[原创]k生素数群的数量公式

白新岭 · 发表于 2019-8-20 16:11

最密70生素数的最终系数C70(L370)=6.08466381366288E+38
第一次出现k70的系数小于k69系数，这非常反常现象。

白新岭 · 发表于 2019-8-20 16:13

n(10的次幂）最密70生素数的数量
136 1.000000000000000000E+00
137 9.000000000000000000E+00
138 5.500000000000000000E+01
139 3.350000000000000000E+02
140 2.027000000000000000E+03
141 1.229500000000000000E+04
142 7.482400000000000000E+04
143 4.569540000000000000E+05
144 2.800266000000000000E+06
145 1.721888400000000000E+07
146 1.062353950000000000E+08
147 6.576154450000000000E+08
148 4.084074829000000000E+09
149 2.544573919000000000E+10
150 1.590440077650000000E+11
151 9.971992687180000000E+11
152 6.271781254874000000E+12
153 3.956639059451800000E+13
154 2.503635856298060000E+14
155 1.588942007228480000E+15
156 1.011394004086060000E+16
157 6.456419756471830000E+16
158 4.133387499145670000E+17
159 2.653674787298200000E+18
160 1.708445061566950000E+19
161 1.102937496798420000E+20
162 7.139740963601520000E+20
163 4.634267096148130000E+21
164 3.016007169051090000E+22
165 1.967987324586750000E+23
166 1.287469694138000000E+24
167 8.444286239191990000E+24
168 5.552476874310900000E+25
169 3.660120278078230000E+26
170 2.418665903350840000E+27
171 1.602196210113730000E+28
172 1.063903897580280000E+29
173 7.081476004051010000E+29
174 4.724630857788260000E+30
175 3.159533089200590000E+31
176 2.117762692168850000E+32
177 1.422720742234370000E+33
178 9.579411660864290000E+33
179 6.464334506799190000E+34
180 4.371835475699840000E+35
181 2.963112732340360000E+36
182 2.012641693943860000E+37
183 1.369961631431440000E+38
184 9.344668119467850000E+38
185 6.387382952400370000E+39
186 4.374977672686400000E+40
187 3.002706721546590000E+41
188 2.065022133905910000E+42
189 1.422990195122530000E+43
190 9.825062833127690000E+43
191 6.796979698763340000E+44
192 4.711236804530330000E+45
193 3.271775355977840000E+46
194 2.276423151544070000E+47
195 1.586846838646250000E+48

白新岭 · 发表于 2019-8-20 19:29

素数式71 素数式71 素数式71 素数式71
0 0 0 0
8 4 8 4
4 2 12 6
2 4 14 10
4 6 18 16
6 8 24 24
6 4 30 28
2 2 32 30
6 4 38 34
4 6 42 40
2 6 44 46
10 2 54 48
6 6 60 54
8 4 68 58
10 2 78 60
2 6 80 66
4 10 84 76
8 8 92 84
6 4 98 88
4 2 102 90
6 4 108 94
2 6 110 100
4 14 114 114
6 4 120 118
2 6 122 124
6 2 128 126
6 10 134 136
6 8 140 144
4 6 144 150
6 4 150 154
14 2 164 156
4 4 168 160
2 6 170 166
10 2 180 168
12 12 192 180
2 4 194 184
4 2 198 186
12 12 210 198
2 10 212 208
6 2 218 210
4 4 222 214
2 14 224 228
4 6 228 234
6 4 234 238
8 6 242 244
10 6 252 250
2 6 254 256
6 2 260 258
4 6 264 264
14 4 278 268
6 2 284 270
4 6 288 276
2 4 290 280
4 6 294 286
8 8 302 294
10 4 312 298
6 2 318 300
2 10 320 310
4 8 324 318
6 6 330 324
2 10 332 334
6 2 338 336
6 4 344 340
4 6 348 346
2 2 350 348
4 6 354 354
8 6 362 360
6 4 368 364
4 2 372 366
2 4 374 370
4 8 378 378
最密71生素数就这两种形式。

白新岭 · 发表于 2019-8-20 19:31

最密71生素数的最终系数C71(L378)=3.05965320927526E+39

白新岭 · 发表于 2019-8-20 19:34

n(10的次幂）最密71生素数的数量
139 5.000000000000000000E+00
140 3.100000000000000000E+01
141 1.910000000000000000E+02
142 1.155000000000000000E+03
143 7.005000000000000000E+03
144 4.263100000000000000E+04
145 2.603240000000000000E+05
146 1.595072000000000000E+06
147 9.806286000000000000E+06
148 6.048781400000000000E+07
149 3.743268370000000000E+08
150 2.323992339000000000E+09
151 1.447439261500000000E+10
152 9.043355110100000000E+10
153 5.667668156950000000E+11
154 3.562929298790000000E+12
155 2.246573686304000000E+13
156 1.420783328263410000E+14
157 9.011812220917740000E+14
158 5.732673482012470000E+15
159 3.657186220361110000E+16
160 2.339731635907230000E+17
161 1.501062332303260000E+18
162 9.656728128894250000E+18
163 6.229383271733920000E+19
164 4.029297323873730000E+20
165 2.613175071710400000E+21
166 1.699216040857550000E+22
167 1.107785868658930000E+23
168 7.240634863973740000E+23
169 4.744580243157620000E+24
170 3.116780529450400000E+25
171 2.052528096213890000E+26
172 1.354983081284250000E+27
173 8.966607066623990000E+27
174 5.947846542984740000E+28
175 3.954729450016380000E+29
176 2.635648369177410000E+30
177 1.760598349482710000E+31
178 1.178755955870080000E+32
179 7.909829971754010000E+32
180 5.319601153551870000E+33
181 3.585493097543200000E+34
182 2.421954640995370000E+35
183 1.639532347970260000E+36
184 1.112245327469020000E+37
185 7.561321766199400000E+37
186 5.151117492315470000E+38
187 3.516430488102920000E+39
188 2.405414126691020000E+40
189 1.648752493770700000E+41
190 1.132373142559570000E+42
191 7.792610829758620000E+42
192 5.373122446873720000E+43
193 3.712033965623680000E+44
194 2.569389044639880000E+45
195 1.781853203232230000E+46
196 1.238025644193820000E+47
197 8.617765862117580000E+47
198 6.009784033016860000E+48

白新岭 · 发表于 2019-8-20 19:36

找到最密k生素数式以后，系数和数量是容易给出的。

白新岭 · 发表于 2019-8-20 19:57

素数式72 素数式72 素数式72 素数式72
0 0 0 0
6 4 6 4
8 2 14 6
4 4 18 10
2 6 20 16
4 8 24 24
6 4 30 28
6 2 36 30
2 4 38 34
6 6 44 40
4 6 48 46
2 2 50 48
10 6 60 54
6 4 66 58
8 2 74 60
10 6 84 66
2 10 86 76
4 8 90 84
8 4 98 88
6 2 104 90
4 4 108 94
6 6 114 100
2 14 116 114
4 4 120 118
6 6 126 124
2 2 128 126
6 10 134 136
6 8 140 144
6 6 146 150
4 4 150 154
6 2 156 156
14 4 170 160
4 6 174 166
2 2 176 168
10 12 186 180
12 4 198 184
2 2 200 186
4 12 204 198
12 10 216 208
2 2 218 210
6 4 224 214
4 14 228 228
2 6 230 234
4 4 234 238
6 6 240 244
8 6 248 250
10 6 258 256
2 2 260 258
6 6 266 264
4 4 270 268
14 2 284 270
6 6 290 276
4 4 294 280
2 6 296 286
4 8 300 294
8 4 308 298
10 2 318 300
6 10 324 310
2 8 326 318
4 6 330 324
6 10 336 334
2 2 338 336
6 4 344 340
6 6 350 346
4 2 354 348
2 6 356 354
4 6 360 360
8 4 368 364
6 2 374 366
4 4 378 370
2 8 380 378
4 6 384 384
最密72生素数就只有这两种形式。

白新岭 · 发表于 2019-8-20 20:01

邻距频率
0 1
2 16
4 19
6 21
8 6
10 5
12 2
14 2
在最密k生素数中邻距出现次数最高的，一般都是2,4,6这三个值，其余值相对来说，出现的很少。

白新岭 · 发表于 2019-8-20 20:07

白新岭发表于 2019-8-20 11:31
最密71生素数的最终系数C71(L378)=3.05965320927526E+39

最密71生素数的最终系数C71(L378)= 3.05891081045346E+39
备注：364#的系数错误，没有最后放缩。

白新岭 · 发表于 2019-8-20 20:11

白新岭发表于 2019-8-20 11:34
n(10的次幂）最密71生素数的数量
139 5.000000000000000000E+00
140 3.100000000000000000E+01

n(10的次幂）最密71生素数的数量
139 5.000000000000000000E+00
140 3.100000000000000000E+01
141 1.910000000000000000E+02
142 1.154000000000000000E+03
143 7.003000000000000000E+03
144 4.262100000000000000E+04
145 2.602610000000000000E+05
146 1.594685000000000000E+06
147 9.803907000000000000E+06
148 6.047313700000000000E+07
149 3.742360100000000000E+08
150 2.323428442000000000E+09
151 1.447088052600000000E+10
152 9.041160816900000000E+10
153 5.666292945490000000E+11
154 3.562064784307000000E+12
155 2.246028574311400000E+13
156 1.420438587275850000E+14
157 9.009625581348650000E+14
158 5.731282497561710000E+15
159 3.656298835237570000E+16
160 2.339163919930610000E+17
161 1.500698112298340000E+18
162 9.654385005966590000E+18
163 6.227871764878350000E+19
164 4.028319649156590000E+20
165 2.612541007010350000E+21
166 1.698803740541000000E+22
167 1.107517073842190000E+23
168 7.238877985522360000E+23
169 4.743429011125250000E+24
170 3.116024269170360000E+25
171 2.052030067732840000E+26
172 1.354654306166840000E+27
173 8.964431395701020000E+27
174 5.946403348621290000E+28
175 3.953769868559460000E+29
176 2.635008851522920000E+30
177 1.760171155271180000E+31
178 1.178469940765430000E+32
179 7.907910718802780000E+32
180 5.318310397587480000E+33
181 3.584623108146000000E+34
182 2.421366974306060000E+35
183 1.639134529394040000E+36
184 1.111975450602530000E+37
185 7.559487075799370000E+37
186 5.149867617478140000E+38
187 3.515577256160360000E+39
188 2.404830473416800000E+40
189 1.648352438004540000E+41
190 1.132098381849980000E+42
191 7.790720019034970000E+42
192 5.371818704422830000E+43
193 3.711133272161370000E+44
194 2.568765604246800000E+45
195 1.781420851711250000E+46
196 1.237725247803530000E+47
197 8.615674834545180000E+47
198 6.008325810048370000E+48
365#数据错误（因为系数没有最后放缩）。

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