400E+45 8.2418058342688200E+44
50 2.4333253352140900E+46 7.7528055113859900E+45
51 2.3380110461981700E+47 7.3017398204068100E+46
52 2.2481896697985900E+48 6.8850001722670400E+47
53 2.1634470714866200E+49 6.4993822208465500E+48
54 2.0834074256031700E+50 6.1420339987261000E+49
55 2.0077290399810200E+51 5.8104115209634400E+50
56 1.9361007020488700E+52 5.5022406685067300E+51
57 1.8682384732842400E+53 5.2154843693352400E+52
58 1.8038828702224400E+54 4.9483142631021300E+53
59 1.7427963796477900E+55 4.6990861717672500E+54
60 1.6847612634437500E+56 4.4663188105871500E+55
61 1.6295776151428000E+57 4.2486752657166400E+56
62 1.5770616357234500E+58 4.0449468404048600E+57
63 1.5270441008341100E+59 3.8540389343920200E+58
64 1.4793689955334500E+60 3.6749586730648000E+59
65 1.4338922959450200E+61 3.5068040461634200E+60
66 1.3904808800312800E+62 3.3487543519231500E+61
67 1.3490115520811200E+63 3.2000617727461100E+62
68 1.3093701675422700E+64 3.0600439338650000E+63
69 1.2714508465728300E+65 2.9280773178145200E+64
70 1.2351552661797600E+66 2.8035914255516600E+65
71 1.2003920220955000E+67 2.6860635903200400E+66
72 1.1670760526496600E+68 2.5750143632955000E+67
73 1.1351281178463100E+69 2.4700034010564000E+68
74 1.1044743276827600E+70 2.3706257943048100E+69
75 1.0750457144611300E+71 2.2765087852812300E+70
76 1.0467778444648100E+72 2.1873088281807700E+71
77 1.0196104649127000E+73 2.1027089527692800E+72
78 9.9348718257555000E+73 2.0224163964648700E+73
79 9.6835517084994500E+74 1.9461604745157600E+74
80 9.4416490244624000E+75 1.8736906616751300E+75
81 9.2086990516216000E+76 1.8047748620350800E+76
82 8.9842653849130300E+77 1.7391978465085000E+77
83 8.7679378905960800E+78 1.6767598399021600E+78
84 8.5593308309777900E+79 1.6172752416600000E+79
85 8.3580811434727200E+80 1.5605714662160000E+80
86 8.1638468596504400E+81 1.5064878905207200E+81
87 7.9763056514063000E+82 1.4548748977255200E+82
88 7.7951534927054400E+83 1.4055930072527300E+83
89 7.6201034265180400E+84 1.3585120825706900E+84
90 7.4508844276008400E+85 1.3135106089516100E+85
91 7.2872403527039000E+86 1.2704750343331600E+86
92 7.1289289706048400E+87 1.2292991671481300E+87
93 6.9757210651077500E+88 1.1898836256423400E+88
94 6.8273996048005600E+89 1.1521353337802000E+89
95 6.6837589739521600E+90 1.1159670593505000E+90
96 6.5446042594574900E+91 1.0812969903390000E+91
97 6.4097505892104100E+92 1.0480483460379600E+92
98 6.2790225177086100E+93 1.0161490197204900E+93
99 6.1522534550760400E+94 9.8553125002653900E+93
100 6.0292851360311500E+95 9.5613131849083300E+94
101 5.9099671256388600E+96 9.2788927089625600E+95
102 5.7941563589626900E+97 9.0074866036189400E+96
103 5.6817167119854600E+98 8.7465631027695600E+97
104 5.5725186013946600E+99 8.4956209537236000E+98
105 5.4664386110342600E+100 8.2541873938361500E+99
106 5.3633591430116700E+101 8.0218162790374900E+100
107 5.2631680916172500E+102 7.7980863515528900E+101
108 5.1657585383675300E+103 7.5825996352739500E+102
109 5.0710284666225700E+104 7.3749799482954800E+103
110 4.9788804943545300E+105 7.1748715230805000E+104
111 4.8892216237600000E+106 6.9819377255708200E+105
112 4.8019630065135600E+107 6.7958598653318200E+106
113 4.7170197235557600E+108 6.6163360895171200E+107
114 4.6343105783959700E+109 6.4430803540679700E+108
115 4.5537579029906400E+110 6.2758214661326300E+109
116 4.4752873753298900E+111 6.1143021922065900E+110
117 4.3988278479322900E+112 5.9582784269624600E+111
118 4.3243111865088000E+113 5.8075184181625100E+112
119 4.2516721181123900E+114 5.6618020434325300E+113
120 4.1808480881412700E+115 5.5209201350253300E+114
121 4.1117791256108100E+116 5.3846738490211000E+115
122 4.0444077161519200E+117 5.2528740757014500E+116
123 3.9786786822339200E+118 5.1253408880983200E+117
124 3.9145390701456800E+119 5.0019030259592900E+118
125 3.8519380433030000E+120 4.8823974125909700E+119
126 3.7908267814804900E+121 4.7666687022423900E+120
127 3.7311583855951400E+122 4.6545688558736600E+121
128 3.6728877876946000E+123 4.5459567433229100E+122
129 3.6159716658276300E+124 4.4406977700376600E+123
130 3.5603683634963500E+125 4.3386635266774300E+124
131 3.5060378134106700E+126 4.2397314600229800E+125
132 3.4529414652842200E+127 4.1437845637456500E+126
133 3.4010422174288700E+128 4.0507110876984900E+127
134 3.3503043519209700E+129 3.9604042644904600E+128
135 3.3006934731280800E+130 3.8727620521962900E+129
136 3.2521764493981500E+131 3.7876868921385000E+130
137 3.2047213577270400E+132 3.7050854807556300E+131
138 3.1582974312313500E+133 3.6248685546416700E+132
139 3.1128750092655200E+134 3.5469506879073100E+133
140 3.0684254900319800E+135 3.4712501010741500E+134
141 3.0249212855429700E+136 3.3976884807685800E+135
142 2.9823357788016300E+137 3.3261908095335300E+136
143 2.9406432830783200E+138 3.2566852051239300E+137
144 2.8998190031656600E+139 3.1891027686953100E+138
145 2.8598389985032600E+140 3.1233774413357700E+139
146 2.8206801480698100E+141 3.0594458684289600E+140
147 2.7823201169461800E+142 2.9972472713704600E+141
148 2.7447373244594500E+143 2.9367233261921000E+142
149 2.7079109138228700E+144 2.8778180486785000E+143
150 2.6718207231920700E+145 2.8204776855877600E+144
151 2.6364472580625800E+146 2.7646506116139200E+145
152 2.6017716649378800E+147 2.7102872317522900E+146
153 2.5677757062018200E+148 2.6573398887512200E+147
154 2.5344417361327300E+149 2.6057627753539400E+148
155 2.5017526780003000E+150 2.5555118510534600E+149
156 2.4696920021898800E+151 2.5065447631011000E+150
157 2.4382437053015900E+152 2.4588207715256100E+151
158 2.4073922901752400E+153 2.4123006779352900E+152
159 2.3771227467941900E+154 2.3669467578897700E+153
160 2.3474205340244700E+155 2.3227226966412300E+154
161 2.3182715621474200E+156 2.2795935280575800E+155
162 2.2896621761469600E+157 2.2375255765511800E+156
163 2.2615791397141800E+158 2.1964864018479900E+157
164 2.2340096199345300E+159 2.1564447464415000E+158
165 2.2069411726243100E+160 2.1173704855858800E+159
166 2.1803617282853600E+161 2.0792345796907200E+160
167 2.1542595786481700E+162 2.0420090289887600E+161
168 2.1286233637756100E+163 2.0056668303549300E+162
169 2.1034420597005100E+164 1.9701819361627800E+163
170 2.0787049665721900E+165 1.9355292150705800E+164
171 2.0544016972880200E+166 1.9016844146360400E+165
172 2.0305221665874600E+167 1.8686241256640800E+166
173 2.0070565805872800E+168 1.8363257481980200E+167
174 1.9839954267375700E+169 1.8047674590692500E+168
175 1.9613294641794300E+170 1.7739281809256300E+169
176 1.9390497144859900E+171 1.7437875526631600E+170
177 1.9171474527694800E+172 1.7143259011898500E+171
178 1.8956141991379300E+173 1.6855242144545600E+172
179 1.8744417104858100E+174 1.6573641156775800E+173
180 1.8536219726038700E+175 1.6298278387228000E+174
181 1.8331471925939800E+176 1.6028982045551300E+175
182 1.8130097915756000E+177 1.5765585987294800E+176
183 1.7932023976712100E+178 1.5507929498609000E+177
184 1.7737178392584100E+179 1.5255857090278200E+178
185 1.7545491384773900E+180 1.5009218300633200E+179
186 1.7356895049825100E+181 1.4767867506915400E+180
187 1.7171323299278500E+182 1.4531663744686100E+181
188 1.6988711801765200E+183 1.4300470534897900E+182
189 1.6808997927244400E+184 1.4074155718263700E+183
190 1.6632120693294500E+185 1.3852591296579200E+184
191 1.6458020713372300E+186 1.3635653280672100E+185
192 1.6286640146957500E+187 1.3423221544667700E+186
193 1.6117922651505500E+188 1.3215179686278600E+187
194 1.5951813336133000E+189 1.3011414892837500E+188
195 1.5788258716965300E+190 1.2811817812812000E+189
196 1.5627206674078500E+191 1.2616282432547100E+190
197 1.5468606409970600E+192 1.2424705957999500E+191
198 1.5312408409501000E+193 1.2236988701236800E+192
199 1.5158564401238000E+194 1.2053033971486300E+193
200 1.5007027320159100E+195 1.1872747970529900E+194
201 1.4857751271650200E+196 1.1696039692250300E+195
202 1.4710691496751000E+197 1.1522820826145000E+196
203 1.4565804338599900E+198 1.1353005664631800E+197
204 1.4423047210028600E+199 1.1186511013979500E+198
205 1.4282378562263500E+200 1.1023256108704900E+199
206 1.4143757854690600E+201 1.0863162529284900E+200
207 1.4007145525642100E+202 1.0706154123040800E+201
208 1.3872502964165700E+203 1.0552156928056300E+202
209 1.3739792482739800E+204 1.0401099100000500E+203
210 1.3608977290897500E+205 1.0252910841731400E+204
211 1.3480021469725100E+206 1.0107524335560700E+205
212 1.3352889947203300E+207 9.9648736780680900E+205
213 1.3227548474357300E+208 9.8248948173573600E+206
214 1.3103963602188200E+209 9.6875254926521200E+207
215 1.2982102659353800E+210 9.5527051761329200E+208
216 1.2861933730573900E+211 9.4203750169230700E+209
217 1.2743425635730800E+212 9.2904777871341500E+210
218 1.2626547909641600E+213 9.1629578298863900E+211
219 1.2511270782476600E+214 9.0377610092228700E+212
220 1.2397565160799900E+215 8.9148346618405300E+213
221 1.2285402609211600E+216 8.7941275505638500E+214
222 1.2174755332567600E+217 8.6755898194910000E+215
223 1.2065596158758100E+218 8.5591729507450100E+216
224 1.1957898522023400E+219 8.4448297227656700E+217
225 1.1851636446789400E+220 8.3325141700806300E+218
226 1.1746784532003400E+221 8.2221815444970300E+219
227 1.1643317935952200E+222 8.1137882776573700E+220
228 1.1541212361547000E+223 8.0072919449060900E+221
229 1.1440444042057400E+224 7.9026512304151600E+222
230 1.1340989727280300E+225 7.7998258935199200E+223
231 1.1242826670126300E+226 7.6987767362177800E+224
232 1.1145932613612400E+227 7.5994655717850100E+225
233 1.1050285778244500E+228 7.5018551944684400E+226
234 1.0955864849777000E+229 7.4059093502108800E+227
235 1.0862648967337500E+230 7.3115927083706500E+228
236 1.0770617711903400E+231 7.2188708343975900E+229
237 1.0679751095119000E+232 7.1277101634290900E+230
238 1.0590029548440700E+233 7.0380779747716800E+231
239 1.0501433912600900E+234 6.9499423672346400E+232
240 1.0413945427378900E+235 6.8632722352839900E+233
241 1.0327545721668100E+236 6.7780372459862000E+234
242 1.0242216803831700E+237 6.6942078167122100E+235
243 1.0157941052335200E+238 6.6117550935739000E+236
244 1.0074701206647600E+239 6.5306509305658900E+237
245 9.9924803584034600E+239 6.4508678693868000E+238
246 9.9112619428148300E+240 6.3723791199152700E+239
247 9.8310297303279600E+241 6.2951585413169400E+240
248 9.7517678185146000E+242 6.2191806237594000E+241
249 9.6734606241915000E+243 6.1444204707133700E+242
250 9.5960928757604400E+244 6.0708537818188800E+243
251 9.5196496057618000E+245 5.9984568362964200E+244
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255 9.2228322058914900E+249 5.7201114721467100E+248
256 9.1507969652811700E+250 5.6532266205505600E+249
跨度42的

白新岭 · 发表于 2021-5-30 14:59

10的n次幂 762238/1755倍最密4生素数的数量 6323407/4032倍最密五生素数的数量
2 4.0000000000000000E+02 0.0000000000000000E+00
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255 1.5273398931550700E+247 2.2964578959759400E+245
256 1.5035742497750600E+248 2.2518784358186300E+246
跨度42的

白新岭 · 发表于 2021-5-30 15:04

10的n次幂 3577186/715倍最密六生素数的数量 2005301/360倍最密七生素数的数量
2 0.0000000000000000E+00 0.0000000000000000E+00
3 7.9600000000000000E+02 0.0000000000000000E+00
4 3.6520000000000000E+03 1.2940000000000000E+03
5 8.8440000000000000E+03 2.9680000000000000E+03
6 2.5070000000000000E+04 7.3080000000000000E+03
7 8.6395000000000000E+04 2.1442000000000000E+04
8 3.4805000000000000E+05 7.3255000000000000E+04
9 1.5965980000000000E+06 2.9174000000000000E+05
10 8.0611250000000000E+06 1.3050350000000000E+06
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12 2.5215183600000000E+08 3.3392021000000000E+07
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15 6.2203010496000000E+10 6.4972706440000000E+09
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26 2.0937088740347000E+20 1.2384102155017400E+19
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29 1.0744525051463800E+23 5.6849930022925100E+21
30 8.7370974910790800E+23 4.4659025432499000E+22
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跨度42的

白新岭 · 发表于 2021-5-30 15:10

10的n次幂 1103591/297倍最密八生素数的数量 845833/600倍最密九生素数的数量
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145 4.3954915451801800E+130 1.7708061349689500E+128
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151 3.1747521233927500E+136 1.2280321149457300E+134
152 3.0109878634363600E+137 1.1570005837427500E+135
153 2.8566660127276600E+138 1.0905049127446600E+136
154 2.7111855029380300E+139 1.0282285184629500E+137
155 2.5739870868093200E+140 9.6987876989043100E+137
156 2.4445501838020700E+141 9.1518503759052200E+138
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163 1.7189681771127900E+148 6.1582886800871300E+145
164 1.6366653737771500E+149 5.8275824742028700E+146
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182 7.0991445381199800E+166 2.2771287378786000E+164
183 6.7939444436327900E+167 2.1672944820030500E+165
184 6.5034262893105200E+168 2.0633151123884400E+166
185 6.2268094908007400E+169 1.9648491396752900E+167
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227 1.2075093198213200E+211 3.1038693717081400E+208
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251 5.3958536655241400E+234 1.2541311556222400E+232
252 5.2266248980436600E+235 1.2099689471924500E+233
253 5.0633436917458800E+236 1.1675278823034600E+234
254 4.9057786985136900E+237 1.1267344615688700E+235
255 4.7537084306892600E+238 1.0875185963775800E+236
256 4.6069208043699600E+239 1.0498134380869000E+237
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[原创]k生素数群的数量公式

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