[原创]k生素数群的数量公式

白新岭 · 发表于 2021-5-8 07:19

二生相邻素数（P，P+12）的数量公式：
2*1.32032372118072*\(∫_1^n\)\(1\over{ln^2(n)}\)\(d_n\)-7*2.85824917688516*\(∫_1^n\)\(1\over{ln^3(n)}\)\(d_n\)+10*4.15118255134627*\(∫_1^n\)\(1\over{ln^4(n)}\)\(d_n\)-2*10.1318018169296*\(∫_1^n\)\(1\over{ln^5(n)}\)\(d_n\)

白新岭 · 发表于 2021-5-8 07:30

白新岭发表于 2021-5-8 07:19
二生相邻素数（P，P+12）的数量公式：
2*1.32032372118072*\(∫_1^n\)\(1\over{ln^2(n)}\)\(d_n\)-7*2.858 ...

在以前只是文字叙述，给出了数据，没有把公式发表上来，是因为自己无法驾驭公式编译器。这回效果很好。自己非常满义。

白新岭 · 发表于 2021-5-8 07:32

白新岭发表于 2021-5-8 07:19
二生相邻素数（P，P+12）的数量公式：
2*1.32032372118072*\(∫_1^n\)\(1\over{ln^2(n)}\)\(d_n\)-7*2.858 ...

大家可以用公式求一下数量，然后在与编程获得的数据比对一下，看一看准确度如何。

白新岭 · 发表于 2021-5-8 07:40

10的n次幂 2倍孪生素数对的数量 7倍最密3生素数的数量
2 2.1000000000000000E+01 3.3000000000000000E+01
3 8.5000000000000000E+01 1.1300000000000000E+02
4 4.2300000000000000E+02 4.2600000000000000E+02
5 2.4920000000000000E+03 1.8940000000000000E+03
6 1.6490000000000000E+04 1.0059000000000000E+04
7 1.1750300000000000E+05 6.0079000000000000E+04
8 8.8073000000000000E+05 3.8837500000000000E+05
9 6.8506110000000000E+06 2.6585570000000000E+06
10 5.4822832000000000E+07 1.9006988000000000E+07
11 4.4873775400000000E+08 1.4062754500000000E+08
12 3.7411199810000000E+09 1.0698141230000000E+09
13 3.1669198750000000E+10 8.3283433670000000E+09
14 2.7156054818900000E+11 6.6107246274000000E+10
15 2.3544171432900000E+12 5.3352456840700000E+11
16 2.0608386505751000E+13 4.3681772006350000E+12
17 1.8189767885037100E+14 3.6215814474039000E+13
18 1.6173519126057300E+15 3.0359976717659200E+14
19 1.4475037106575400E+16 2.5702300485082500E+15
20 1.3030853968928700E+17 2.1951186615966000E+16
21 1.1792599972705000E+18 1.8896263272845200E+17
22 1.0722887652785200E+19 1.6383153224849900E+18
23 9.7924485800636300E+19 1.4296820811262000E+19
24 8.9781050453224500E+20 1.2550349627333600E+20
25 8.2613094582510900E+21 1.1077236148801100E+21
26 7.6270767903820400E+22 9.8260065323180000E+21
27 7.0631936284605700E+23 8.7563971818633200E+22
28 6.5596248323867000E+24 7.8366058722092900E+23
29 6.1080633091541200E+25 7.0412872355953700E+24
30 5.7015847576925300E+26 6.3500732491996100E+25
31 5.3343803107348400E+27 5.7464689206576600E+26
32 5.0015476115657500E+28 5.2170194082838400E+27
33 4.6989261690599100E+29 4.7506757500440300E+28
34 4.4229665799111000E+30 4.3383074589894700E+29
35 4.1706258826518500E+31 3.9723248005682300E+30
36 3.9392832407946700E+32 3.6463837424654900E+31
37 3.7266715630228400E+33 3.3551537614089400E+32
38 3.5308217079207300E+34 3.0941338320697600E+33
39 3.3500166938770300E+35 2.8595056338881600E+34
40 3.1827539147557300E+36 2.6480157156269000E+35
41 3.0277138005171600E+37 2.4568803455086600E+36
42 2.8837336961940800E+38 2.2837082488601200E+37
43 2.7497859891721300E+39 2.1264375369090900E+38
44 2.6249597129980600E+40 1.9832839600663000E+39
45 2.5084450101809100E+41 1.8526982483429900E+40
46 2.3995199571837300E+42 1.7333307821635800E+41
47 2.2975393498647000E+43 1.6240022062612600E+42
48 2.2019251228968700E+44 1.5236788850731000E+43
49 2.1121581366146200E+45 1.4314523203515200E+44
50 2.0277711126784100E+46 1.3465218256372700E+45
51 1.9483425384984700E+47 1.2681798890560300E+46
52 1.8734913914988300E+48 1.1957997640800500E+47
53 1.8028725595721900E+49 1.1288249138554900E+48
54 1.7361728546693100E+50 1.0667600033232700E+49
55 1.6731075333175200E+51 1.0091631883995000E+50
56 1.6134172517073900E+52 9.5563949581508100E+50
57 1.5568653944035400E+53 9.0583512307461800E+51
58 1.5032357251853700E+54 8.5943251711831500E+52
59 1.4523303163731600E+55 8.1614611401540100E+53
60 1.4039677195364600E+56 7.7571864144889900E+54
61 1.3579813459523300E+57 7.3791790171064500E+55
62 1.3142180297695500E+58 7.0253396607829200E+56
63 1.2725367506950900E+59 6.6937672232240700E+57
64 1.2328074962778800E+60 6.3827372611493100E+58
65 1.1949102466208500E+61 6.0906831461943200E+59
66 1.1587340666927400E+62 5.8161794681164100E+60
67 1.1241762934009300E+63 5.5579274032630700E+61
68 1.0911418062852200E+64 5.3147417903193600E+62
69 1.0595423721440300E+65 5.0855396924381600E+63
70 1.0292960551498000E+66 4.8693302561641600E+64
71 1.0003266850795800E+67 4.6652057040560700E+65
72 9.7256337720805300E+67 4.4723333203891700E+66
73 9.4594009820525600E+68 4.2899483084364700E+67
74 9.2039527306896500E+69 4.1173474141226600E+68
75 8.9587142871761100E+70 3.9538832247684600E+69
76 8.7231487038733900E+71 3.7989590635660700E+70
77 8.4967538742725100E+72 3.6520244106582000E+71
78 8.2790598547962500E+73 3.5125707904928200E+72
79 8.0696264237495400E+74 3.3801280727079200E+73
80 7.8680408537186700E+75 3.2542611403484700E+74
81 7.6739158763513400E+76 3.1345668848814900E+75
82 7.4868878207608500E+77 3.0206714923851600E+76
83 7.3066149088300600E+78 2.9122279895509300E+77
84 7.1327756924815000E+79 2.8089140218463400E+78
85 6.9650676195606000E+80 2.7104298394181300E+79
86 6.8032057163753700E+81 2.6164964691365600E+80
87 6.6469213761719200E+82 2.5268540536482300E+81
88 6.4959612439212000E+83 2.4412603404655200E+82
89 6.3500861887650300E+84 2.3594893060155500E+83
90 6.2090703563340400E+85 2.2813299012362900E+84
91 6.0727002939199100E+86 2.2065849067727000E+85
92 5.9407741421707000E+87 2.1350698871159400E+86
93 5.8131008875898000E+88 2.0666122341683500E+87
94 5.6894996706671300E+89 2.0010502917228100E+88
95 5.5697991449601300E+90 1.9382325532361300E+89
96 5.4538368828812400E+91 1.8780169260650700E+90
97 5.3414588243420000E+92 1.8202700560340300E+91
98 5.2325187647571800E+93 1.7648667068251300E+92
99 5.1268778792300400E+94 1.7116891892352800E+93
100 5.0244042800259600E+95 1.6606268358369800E+94
101 4.9249726046990500E+96 1.6115755170196400E+95
102 4.8284636324689100E+97 1.5644371947800700E+96
103 4.7347639266545500E+98 1.5191195109816900E+97
104 4.6437655011622200E+99 1.4755354071154800E+98
105 4.5553655091952200E+100 1.4336027728771700E+99
106 4.4694659525097300E+101 1.3932441211265800E+100
107 4.3859734096810400E+102 1.3543862870220300E+101
108 4.3047987819729500E+103 1.3169601493253800E+102
109 4.2258570555188100E+104 1.2809003720566400E+103
110 4.1490670786287700E+105 1.2461451648416300E+104
111 4.0743513531333300E+106 1.2126360604447300E+105
112 4.0016358387613000E+107 1.1803177081125700E+106
113 3.9308497696298000E+108 1.1491376814757200E+107
114 3.8619254819966400E+109 1.1190462998647100E+108
115 3.7947982524922000E+110 1.0899964619955600E+109
116 3.7294061461082400E+111 1.0619434910700000E+110
117 3.6656898732769000E+112 1.0348449904161600E+111
118 3.6035926554240000E+113 1.0086607088700500E+112
119 3.5430600984269900E+114 9.8335241516417900E+112
120 3.4840400734510600E+115 9.5888378065127600E+113
121 3.4264826046756700E+116 9.3522026974580000E+114
122 3.3703397634599300E+117 9.1232903751660100E+115
123 3.3155655685282600E+118 8.9017883390985400E+116
124 3.2621158917880700E+119 8.6873991412319000E+117
125 3.2099483694191700E+120 8.4798395469014600E+118
126 3.1590223179004100E+121 8.2788397486886000E+119
127 3.1092986546626200E+122 8.0841426296077800E+120
128 3.0607398230788300E+123 7.8955030721425900E+121
129 3.0133097215230200E+124 7.7126873099457800E+122
130 2.9669736362469600E+125 7.5354723192625200E+123
131 2.9216981778422200E+126 7.3636452473593700E+124
132 2.8774512210701900E+127 7.1970028754465900E+125
133 2.8342018478573900E+128 7.0353511137696400E+126
134 2.7919202932674800E+129 6.8785045267180400E+127
135 2.7505778942734000E+130 6.7262858859590000E+128
136 2.7101470411651300E+131 6.5785257497487500E+129
137 2.6706011314392000E+132 6.4350620667089400E+130
138 2.6319145260261200E+133 6.2957398024791000E+131
139 2.5940625077212700E+134 6.1604105877698900E+132
140 2.5570212416933200E+135 6.0289323864469100E+133
141 2.5207677379524700E+136 5.9011691823716500E+134
142 2.4852798156680300E+137 5.7769906838154300E+135
143 2.4505360692319400E+138 5.6562720443446200E+136
144 2.4165158359713800E+139 5.5388935991518000E+137
145 2.3831991654193800E+140 5.4247406158778100E+138
146 2.3505667900581800E+141 5.3137030590347800E+139
147 2.3186000974551500E+142 5.2056753672007900E+140
148 2.2872811037162100E+143 5.1005562422122400E+141
149 2.2565924281857200E+144 4.9982484496321200E+142
150 2.2265172693267300E+145 4.8986586298201200E+143
151 2.1970393817188200E+146 4.8016971189750000E+144
152 2.1681430541149000E+147 4.7072777795609200E+145
153 2.1398130885015100E+148 4.6153178395679200E+146
154 2.1120347801106000E+149 4.5257377400919100E+147
155 2.0847938983335900E+150 4.4384609907530100E+148
156 2.0580766684915700E+151 4.3534140325016800E+149
157 2.0318697544179900E+152 4.2705261073905100E+150
158 2.0061602418127000E+153 4.1897291349164100E+151
159 1.9809356223284900E+154 4.1109575945626400E+152
160 1.9561837783537200E+155 4.0341484141930100E+153
161 1.9318929684561900E+156 3.9592408639724000E+154
162 1.9080518134558000E+157 3.8861764555075900E+155
163 1.8846492830951500E+158 3.8148988459211800E+156
164 1.8616746832787800E+159 3.7453537465887000E+157
165 1.8391176438535900E+160 3.6774888362856200E+158
166 1.8169681069044600E+161 3.6112536785058200E+159
167 1.7952163155401400E+162 3.5465996427274800E+160
168 1.7738528031463400E+163 3.4834798294157300E+161
169 1.7528683830837500E+164 3.4218489985636100E+162
170 1.7322541388101600E+165 3.3616635015847100E+163
171 1.7120014144066800E+166 3.3028812163816100E+164
172 1.6921018054895500E+167 3.2454614854245500E+165
173 1.6725471504894000E+168 3.1893650566842000E+166
174 1.6533295222813100E+169 3.1345540272713600E+167
175 1.6344412201495300E+170 3.0809917896448700E+168
176 1.6158747620716600E+171 3.0286429802568000E+169
177 1.5976228773079000E+172 2.9774734305113900E+170
178 1.5796784992816100E+173 2.9274501199210900E+171
179 1.5620347587381700E+174 2.8785411313496400E+172
180 1.5446849771698900E+175 2.8307156082381000E+173
181 1.5276226604949800E+176 2.7839437137156000E+174
182 1.5108414929796700E+177 2.7381965915018100E+175
183 1.4943353313926700E+178 2.6934463285134000E+176
184 1.4780981993820100E+179 2.6496659190912900E+177
185 1.4621242820644900E+180 2.6068292307701400E+178
186 1.4464079208187600E+181 2.5649109715156500E+179
187 1.4309436082732100E+182 2.5238866583593100E+180
188 1.4157259834804300E+183 2.4837325873637500E+181
189 1.4007498272703700E+184 2.4444258048557200E+182
190 1.3860100577745400E+185 2.4059440798666600E+183
191 1.3715017261143600E+186 2.3682658777241700E+184
192 1.3572200122464600E+187 2.3313703347407000E+185
193 1.3431602209588000E+188 2.2952372339482500E+186
194 1.3293177780110900E+189 2.2598469818308800E+187
195 1.3156882264137800E+190 2.2251805860090000E+188
196 1.3022672228398700E+191 2.1912196338318400E+189
197 1.2890505341642200E+192 2.1579462718368700E+190
198 1.2760340341250900E+193 2.1253431860367000E+191
199 1.2632137001031700E+194 2.0933935829963000E+192
200 1.2505856100132600E+195 2.0620811716649200E+193
201 1.2381459393041800E+196 2.0313901459291600E+194
202 1.2258909580625800E+197 2.0013051678550400E+195
203 1.2138170282166600E+198 1.9718113515886800E+196
204 1.2019206008357100E+199 1.9428942478865600E+197
205 1.1901982135219600E+200 1.9145398292478100E+198
206 1.1786464878908900E+201 1.8867344756223700E+199
207 1.1672621271368400E+202 1.8594649606699200E+200
208 1.1560419136804700E+203 1.8327184385458800E+201
209 1.1449827068949800E+204 1.8064824311919300E+202
210 1.1340814409081200E+205 1.7807448161093100E+203
211 1.1233351224770900E+206 1.7554938145945100E+204
212 1.1127408289336100E+207 1.7307179804176700E+205
213 1.1022957061964400E+208 1.7064061889251600E+206
214 1.0919969668490200E+209 1.6825476265483500E+207
215 1.0818418882794800E+210 1.6591317807018600E+208
216 1.0718278108811500E+211 1.6361484300548700E+209
217 1.0619521363109000E+212 1.6135876351602100E+210
218 1.0522123258034700E+213 1.5914397294264400E+211
219 1.0426058985397200E+214 1.5696953104188600E+212
220 1.0331304300666600E+215 1.5483452314760700E+213
221 1.0237835507676300E+216 1.5273805936291700E+214
222 1.0145629443806400E+217 1.5067927378114600E+215
223 1.0054663465631700E+218 1.4865732373469400E+216
224 9.9649154350194600E+218 1.4667138907063100E+217
225 9.8763637056578600E+219 1.4472067145199900E+218
226 9.7889871100028600E+220 1.4280439368377600E+219
227 9.7027649466268500E+221 1.4092179906254700E+220
228 9.6176769679558100E+222 1.3907215074892300E+221
229 9.5337033683812000E+223 1.3725473116184100E+222
230 9.4508247727335500E+224 1.3546884139387700E+223
231 9.3690222251052300E+225 1.3371380064676000E+224
232 9.2882771780103700E+226 1.3198894568629700E+225
233 9.2085714818704400E+227 1.3029363031597800E+226
234 9.1298873748141500E+228 1.2862722486852700E+227
235 9.0522074727812100E+229 1.2698911571472300E+228
236 8.9755147599195100E+230 1.2537870478882800E+229
237 8.8997925792658100E+231 1.2379540913000500E+230
238 8.8250246237005600E+232 1.2223866043910000E+231
239 8.7511949271674400E+233 1.2070790465024300E+232
240 8.6782878561490400E+234 1.1920260151667400E+233
241 8.6062881013900600E+235 1.1772222421030500E+234
242 8.5351806698597500E+236 1.1626625893447900E+235
243 8.4649508769459600E+237 1.1483420454944500E+236
244 8.3955843388730300E+238 1.1342557221009400E+237
245 8.3270669653362200E+239 1.1203988501549100E+238
246 8.2593849523456900E+240 1.1067667766977300E+239
247 8.1925247752733000E+241 1.0933549615402000E+240
248 8.1264731820955000E+242 1.0801589740867000E+241
249 8.0612171868262500E+243 1.0671744902612500E+242
250 7.9967440631337000E+244 1.0543972895316800E+243
251 7.9330413381348300E+245 1.0418232520284400E+244
252 7.8700967863625300E+246 1.0294483557546800E+245
253 7.8078984238994100E+247 1.0172686738843200E+246
254 7.7464345026733600E+248 1.0052803721450700E+247
255 7.6856935049095700E+249 9.9347970628334600E+247
256 7.6256641377343100E+250 9.8186301960824900E+248

白新岭 · 发表于 2021-5-8 07:45

10的n次幂 10倍最密4生素数的数量 2倍最密5生素数的数量
2 9.0000000000000000E+00 0.0000000000000000E+00
3 3.6000000000000000E+01 2.0000000000000000E+00
4 1.1700000000000000E+02 7.0000000000000000E+00
5 4.0300000000000000E+02 2.0000000000000000E+01
6 1.7090000000000000E+03 6.9000000000000000E+01
7 8.5050000000000000E+03 2.8700000000000000E+02
8 4.7221000000000000E+04 1.3620000000000000E+03
9 2.8384200000000000E+05 7.1700000000000000E+03
10 1.8106260000000000E+06 4.0743000000000000E+04
11 1.2099442000000000E+07 2.4565500000000000E+05
12 8.3945688000000000E+07 1.5533380000000000E+06
13 6.0075450100000000E+08 1.0214435000000000E+07
14 4.4129089930000000E+09 6.9412238000000000E+07
15 3.3145516251000000E+10 4.8509023700000000E+08
16 2.5379451643400000E+11 3.4730294700000000E+09
17 1.9762249314470000E+12 2.5395289408000000E+10
18 1.5617724370000000E+13 1.8917339592300000E+11
19 1.2505600932499200E+14 1.4325840645440000E+12
20 1.0131897359861100E+15 1.1009585412642000E+13
21 8.2958808913679200E+15 8.5736689450271000E+13
22 6.8577258578144200E+16 6.7570197606888800E+14
23 5.7182685361685200E+17 5.3834485809702300E+15
24 4.8060313243081100E+18 4.3318142750659900E+16
25 4.0687269842203100E+19 3.5174028795554000E+17
26 3.4675876187366100E+20 2.8800517042622500E+18
27 2.9735119360639400E+21 2.3764248747510900E+19
28 2.5644052737636400E+22 1.9748979166413900E+20
29 2.2233157123569500E+23 1.6521137092449100E+21
30 1.9371100571283500E+24 1.3906281313551200E+22
31 1.6955213540189900E+25 1.1772777873151500E+23
32 1.4904555983814100E+26 1.0020334625761700E+24
33 1.3154815656002200E+27 8.5718491231829400E+24
34 1.1654515518824500E+28 7.3675462040121100E+25
35 1.0362167352077700E+29 6.3607172151680800E+26
36 9.2441163421941400E+29 5.5145923560830800E+27
37 8.2728951667493600E+30 4.8000232658038800E+28
38 7.4259571823618300E+31 4.1937508031288100E+29
39 6.6846941157115500E+32 3.6770994797161900E+30
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41 5.4600131465020900E+34 2.8551590127509500E+32
42 4.9529492206142100E+35 2.5276169166300800E+33
43 4.5034115672543000E+36 2.2441514933964000E+34
44 4.1037424459507100E+37 1.9979950284106000E+35
45 3.7474475634748600E+38 1.7835418533227500E+36
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48 2.8874165254427600E+41 1.2874679683193300E+39
49 2.6567505188522000E+42 1.1602029444290700E+40
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51 2.2605641323453500E+44 9.4811061481546100E+41
52 2.0901828313731500E+45 8.5963657654583900E+42
53 1.9355567291919500E+46 7.8088790258554500E+43
54 1.7949693275994200E+47 7.1063985857272400E+44
55 1.6669184124581000E+48 6.4784085557939700E+45
56 1.5500860173217800E+49 5.9158539116908700E+46
57 1.4433130419668400E+50 5.4109160871445700E+47
58 1.3455777378504200E+51 4.9568262250987800E+48
59 1.2559774168009300E+52 4.5477092503416900E+49
60 1.1737128551815500E+53 4.1784532590911300E+50
61 1.0980749592899700E+54 3.8445997762836200E+51
62 1.0284333334878000E+55 3.5422512708840400E+52
63 9.6422645409980900E+55 3.2679929901350800E+53
64 9.0495320232124100E+56 3.0188267113634400E+54
65 8.5016555045181200E+57 2.7921144426919600E+55
66 7.9946222950683200E+58 2.5855304535134500E+56
67 7.5248323404081800E+59 2.3970202988494300E+57
68 7.0890504297731300E+60 2.2247657320695400E+58
69 6.6843645426525300E+61 2.0671545883796000E+59
70 6.3081494699648000E+62 1.9227548752928500E+60
71 5.9580349780025400E+63 1.7902924325616300E+61
72 5.6318778934723700E+64 1.6686316280046300E+62
73 5.3277375802743800E+65 1.5567586415050900E+63
74 5.0438543562282600E+66 1.4537669605326500E+64
75 4.7786304632817600E+67 1.3588447695547200E+65
76 4.5306132598935700E+68 1.2712639648292400E+66
77 4.2984803509619600E+69 1.1903705670699200E+67
78 4.0810264102655900E+70 1.1155763387783400E+68
79 3.8771514840443100E+71 1.0463514418062900E+69
80 3.6858505930269400E+72 9.8221799489764800E+69
81 3.5062044746985400E+73 9.2274441133712100E+70
82 3.3373713285487900E+74 8.6754041404274000E+71
83 3.1785794450017800E+75 8.1625264000326300E+72
84 3.0291206141529700E+76 7.6856075831380200E+73
85 2.8883442237142900E+77 7.2417403656079300E+74
86 2.7556519670136800E+78 6.8282829924694200E+75
87 2.6304930917815600E+79 6.4428322957457400E+76
88 2.5123601290106800E+80 6.0831997242668600E+77
89 2.4007850485907800E+81 5.7473900197005200E+78
90 2.2953357948565100E+82 5.4335822209711400E+79
91 2.1956131607861700E+83 5.1401127204276100E+80
92 2.1012479644652300E+84 4.8654601305938600E+81
93 2.0118984956833500E+85 4.6082317509322800E+82
94 1.9272482042512600E+86 4.3671514504861000E+83
95 1.8470036048772800E+87 4.1410488051440500E+84
96 1.7708923762939600E+88 3.9288493481004900E+85
97 1.6986616348281400E+89 3.7295658092991900E+86
98 1.6300763648064700E+90 3.5422902346165700E+87
99 1.5649179901241100E+91 3.3661868885735500E+88
100 1.5029830730098700E+92 3.2004858557302100E+89
101 1.4440821275264400E+93 3.0444772658429100E+90
102 1.3880385366738400E+94 2.8975060765425800E+91
103 1.3346875631413500E+95 2.7589673548937800E+92
104 1.2838754447949000E+96 2.6283020058588100E+93
105 1.2354585669113600E+97 2.5049929015428100E+94
106 1.1893027039920900E+98 2.3885613702409400E+95
107 1.1452823247171500E+99 2.2785640088372200E+96
108 1.1032799542515900E+100 2.1745897860962400E+97
109 1.0631855886930500E+101 2.0762574079113700E+98
110 1.0248961569664600E+102 1.9832129186848900E+99
111 9.8831502593209200E+102 1.8951275157681900E+100
112 9.5335154488517400E+103 1.8116955563277000E+101
113 9.1992062599384800E+104 1.7326327381631600E+102
114 8.8794235755229700E+105 1.6576744379229600E+103
115 8.5734164722188600E+106 1.5865741918652100E+104
116 8.2804789269879300E+107 1.5191023058288600E+105
117 7.9999467748522100E+108 1.4550445824288800E+106
118 7.7311948965593800E+109 1.3942011546922300E+107
119 7.4736346170495900E+110 1.3363854164242600E+108
120 7.2267112973125000E+111 1.2814230405540900E+109
121 6.9899021037920100E+112 1.2291510775636900E+110
122 6.7627139409120700E+113 1.1794171268724500E+111
123 6.5446815335763500E+114 1.1320785747353200E+112
124 6.3353656476503600E+115 1.0870018928285500E+113
125 6.1343514374814000E+116 1.0440619922489000E+114
126 5.9412469104588000E+117 1.0031416281486600E+115
127 5.7556814994756300E+118 9.6413085067457100E+115
128 5.5773047349321300E+119 9.2692649827975900E+116
129 5.4057850086279300E+120 8.9143172983932200E+117
130 5.2408084225322800E+121 8.5755559232545000E+118
131 5.0820777160056600E+122 8.2521262109180100E+119
132 4.9293112655774000E+123 7.9432247008174800E+120
133 4.7822421518672300E+124 7.6480956951466000E+121
134 4.6406172886800000E+125 7.3660280882077900E+122
135 4.5041966097042400E+126 7.0963524279120900E+123
136 4.3727523086120300E+127 6.8384381908681700E+124
137 4.2460681286925700E+128 6.5916912541067400E+125
138 4.1239386984576600E+129 6.3555515479433700E+126
139 4.0061689099369100E+130 6.1294908758060300E+127
140 3.8925733366366900E+131 5.9130108880549400E+128
141 3.7829756883709200E+132 5.7056411979139700E+129
142 3.6772083003864500E+133 5.5069376286259800E+130
143 3.5751116544027500E+134 5.3164805818481100E+131
144 3.4765339293658400E+135 5.1338735181259000E+132
145 3.3813305798823200E+136 4.9587415410352900E+133
146 3.2893639404513300E+137 4.7907300772653400E+134
147 3.2005028537522300E+138 4.6295036455386800E+135
148 3.1146223213741700E+139 4.4747447078364200E+136
149 3.0316031754922300E+140 4.3261525969151300E+137
150 2.9513317701035200E+141 4.1834425145791500E+138
151 2.8736996905370200E+142 4.0463445956074100E+139
152 2.7986034800432500E+143 3.9146030326318900E+140
153 2.7259443823554300E+144 3.7879752576306300E+141
154 2.6556280991918400E+145 3.6662311760320500E+142
155 2.5875645617423100E+146 3.5491524497347800E+143
156 2.5216677152484100E+147 3.4365318256280200E+144
157 2.4578553158490200E+148 3.3281725064565000E+145
158 2.3960487389201500E+149 3.2238875611108500E+146
159 2.3361727981910600E+150 3.1234993716428400E+147
160 2.2781555749674500E+151 3.0268391145050900E+148
161 2.2219282568383200E+152 2.9337462736997200E+149
162 2.1674249852846800E+153 2.8440681836902000E+150
163 2.1145827116478000E+154 2.7576596000868800E+151
164 2.0633410609503100E+155 2.6743822962613500E+152
165 2.0136422030975400E+156 2.5941046841770600E+153
166 1.9654307310171500E+157 2.5167014578469500E+154
167 1.9186535453243700E+158 2.4420532579413400E+155
168 1.8732597451267400E+159 2.3700463561742100E+156
169 1.8292005246075300E+160 2.3005723581925400E+157
170 1.7864290750498500E+161 2.2335279237821600E+158
171 1.7449004919854000E+162 2.1688145032866300E+159
172 1.7045716871716800E+163 2.1063380892115700E+160
173 1.6654013051203300E+164 2.0460089820575700E+161
174 1.6273496439165500E+165 1.9877415694902500E+162
175 1.5903785800860100E+166 1.9314541180167800E+163
176 1.5544514972805400E+167 1.8770685763938100E+164
177 1.5195332185682600E+168 1.8245103900445500E+165
178 1.4855899421267400E+169 1.7737083258103300E+166
179 1.4525891801503200E+170 1.7245943064072700E+167
180 1.4204997007940300E+171 1.6771032539999900E+168
181 1.3892914729873100E+172 1.6311729423432600E+169
182 1.3589356139608000E+173 1.5867438569779200E+170
183 1.3294043393387800E+174 1.5437590630013200E+171
184 1.3006709156586700E+175 1.5021640799631200E+172
185 1.2727096151870900E+176 1.4619067634664900E+173
186 1.2454956729097800E+177 1.4229371930813400E+174
187 1.2190052455797600E+178 1.3852075662015100E+175
188 1.1932153727148300E+179 1.3486720975009900E+176
189 1.1681039394419000E+180 1.3132869236659700E+177
190 1.1436496410915400E+181 1.2790100130997300E+178
191 1.1198319494515000E+182 1.2458010803165200E+179
192 1.0966310805933500E+183 1.2136215047577100E+180
193 1.0740279641911900E+184 1.1824342537804100E+181
194 1.0520042142559200E+185 1.1522038095838100E+182
195 1.0305421012128600E+186 1.1228960998528000E+183
196 1.0096245252545600E+187 1.0944784319121200E+184
197 9.8923499090449000E+187 1.0669194301963600E+185
198 9.6935758273059900E+188 1.0401889768531900E+186
199 9.4997694215151500E+189 1.0142581553078600E+187
200 9.3107824528083800E+190 9.8909919662758900E+187
201 9.1264718175827200E+191 9.6468542853350400E+188
202 8.9466993451893500E+192 9.4099122691734900E+189
203 8.7713316045492800E+193 9.1799196972810500E+190
204 8.6002397192560000E+194 8.9566399310179600E+191
205 8.4332991907536200E+195 8.7398454961498400E+192
206 8.2703897292003100E+196 8.5293176854945600E+193
207 8.1113950916478200E+197 8.3248461806199500E+194
208 7.9562029271869600E+198 8.1262286915926800E+195
209 7.8047046287275800E+199 7.9332706138352000E+196
210 7.6567951910987500E+200 7.7457847012013800E+197
211 7.5123730751708900E+201 7.5635907544314900E+198
212 7.3713400777175700E+202 7.3865153241945300E+199
213 7.2336012067484900E+203 7.2143914279699400E+200
214 7.0990645620595000E+204 7.0470582800626100E+201
215 6.9676412207581300E+205 6.8843610340842300E+202
216 6.8392451275353900E+206 6.7261505372704700E+203
217 6.7137929894662400E+207 6.5722830960385600E+204
218 6.5912041751319200E+208 6.4226202522220600E+205
219 6.4714006178679100E+209 6.2770285694503400E+206
220 6.3543067229506800E+210 6.1353794291691500E+207
221 6.2398492785461200E+211 5.9975488358258500E+208
222 6.1279573702507200E+212 5.8634172307683200E+209
223 6.0185622990654600E+213 5.7328693144307700E+210
224 5.9115975026496700E+214 5.6057938764023100E+211
225 5.8069984797098800E+215 5.4820836329956800E+212
226 5.7047027173855400E+216 5.3616350719534500E+213
227 5.6046496215002600E+217 5.2443483039483600E+214
228 5.5067804495534300E+218 5.1301269205521300E+215
229 5.4110382463331900E+219 5.0188778583642600E+216
230 5.3173677820371300E+220 4.9105112690080900E+217
231 5.2257154927929200E+221 4.8049403947167800E+218
232 5.1360294234755800E+222 4.7020814492457600E+219
233 5.0482591727236200E+223 4.6018535038620300E+220
234 4.9623558400602400E+224 4.5041783781732100E+221
235 4.8782719750305000E+225 4.4089805355712000E+222
236 4.7959615282694600E+226 4.3161869830769600E+223
237 4.7153798044202100E+227 4.2257271753833800E+224
238 4.6364834168242200E+228 4.1375329229034200E+225
239 4.5592302439104800E+229 4.0515383036406200E+226
240 4.4835793872126700E+230 3.9676795787075900E+227
241 4.4094911309472900E+231 3.8858951113274100E+228
242 4.3369269030885200E+232 3.8061252891603300E+229
243 4.2658492378783300E+233 3.7283124498064500E+230
244 4.1962217397135100E+234 3.6524008093419900E+231
245 4.1280090483534700E+235 3.5783363937538400E+232
246 4.0611768053954100E+236 3.5060669731436600E+233
247 3.9956916219658400E+237 3.4355419985788700E+234
248 3.9315210475795300E+238 3.3667125414739900E+235
249 3.8686335401192100E+239 3.2995312353912100E+236
250 3.8069984368914200E+240 3.2339522201542900E+237
251 3.7465859267158400E+241 3.1699310881752400E+238
252 3.6873670230071400E+242 3.1074248328976600E+239
253 3.6293135378104700E+243 3.0463917992652900E+240
254 3.5723980567529900E+244 2.9867916361286300E+241
255 3.5165939148758600E+245 2.9285852505065600E+242
256 3.4618751733123100E+246 2.8717347636236900E+243

白新岭 · 发表于 2021-5-8 07:52

公式涉及到的4类k生素数的数据已有，根据公式获得数据：
10的n次幂 2生相邻素数（P，P+12）的数量
2 -3.0000000000000000E+00
3 6.0000000000000000E+00
4 1.0700000000000000E+02
5 9.8100000000000000E+02
6 8.0710000000000000E+03
7 6.5642000000000000E+04
8 5.3821400000000000E+05
9 4.4687260000000000E+06
10 3.7585727000000000E+07
11 3.1996399600000000E+08
12 2.7536982080000000E+09
13 2.3931395449000000E+10
14 2.0979679867000000E+11
15 1.8535530008970000E+12
16 1.6490530792080000E+13
17 1.4763269401837100E+14
18 1.3291806964032100E+15
19 1.2028430483327600E+16
20 1.0935953322389400E+17
21 9.9850750874396600E+17
22 9.1524738869022800E+18
23 8.4194108394410200E+19
24 7.7706972144046600E+20
25 7.1939213729252300E+21
26 6.6788640081671800E+22
27 6.2170513871474000E+23
28 5.8014108081117400E+24
29 5.4260025313472300E+25
30 5.0858094705307200E+26
31 4.7765709044305300E+27
32 4.4946500233749200E+28
33 4.2369276912202800E+29
34 4.0007166740689400E+30
35 3.7836919627749500E+31
36 3.5838338369667500E+32
37 3.3993810818160400E+33
38 3.2287923443880800E+34
39 3.0707140536091300E+35
40 2.9239536623279900E+36
41 2.7874572275226700E+37
42 2.6602905443595200E+38
43 2.5416232055335400E+39
44 2.4307150794871000E+40
45 2.3269047974915500E+41
46 2.2295999160329800E+42
47 2.1382684819023400E+43
48 2.0524317762353200E+44
49 1.9716580530688800E+45
50 1.8955571197822000E+46
51 1.8237756326190600E+47
52 1.7559930015564300E+48
53 1.6919178160368100E+49
54 1.6312847172660000E+50
55 1.5738516544814700E+51
56 1.5193974722892900E+52
57 1.4677197842219600E+53
58 1.4186330943851600E+54
59 1.3719671346791700E+55
60 1.3275653897934900E+56
61 1.2852837861407800E+57
62 1.2449895242439400E+58
63 1.2065600369239600E+59
64 1.1698820580420000E+60
65 1.1348507885949200E+61
66 1.1013691487106300E+62
67 1.0693471055820400E+63
68 1.0387010686592700E+64
69 1.0093533445193300E+65
70 9.8123164478028000E+65
71 9.5426864124438700E+66
72 9.2840156316188100E+67
73 9.0357183212027700E+68
74 8.7972473059640100E+69
75 8.5680910067148500E+70
76 8.3477706981370300E+71
77 8.1358380098519800E+72
78 7.9318726463938400E+73
79 7.7354803044483700E+74
80 7.5462907680969000E+75
81 7.3639561648937800E+76
82 7.1881493674467400E+77
83 7.0185625267935700E+78
84 6.8549057253034400E+79
85 6.6969057381021300E+80
86 6.5443048931457300E+81
87 6.3968600210665800E+82
88 6.2543414868039400E+83
89 6.1165322958220500E+84
90 5.9832272684230500E+85
91 5.8542322762907100E+86
92 5.7293635359634400E+87
93 5.6084469544369000E+88
94 5.4913175225476500E+89
95 5.3778187521925900E+90
96 5.2678021538016800E+91
97 5.1611267508076200E+92
98 5.0576586281492400E+93
99 4.9572705121097500E+94
100 4.8598413790294200E+95
101 4.7652560906473500E+96
102 4.6734050540215000E+97
103 4.5841839041521700E+98
104 4.4974932075934600E+99
105 4.4132381854815100E+100
106 4.3313284545396900E+101
107 4.2516777847395500E+102
108 4.1742038724048800E+103
109 4.0988281276444300E+104
110 4.0254754750886500E+105
111 3.9540741669872700E+106
112 3.8845556077993700E+107
113 3.8168541894754800E+108
114 3.7509071366932800E+109
115 3.6866543613656700E+110
116 3.6240383257916300E+111
117 3.5630039138681900E+112
118 3.5034983098255000E+113
119 3.4454708839868600E+114
120 3.3888730850926200E+115
121 3.3336583387603900E+116
122 3.2797819516852300E+117
123 3.2272010212120600E+118
124 3.1758743499386200E+119
125 3.1257623650319100E+120
126 3.0768270419629400E+121
127 3.0290318323856400E+122
128 2.9823415959044000E+123
129 2.9367225354927000E+124
130 2.8921421363410000E+125
131 2.8485691079276100E+126
132 2.8059733291198100E+127
133 2.7643257961253100E+128
134 2.7235985731263600E+129
135 2.6837647454395400E+130
136 2.6447983750546800E+131
137 2.6066744584158500E+132
138 2.5693688863160200E+133
139 2.5328584057854800E+134
140 2.4971205838614300E+135
141 2.4621337731334700E+136
142 2.4278770789661500E+137
143 2.3943303283058800E+138
144 2.3614740399854500E+139
145 2.3292893964444400E+140
146 2.2977582167888700E+141
147 2.2668629311181500E+142
148 2.2365865560517500E+143
149 2.2069126713916900E+144
150 2.1778253978612900E+145
151 2.1493093758636600E+146
152 2.1213497452069900E+147
153 2.0939321257465400E+148
154 2.0670425988964800E+149
155 2.0406676899669900E+150
156 2.0147943512849000E+151
157 1.9894099460584200E+152
158 1.9645022329486700E+153
159 1.9400593513127500E+154
160 1.9160698070853800E+155
161 1.8925224592675200E+156
162 1.8694065069924300E+157
163 1.8467114771411400E+158
164 1.8244272124807600E+159
165 1.8025438603005800E+160
166 1.7810518615223600E+161
167 1.7599419402620700E+162
168 1.7392050938220600E+163
169 1.7188325830933400E+164
170 1.6988159233490300E+165
171 1.6791468754106100E+166
172 1.6598174371702100E+167
173 1.6408198354521700E+168
174 1.6221465181988300E+169
175 1.6037901469656800E+170
176 1.5857435897119600E+171
177 1.5679999138736000E+172
178 1.5505523797057800E+173
179 1.5333944338832600E+174
180 1.5165197033472600E+175
181 1.4999219893878300E+176
182 1.4835952619516600E+177
183 1.4675336541655600E+178
184 1.4517314570662600E+179
185 1.4361831145276300E+180
186 1.4208832183771800E+181
187 1.4058265036934200E+182
188 1.3910078442768500E+183
189 1.3764222482870600E+184
190 1.3620648540389800E+185
191 1.3479309259519600E+186
192 1.3340158506449600E+187
193 1.3203151331723100E+188
194 1.3068243933938300E+189
195 1.2935393624742000E+190
196 1.2804558795062300E+191
197 1.2675698882530000E+192
198 1.2548774340041000E+193
199 1.2423746605416100E+194
200 1.2300578072112200E+195
201 1.2179232060945200E+196
202 1.2059672792783600E+197
203 1.1941865362176200E+198
204 1.1825775711876400E+199
205 1.1711370608229300E+200
206 1.1598617617387800E+201
207 1.1487485082326000E+202
208 1.1377942100620000E+203
209 1.1269958502966400E+204
210 1.1163504832410900E+205
211 1.1058552324259900E+206
212 1.0955072886650600E+207
213 1.0853039081753400E+208
214 1.0752424107585700E+209
215 1.0653201780410600E+210
216 1.0555346517703700E+211
217 1.0458833321663600E+212
218 1.0363637763247500E+213
219 1.0269735966714200E+214
220 1.0177104594653300E+215
221 1.0085720833486400E+216
222 9.9955623794205600E+216
223 9.9066074248399800E+217
224 9.8188346451197100E+218
225 9.7322231858454700E+219
226 9.6467526504273200E+220
227 9.5624030880916200E+221
228 9.4791549822391500E+222
229 9.3969892391562100E+223
230 9.3158871770667500E+224
231 9.2358305155137100E+225
232 9.1568013650582800E+226
233 9.0787822172863800E+227
234 9.0017559351117900E+228
235 8.9257057433659400E+229
236 8.8506152196648100E+230
237 8.7764682855435300E+231
238 8.7032491978498500E+232
239 8.6309425403877600E+233
240 8.5595332158031300E+234
241 8.4890064377033400E+235
242 8.4193477230030500E+236
243 8.3505428844890600E+237
244 8.2825780235968300E+238
245 8.2154395233919300E+239
246 8.1491140417497600E+240
247 8.0835885047272800E+241
248 8.0188501001203300E+242
249 7.9548862712010100E+243
250 7.8916847106290000E+244
251 7.8292333545315500E+245
252 7.7675203767468800E+246
253 7.7065341832255800E+247
254 7.6462634065853700E+248
255 7.5866969008142000E+249
256 7.5278237361173400E+250
从这里可以看出，二生相邻素数的数量并不与最密二生素数的数量成恒比例（是一个变量），只有只确定跨度的二生素数的数量比才是恒等比例。

白新岭 · 发表于 2021-5-8 08:04

在寻找二生相邻素数时，找到一组二连跳的，（199,211,223）为连续素数，切跨度一致，都为12.

白新岭 · 发表于 2021-5-8 08:12

10的n次幂 2生相邻素数（P，P+12）的数量实际数据实际-理论相对误差
2 -3.0000000000000000E+00
3 6.0000000000000000E+00 8 2 25.000000%
4 1.0700000000000000E+02 105 -2 -1.904762%
5 9.8100000000000000E+02 965 -16 -1.658031%
6 8.0710000000000000E+03 8005 -66 -0.824485%
7 6.5642000000000000E+04 65513 -129 -0.196907%
8 5.3821400000000000E+05 538382 168 0.031205%
从与实际数据的比对来看，理论值还是非常可靠的，能做为很好的预测工具使用。

白新岭 · 发表于 2021-5-8 08:15

天姥连天向天横，势拔五岳掩赤城。
天台四万八千丈，对此欲倒东南倾
素数问题的大厦在这种新的数学工具面前将要坍塌，震耳欲聋。

白新岭 · 发表于 2021-5-8 08:19

她的诞生，将是素数问题噩梦的开始，蒙在素数问题上的面纱将彻底被解开。

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