[原创]k生素数群的数量公式

白新岭 · 发表于 2019-8-23 15:24

白新岭发表于 2019-8-22 11:12
n(10的次幂）最密79生素数的数量
157 2.000000000000000000E+00
158 1.200000000000000000E+01

n(10的次幂）最密79生素数的数量
157 2.000000000000000000E+00
158 1.200000000000000000E+01
159 7.800000000000000000E+01
160 4.750000000000000000E+02
161 2.904000000000000000E+03
162 1.777700000000000000E+04
163 1.091470000000000000E+05
164 6.721370000000000000E+05
165 4.151346000000000000E+06
166 2.571518000000000000E+07
167 1.597513860000000000E+08
168 9.952659410000000000E+08
169 6.218108757000000000E+09
170 3.895718992500000000E+10
171 2.447444212150000000E+11
172 1.541770857221000000E+12
173 9.738564489778000000E+12
174 6.167719379117200000E+13
175 3.916476438918870000E+14
176 2.493415256813080000E+15
177 1.591508795234750000E+16
178 1.018418271474340000E+17
179 6.533315284185740000E+17
180 4.201642924146880000E+18
181 2.708761414302990000E+19
182 1.750558605730720000E+20
183 1.134031807583320000E+21
184 7.363852520649260000E+21
185 4.792972799007280000E+22
186 3.126898873963670000E+23
187 2.044658723210610000E+24
188 1.340032255289640000E+25
189 8.802105744618370000E+25
190 5.794613365055150000E+26
191 3.823126849492830000E+27
192 2.527896474222300000E+28
193 1.675082955379770000E+29
194 1.112346505932420000E+30
195 7.402203867241240000E+30
196 4.936165812899900000E+31
197 3.298503218152140000E+32
198 2.208683181407640000E+33
199 1.481938837594290000E+34
200 9.963194742740390000E+34
201 6.711656406408080000E+35
202 4.530174924143400000E+36
203 3.063697768705530000E+37
204 2.075937230575370000E+38
205 1.409326584447430000E+39
206 9.585838329807350000E+39
207 6.532232050659150000E+40
208 4.459624483051170000E+41
209 3.050228741055810000E+42
210 2.090048276309230000E+43
211 1.434704585147990000E+44
212 9.866054069226130000E+44
213 6.796604741310750000E+45
214 4.690302355055600000E+46
215 3.242372108367500000E+47
216 2.245282774847320000E+48
408#数据错误（因为系数没有最后放缩）。

白新岭 · 发表于 2019-8-23 15:38

最密80生素数的最终系数C80(L432)=1.30981813456257E+46

白新岭 · 发表于 2019-8-23 15:42

n(10的次幂）最密80生素数的数量
159 1.000000000000000000E+00
160 8.000000000000000000E+00
161 5.000000000000000000E+01
162 3.040000000000000000E+02
163 1.859000000000000000E+03
164 1.138200000000000000E+04
165 6.987300000000000000E+04
166 4.302090000000000000E+05
167 2.656536000000000000E+06
168 1.645154500000000000E+07
169 1.021733940000000000E+08
170 6.363476430000000000E+08
171 3.974313401000000000E+09
172 2.489009983500000000E+10
173 1.563054335610000000E+11
174 9.842166714630000000E+11
175 6.213883354540000000E+12
176 3.933489341542000000E+13
177 2.496447005965100000E+14
178 1.588486138339200000E+15
179 1.013324725626670000E+16
180 6.480456831966310000E+16
181 4.154724415522690000E+17
182 2.670216580777850000E+18
183 1.720309811611790000E+19
184 1.110992673658920000E+20
185 7.191983834752410000E+20
186 4.666679786051210000E+21
187 3.035135517387470000E+22
188 1.978555005628650000E+23
189 1.292728939268830000E+24
190 8.465363833321380000E+24
191 5.555872622808420000E+25
192 3.654409987095050000E+26
193 2.408965589071350000E+27
194 1.591411233360820000E+28
195 1.053569155998860000E+29
196 6.989770899496050000E+29
197 4.647000351999310000E+30
198 3.095872661857810000E+31
199 2.066735894554000000E+32
200 1.382513599057500000E+33
201 9.266751997430370000E+33
202 6.223728826624150000E+34
203 4.188226885189560000E+35
204 2.823954576535480000E+36
205 1.907764911232560000E+37
206 1.291288988705100000E+38
207 8.756799315476080000E+38
208 5.949531098488270000E+39
209 4.049744494702400000E+40
210 2.761673380111920000E+41
211 1.886727513251620000E+42
212 1.291310588716130000E+43
213 8.853795595611350000E+43
214 6.081324992400270000E+44
215 4.184366086817810000E+45
216 2.884142864716350000E+46
217 1.991372453621360000E+47
218 1.377304430219690000E+48

白新岭 · 发表于 2019-8-23 18:38

素数式81 素数式81 素数式81 素数式81
0 0 0 0
2 6 2 6
4 4 6 10
2 2 8 12
4 4 12 16
6 2 18 18
2 10 20 28
6 12 26 40
4 2 30 42
2 4 32 46
4 6 36 52
6 6 42 58
6 8 48 66
2 6 50 72
6 4 56 76
12 12 68 88
4 2 72 90
6 6 78 96
8 4 86 100
4 2 90 102
8 6 98 108
4 10 102 118
8 8 110 126
6 4 116 130
4 2 120 132
8 10 128 142
4 8 132 150
6 6 138 156
2 4 140 160
6 6 146 166
6 2 152 168
4 10 156 178
2 8 158 186
4 6 162 192
6 4 168 196
8 2 176 198
6 10 182 208
4 2 186 210
2 12 188 222
12 4 200 226
10 2 210 228
2 10 212 238
4 12 216 250
12 2 228 252
2 4 230 256
10 6 240 262
2 8 242 270
4 6 246 276
6 4 252 280
8 2 260 282
10 4 270 286
2 6 272 292
6 6 278 298
4 2 282 300
6 6 288 306
8 4 296 310
10 8 306 318
2 4 308 322
4 6 312 328
8 8 320 336
10 4 330 340
6 8 336 348
2 4 338 352
4 8 342 360
6 6 348 366
2 4 350 370
12 12 362 382
4 6 366 388
6 2 372 390
8 6 380 396
6 6 386 402
6 4 392 406
4 2 396 408
2 4 398 412
12 6 410 418
10 2 420 420
2 6 422 426
4 4 426 430
2 2 428 432
4 4 432 436
6 2 438 438
438 438 17078 18400
这是最密81生素数式，只有这两种排列形式，在至23的素数式中，有546组总间距为438的81生素数式，只有上述两种最密81生素数式通过了每个素数关卡。

白新岭 · 发表于 2019-8-23 18:43

最密81生素数的最终系数C81(L438)=8.98637299046840E+46

白新岭 · 发表于 2019-8-23 18:46

n(10的次幂）最密81生素数的数量
162 5.000000000000000000E+00
163 3.400000000000000000E+01
164 2.070000000000000000E+02
165 1.266000000000000000E+03
166 7.747000000000000000E+03
167 4.755400000000000000E+04
168 2.927380000000000000E+05
169 1.807269000000000000E+06
170 1.118940200000000000E+07
171 6.947314900000000000E+07
172 4.325526150000000000E+08
173 2.700589903000000000E+09
174 1.690683050900000000E+10
175 1.061294670680000000E+11
176 6.679848166710000000E+11
177 4.215419971417000000E+12
178 2.667139968002500000E+13
179 1.691876807878760000E+14
180 1.075962466459980000E+15
181 6.859913737701960000E+15
182 4.384511699736070000E+16
183 2.809266600980680000E+17
184 1.804355534900500000E+18
185 1.161708585471840000E+19
186 7.497334311039670000E+19
187 4.849980640684180000E+20
188 3.144746328593870000E+21
189 2.043774274105880000E+22
190 1.331285848176320000E+23
191 8.691411864402730000E+23
192 5.686953646223800000E+24
193 3.729316689583630000E+25
194 2.450919760401930000E+26
195 1.614244674060510000E+27
196 1.065468000354460000E+28
197 7.047461745161210000E+28
198 4.671291227055090000E+29
199 3.102728937145150000E+30
200 2.065115367998750000E+31
201 1.377302838406880000E+32
202 9.204292104385770000E+32
203 6.163373487893380000E+33
204 4.135282338002450000E+34
205 2.779982139442570000E+35
206 1.872495135131480000E+36
207 1.263668207686310000E+37
208 8.544192495730250000E+37
209 5.787974964124730000E+38
210 3.928186366599900000E+39
211 2.670912263930500000E+40
212 1.819372584879880000E+41
213 1.241568403672870000E+42
214 8.487880184383920000E+42
215 5.812997250077780000E+43
216 3.988100468830470000E+44
217 2.740880285999280000E+45
218 1.886970249695500000E+46
219 1.301320137505000000E+47
220 8.989603896167370000E+47
221 6.220532448846350000E+48

独舟星海 · 发表于 2019-8-23 19:48

这是最密82生素数式的邻距表示形式，只有这8种排列顺序。
在至23的素数式中，总间距为450的82生素数式组有3800，只有这8个通过素数关卡。
素数式82 素数式82 素数式82 素数式82 素数式82 素数式82 素数式82 素数式82
0 0 0 0 0 0 0 0
4 4 2 2 4 4 2 2
8 2 10 10 2 2 4 4
6 4 2 2 4 4 6 2
4 6 10 10 6 6 2 4
2 8 2 2 2 2 6 6
4 4 4 6 10 6 6 2
2 2 2 10 2 4 4 6
10 4 10 14 4 2 2 4
2 6 14 4 6 4 10 2
10 6 4 2 8 6 2 4
2 2 6 4 6 6 10 6
4 6 6 6 4 2 2 6
6 6 8 8 2 6 4 2
6 6 6 4 6 6 6 6
8 4 4 2 4 6 14 12
6 6 12 4 6 4 6 4
4 8 2 12 8 6 4 6
12 4 6 2 4 8 12 8
2 6 4 6 6 4 2 4
6 2 2 4 2 6 10 12
4 4 16 2 4 2 2 8
2 8 8 16 8 4 6 6
6 6 4 12 6 8 10 4
10 4 2 2 4 6 8 8
8 8 18 4 8 4 4 4
4 4 6 14 4 8 2 6
2 6 4 6 6 4 10 2
10 2 6 4 2 6 8 6
14 6 2 6 6 2 6 6
4 12 4 2 6 6 4 4
6 4 6 4 4 6 6 2
2 6 8 6 6 4 2 4
10 8 6 2 6 2 10 6
8 4 4 6 8 4 8 8
6 2 2 10 6 6 6 4
4 4 10 2 4 8 4 2
2 2 14 4 2 6 2 4
10 10 4 6 10 4 10 2
2 2 2 14 2 2 14 12
12 10 10 4 10 10 4 10
6 2 2 2 2 2 2 6
10 4 10 10 4 10 10 12
12 14 2 2 14 2 2 2
2 10 4 10 6 4 10 10
4 2 6 2 4 14 2 2
2 4 8 4 2 10 4 4
4 6 6 6 10 2 2 6
8 8 4 8 6 4 4 8
6 10 2 6 2 6 8 10
4 2 4 6 6 8 6 2
2 6 6 4 4 6 4 6
4 4 6 6 2 4 12 4
6 6 2 6 6 2 6 14
6 8 6 2 4 6 2 10
2 10 4 6 6 4 6 2
6 2 8 4 14 6 4 4
4 4 4 8 4 18 8 8
8 8 6 4 2 2 4 10
4 10 8 6 12 4 6 6
6 6 4 8 16 8 8 2
8 2 2 4 2 16 4 4
12 10 6 2 4 2 2 6
4 2 4 6 6 4 6 2
8 12 8 4 2 6 4 12
6 4 6 8 12 2 8 4
4 6 4 6 4 12 6 6
12 14 6 4 2 4 4 8
6 6 6 6 4 6 6 6
2 4 6 2 8 8 6 6
6 2 2 4 6 6 6 4
6 10 6 6 4 6 2 2
4 2 6 8 2 4 6 10
2 10 4 6 4 14 6 2
4 2 2 4 14 10 4 10
6 4 4 2 10 2 2 2
2 6 6 10 6 4 4 4
6 6 2 2 2 2 8 2
4 2 6 6 10 10 6 4
2 6 4 4 2 2 4 6
4 4 2 2 10 10 2 8
2 2 4 4 2 2 4 4
450 450 450 450 450 450 450 450

独舟星海 · 发表于 2019-8-23 19:49

素数式82 素数式82 素数式82 素数式82 素数式82 素数式82 素数式82 素数式82
0 0 0 0 0 0 0 0
4 4 2 2 4 4 2 2
12 6 12 12 6 6 6 6
18 10 14 14 10 10 12 8
22 16 24 24 16 16 14 12
24 24 26 26 18 18 20 18
28 28 30 32 28 24 26 20
30 30 32 42 30 28 30 26
40 34 42 56 34 30 32 30
42 40 56 60 40 34 42 32
52 46 60 62 48 40 44 36
54 48 66 66 54 46 54 42
58 54 72 72 58 48 56 48
64 60 80 80 60 54 60 50
70 66 86 84 66 60 66 56
78 70 90 86 70 66 80 68
84 76 102 90 76 70 86 72
88 84 104 102 84 76 90 78
100 88 110 104 88 84 102 86
102 94 114 110 94 88 104 90
108 96 116 114 96 94 114 102
112 100 132 116 100 96 116 110
114 108 140 132 108 100 122 116
120 114 144 144 114 108 132 120
130 118 146 146 118 114 140 128
138 126 164 150 126 118 144 132
142 130 170 164 130 126 146 138
144 136 174 170 136 130 156 140
154 138 180 174 138 136 164 146
168 144 182 180 144 138 170 152
172 156 186 182 150 144 174 156
178 160 192 186 154 150 180 158
180 166 200 192 160 154 182 162
190 174 206 194 166 156 192 168
198 178 210 200 174 160 200 176
204 180 212 210 180 166 206 180
208 184 222 212 184 174 210 182
210 186 236 216 186 180 212 186
220 196 240 222 196 184 222 188
222 198 242 236 198 186 236 200
234 208 252 240 208 196 240 210
240 210 254 242 210 198 242 216
250 214 264 252 214 208 252 228
262 228 266 254 228 210 254 230
264 238 270 264 234 214 264 240
268 240 276 266 238 228 266 242
270 244 284 270 240 238 270 246
274 250 290 276 250 240 272 252
282 258 294 284 256 244 276 260
288 268 296 290 258 250 284 270
292 270 300 296 264 258 290 272
294 276 306 300 268 264 294 278
298 280 312 306 270 268 306 282
304 286 314 312 276 270 312 296
310 294 320 314 280 276 314 306
312 304 324 320 286 280 320 308
318 306 332 324 300 286 324 312
322 310 336 332 304 304 332 320
330 318 342 336 306 306 336 330
334 328 350 342 318 310 342 336
340 334 354 350 334 318 350 338
348 336 356 354 336 334 354 342
360 346 362 356 340 336 356 348
364 348 366 362 346 340 362 350
372 360 374 366 348 346 366 362
378 364 380 374 360 348 374 366
382 370 384 380 364 360 380 372
394 384 390 384 366 364 384 380
400 390 396 390 370 370 390 386
402 394 402 392 378 378 396 392
408 396 404 396 384 384 402 396
414 406 410 402 388 390 404 398
418 408 416 410 390 394 410 408
420 418 420 416 394 408 416 410
424 420 422 420 408 418 420 420
430 424 426 422 418 420 422 422
432 430 432 432 424 424 426 426
438 436 434 434 426 426 434 428
442 438 440 440 436 436 440 432
444 444 444 444 438 438 444 438
448 448 446 446 448 448 446 446
450 450 450 450 450 450 450 450
18936 17940 19706 19304 17596 17194 18960 17964
这是最密82生素数式的间距表示形式。

独舟星海 · 发表于 2019-8-23 19:53

最密82生素数的最终系数C82(L450)=1.30664594717357E+47

独舟星海 · 发表于 2019-8-23 19:55

n(10的次幂）最密82生素数的数量
165 4.000000000000000000E+00
166 2.900000000000000000E+01
167 1.800000000000000000E+02
168 1.103000000000000000E+03
169 6.775000000000000000E+03
170 4.169800000000000000E+04
171 2.573800000000000000E+05
172 1.593146000000000000E+06
173 9.888892000000000000E+06
174 6.155141600000000000E+07
175 3.841609140000000000E+08
176 2.404138316000000000E+09
177 1.508563279300000000E+10
178 9.491007425800000000E+10
179 5.986774566430000000E+11
180 3.786104842160000000E+12
181 2.400485276267700000E+13
182 1.525807987549550000E+14
183 9.722615225711020000E+14
184 6.210646905112680000E+15
185 3.976943733313620000E+16
186 2.552756867930120000E+17
187 1.642500749486160000E+18
188 1.059318884688940000E+19
189 6.847971500982140000E+19
190 4.437113272293160000E+20
191 2.881587750393260000E+21
192 1.875622924465680000E+22
193 1.223577027539510000E+23
194 7.999799575486240000E+23
195 5.241782229809440000E+24
196 3.442081407252970000E+25
197 2.265144780385640000E+26
198 1.493805232033380000E+27
199 9.872015514934040000E+27
200 6.537659940531420000E+28
201 4.338448126697470000E+29
202 2.884915864203630000E+30
203 1.922249531477580000E+31
204 1.283380934862320000E+32
205 8.585430508335220000E+32
206 5.754675472370650000E+33
207 3.864769322930600000E+34
208 2.600531580615170000E+35
209 1.753187859971270000E+36
210 1.184171523834350000E+37
211 8.013325605761240000E+37
212 5.432694424465090000E+38
213 3.689899007581280000E+39
214 2.510746728860280000E+40
215 1.711485288287540000E+41
216 1.168740227287360000E+42
217 7.995215820221490000E+42
218 5.479017486119510000E+43
219 3.761217899697380000E+44
220 2.586429990084030000E+45
221 1.781609797848930000E+46
222 1.229298604090330000E+47
223 8.496273913171140000E+47
224 5.881924175422930000E+48

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[原创]k生素数群的数量公式

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