[原创]k生素数群的数量公式

独舟星海 · 发表于 2019-8-8 19:26

n(10的次幂）最密57生素数的数量
106 1.000000000000000000E+00
107 8.000000000000000000E+00
108 4.700000000000000000E+01
109 2.770000000000000000E+02
110 1.642000000000000000E+03
111 9.781000000000000000E+03
112 5.851300000000000000E+04
113 3.516470000000000000E+05
114 2.122861000000000000E+06
115 1.287246700000000000E+07
116 7.839616100000000000E+07
117 4.794991490000000000E+08
118 2.945160936000000000E+09
119 1.816466023400000000E+10
120 1.124895755260000000E+11
121 6.994142646650000000E+11
122 4.365812648404000000E+12
123 2.735747497681300000E+13
124 1.720837363720450000E+14
125 1.086500184066940000E+15
126 6.885252109794990000E+15
127 4.379096186175220000E+16
128 2.795109655402510000E+17
129 1.790352981193930000E+18
130 1.150747951939160000E+19
131 7.421647561390760000E+19
132 4.802599602475890000E+20
133 3.118072844460460000E+21
134 2.030992602645900000E+22
135 1.327154567295820000E+23
136 8.699716351103680000E+23
137 5.720564710190480000E+24
138 3.773142254509500000E+25
139 2.496195510971460000E+26
140 1.656327651370040000E+27
141 1.102269124246550000E+28
142 7.356727403693900000E+28
143 4.924017587978790000E+29
144 3.305027587827020000E+30
145 2.224508957656880000E+31
146 1.501343860137280000E+32
147 1.016007324330450000E+33
148 6.893951150636090000E+33
149 4.690062485377430000E+34
150 3.198989416714620000E+35
151 2.187538552599570000E+36
152 1.499659473709350000E+37
153 1.030645243258380000E+38
154 7.100537463584970000E+38
155 4.903710869226980000E+39
156 3.394661770320680000E+40
157 2.355552869413190000E+41
158 1.638327881510190000E+42
159 1.142109076408810000E+43
160 7.979957090818480000E+43
161 5.588141521213190000E+44
162 3.921895234346870000E+45
163 2.758509232228500000E+46
164 1.944424507289880000E+47
165 1.373518345739450000E+48
166 9.722844244918830000E+48
167 6.896942956174600000E+49
168 4.902454087057250000E+50
169 3.491832318464180000E+51
170 2.492101390283530000E+52
171 1.782133523018630000E+53
172 1.276929382321690000E+54
173 9.167178954000790000E+54
174 6.593818357375500000E+55
175 4.751832359577990000E+56
176 3.430825970386600000E+57
177 2.481649595209750000E+58
178 1.798362867233180000E+59
179 1.305570552811940000E+60
180 9.495125838155690000E+60
181 6.917828905132930000E+61
182 5.048927317296820000E+62
183 3.691307871283950000E+63
184 2.703367208291170000E+64
185 1.983194668503720000E+65
186 1.457314290137490000E+66
187 1.072656929264160000E+67
188 7.908251975056440000E+67
189 5.839889226370040000E+68
190 4.319422773791360000E+69
191 3.199900457108610000E+70
192 2.374267488247320000E+71
193 1.764404393061130000E+72
194 1.313212230831590000E+73
195 9.788882502480920000E+73
196 7.307787852498840000E+74
197 5.463697925436670000E+75
198 4.090993407241840000E+76
199 3.067649562361080000E+77
200 2.303621871624830000E+78
201 1.732362732142350000E+79
202 1.304615299361870000E+80
203 9.838660948080110000E+80
204 7.430078478689330000E+81
205 5.618867121489600000E+82
206 4.254967420007130000E+83
207 3.226488192469110000E+84
208 2.449878890406980000E+85
209 1.862662872113080000E+86
210 1.418056386709060000E+87
211 1.080978145619100000E+88
212 8.250858662089070000E+88
213 6.305723544180450000E+89
214 4.825241443082870000E+90
215 3.696973929608990000E+91
216 2.836036960496840000E+92
217 2.178264223504400000E+93
218 1.675087459157110000E+94
219 1.289697396612520000E+95
220 9.941611405958500000E+95
221 7.672548651294600000E+96
222 5.928321826323610000E+97
223 4.585941978535300000E+98
224 3.551611666976800000E+99
225 2.753709092596840000E+100
226 2.137479219713610000E+101
227 1.661011549410130000E+102
228 1.292188938999550000E+103
229 1.006370196049590000E+104
230 7.846278407508180000E+104
231 6.124064217389340000E+105
232 4.784998001847220000E+106
233 3.742706476841220000E+107
234 2.930540937724830000E+108
235 2.297015446488800000E+109
236 1.802313233291650000E+110
237 1.415608112071480000E+111
238 1.113008446777780000E+112
239 8.759772007024540000E+112
240 6.901164754278840000E+113
241 5.442314184323050000E+114
242 4.296084968377110000E+115
243 3.394584419684660000E+116
244 2.684858292575230000E+117
245 2.125561497505240000E+118
246 1.684380178437950000E+119
247 1.336033482847320000E+120
248 1.060723053698420000E+121
249 8.429286819659120000E+121
250 6.704718768930580000E+122
251 5.337870119296140000E+123
252 4.253534606685030000E+124
253 3.392527198737790000E+125
254 2.708226666042000000E+126
255 2.163873793477030000E+127
256 1.730458017200770000E+128
最密k生素数在k=57时，首例到10的256次方时，其数量的平方才追上其范围值（量级相同），所以最密57生素数的中项合成的偶数最小得到10的256次方后，才能从理论上保证每个应该有素数对的偶数至少拥有一组中项和。

独舟星海 · 发表于 2019-8-8 19:32

素数式58 素数式58 素数式58 素数式58
0 0 0 0
6 2 6 2
4 4 10 6
6 2 16 8
2 4 18 12
4 6 22 18
6 2 28 20
8 6 36 26
6 4 42 30
4 2 46 32
2 4 48 36
10 6 58 42
14 6 72 48
4 2 76 50
2 6 78 56
10 6 88 62
2 6 90 68
10 4 100 72
2 6 102 78
4 8 106 86
6 4 112 90
8 6 120 96
6 2 126 98
4 4 130 102
2 8 132 110
4 6 136 116
6 4 142 120
6 8 148 128
2 4 150 132
6 6 156 138
4 2 160 140
8 6 168 146
4 6 172 152
6 4 178 156
8 2 186 158
4 4 190 162
2 6 192 168
6 8 198 176
4 6 202 182
8 4 210 186
6 2 216 188
4 10 220 198
6 2 226 200
6 10 232 210
6 2 238 212
2 4 240 216
6 14 246 230
6 10 252 240
4 2 256 242
2 4 258 246
4 6 262 252
6 8 268 260
2 6 270 266
6 4 276 270
4 2 280 272
2 6 282 278
4 4 286 282
2 6 288 288

独舟星海 · 发表于 2019-8-8 19:36

最密58生素数的最终系数C58(L288)=7.33523578861799E+30

独舟星海 · 发表于 2019-8-8 19:39

n(10的次幂）最密58生素数的数量
108 1.000000000000000000E+00
109 6.000000000000000000E+00
110 3.700000000000000000E+01
111 2.190000000000000000E+02
112 1.298000000000000000E+03
113 7.735000000000000000E+03
114 4.628800000000000000E+04
115 2.782240000000000000E+05
116 1.679748000000000000E+06
117 1.018560000000000000E+07
118 6.202820900000000000E+07
119 3.793329830000000000E+08
120 2.329431020000000000E+09
121 1.436305833300000000E+10
122 8.891652833800000000E+10
123 5.526217606980000000E+11
124 3.447906545880000000E+12
125 2.159423360997100000E+13
126 1.357526615936110000E+14
127 8.565668006675760000E+14
128 5.424392943361140000E+15
129 3.447413327069000000E+16
130 2.198688707582830000E+17
131 1.407144628857290000E+18
132 9.036396912285250000E+18
133 5.822519118745220000E+19
134 3.764121341512930000E+20
135 2.441360265057120000E+21
136 1.588527257425440000E+22
137 1.036887064366880000E+23
138 6.789255027601590000E+23
139 4.459097856247410000E+24
140 2.937560758526560000E+25
141 1.940988045397730000E+26
142 1.286283166811580000E+27
143 8.548895352991300000E+27
144 5.698039431380880000E+28
145 3.808602507037410000E+29
146 2.552781654941770000E+30
147 1.715745768178120000E+31
148 1.156291169770490000E+32
149 7.813409389399470000E+32
150 5.293677288318540000E+33
151 3.595858402705990000E+34
152 2.448843144527740000E+35
153 1.671929451003230000E+36
154 1.144350689972530000E+37
155 7.851821674310240000E+37
156 5.400550019891770000E+38
157 3.723473503610270000E+39
158 2.573285354149360000E+40
159 1.782559288725220000E+41
160 1.237666311691150000E+42
161 8.612993987303380000E+42
162 6.007356110411470000E+43
163 4.199321929630060000E+44
164 2.941911781118540000E+45
165 2.065490229773950000E+46
166 1.453276404279310000E+47
167 1.024692690629720000E+48

独舟星海 · 发表于 2019-8-9 19:51

素数式59 素数式59 素数式59 素数式59 素数式59 素数式59 素数式59 素数式59
0 0 0 0 0 0 0 0
4 4 2 2 4 4 2 2
2 2 10 4 6 6 12 6
10 10 2 6 16 16 14 12
2 2 10 2 18 18 24 14
10 10 2 6 28 28 26 20
2 2 4 4 30 30 30 24
4 4 2 6 34 34 32 30
2 2 10 2 36 36 42 32
10 10 2 12 46 46 44 44
2 2 10 10 48 48 54 54
10 10 2 2 58 58 56 56
2 2 4 4 60 60 60 60
4 4 2 2 64 64 62 62
2 2 4 4 66 66 66 66
4 4 14 6 70 70 80 72
14 14 4 2 84 84 84 74
4 4 2 6 88 88 86 80
2 2 4 10 90 90 90 90
4 4 12 6 94 94 102 96
12 12 2 6 106 106 104 102
2 2 6 2 108 108 110 104
6 6 4 6 114 114 114 110
4 4 8 6 118 118 122 116
8 8 4 6 126 126 126 122
4 4 6 4 130 130 132 126
6 6 8 6 136 136 140 132
8 8 4 8 144 144 144 140
4 4 2 4 148 148 146 144
2 2 6 6 150 150 152 150
6 6 4 2 156 156 156 152
4 4 8 4 160 160 164 156
8 8 6 8 168 168 170 164
6 6 4 6 174 174 174 170
4 4 6 4 178 178 180 174
6 6 6 8 184 184 186 182
6 6 6 4 190 190 192 186
6 6 2 6 196 196 194 192
2 2 6 2 198 198 200 194
6 6 6 12 204 204 206 206
6 6 10 4 210 210 216 210
10 6 6 2 220 216 222 212
6 4 2 4 226 220 224 216
2 6 6 14 228 226 230 230
6 2 4 4 234 228 234 234
4 6 2 2 238 234 236 236
2 6 4 4 240 240 240 240
4 4 2 2 244 244 242 242
2 2 10 10 246 246 252 252
10 10 12 2 256 256 264 254
12 12 2 10 268 268 266 264
2 2 6 2 270 270 272 266
6 6 4 4 276 276 276 270
4 4 6 2 280 280 282 272
6 6 2 10 286 286 284 282
2 2 6 2 288 288 290 284
6 6 4 10 294 294 294 294
4 4 2 2 298 298 296 296
2 2 4 4 300 300 300 300
这是最密59生素数的两种表示形式。在至23的素数式中预选项为16组，只有这4组过关，其余12组没有过素数29的关卡。

独舟星海 · 发表于 2019-8-9 19:54

最密59生素数的最终系数C59(L300)=6.15512802258519E+31

独舟星海 · 发表于 2019-8-9 19:57

n(10的次幂）最密59生素数的数量
110 1.000000000000000000E+00
111 7.000000000000000000E+00
112 4.200000000000000000E+01
113 2.500000000000000000E+02
114 1.487000000000000000E+03
115 8.859000000000000000E+03
116 5.302600000000000000E+04
117 3.187730000000000000E+05
118 1.924715000000000000E+06
119 1.167107500000000000E+07
120 7.106964800000000000E+07
121 4.345661540000000000E+08
122 2.668064013000000000E+09
123 1.644659935300000000E+10
124 1.017810962700000000E+11
125 6.323268041080000000E+11
126 3.943415107189000000E+12
127 2.468501886936400000E+13
128 1.550953394800130000E+14
129 9.780098026688700000E+14
130 6.189310782684990000E+15
131 3.930719121722780000E+16
132 2.505006969803100000E+17
133 1.601880719559080000E+18
134 1.027811184916060000E+19
135 6.616625566371390000E+19
136 4.273448200944190000E+20
137 2.768968925741990000E+21
138 1.799844635123970000E+22
139 1.173570661761900000E+23
140 7.675756444718000000E+23
141 5.035605395689690000E+24
142 3.313462138425520000E+25
143 2.186723164442800000E+26
144 1.447335147277970000E+27
145 9.607056316146360000E+27
146 6.394995875103480000E+28
147 4.268762962850490000E+29
148 2.857321637233060000E+30
149 1.917764851947140000E+31
150 1.290609498691540000E+32
151 8.708474765910730000E+32
152 5.891445263575930000E+33
153 3.995942009911690000E+34
154 2.717186529911840000E+35
155 1.852287202785720000E+36
156 1.265819339504570000E+37
157 8.671532482475620000E+37
158 5.954799969912250000E+38
159 4.098948072786340000E+39
160 2.828124646257830000E+40
161 1.955837580847930000E+41
162 1.355696874509380000E+42
163 9.418368131253040000E+42
164 6.557826230426730000E+43
165 4.576183840412190000E+44
166 3.200329485862350000E+45
167 2.242963260319780000E+46
168 1.575341218956550000E+47
169 1.108769053008340000E+48

独舟星海 · 发表于 2019-8-9 20:07

素数式60 素数式60 素数式60 素数式60
0 0 0 0
4 4 4 4
2 2 6 6
10 4 16 10
2 6 18 16
10 2 28 18
2 6 30 24
4 4 34 28
2 6 36 34
10 2 46 36
2 12 48 48
10 10 58 58
2 2 60 60
4 4 64 64
2 2 66 66
4 4 70 70
14 6 84 76
4 2 88 78
2 6 90 84
4 10 94 94
12 6 106 100
2 6 108 106
6 2 114 108
4 6 118 114
8 6 126 120
4 6 130 126
6 4 136 130
8 6 144 136
4 8 148 144
2 4 150 148
6 6 156 154
4 2 160 156
8 4 168 160
6 8 174 168
4 6 178 174
6 4 184 178
6 8 190 186
6 4 196 190
2 6 198 196
6 2 204 198
6 12 210 210
10 4 220 214
6 2 226 216
2 4 228 220
6 14 234 234
4 4 238 238
2 2 240 240
4 4 244 244
2 2 246 246
10 10 256 256
12 2 268 258
2 10 270 268
6 2 276 270
4 4 280 274
6 2 286 276
2 10 288 286
6 2 294 288
4 10 298 298
2 2 300 300
4 4 304 304
这是最密60生素数的两种表示形式，至23的素数式中，预选为6组，其余4组未通过素数29的关卡。

独舟星海 · 发表于 2019-8-9 20:07

素数式60 素数式60 素数式60 素数式60
0 0 0 0
4 4 4 4
2 2 6 6
10 4 16 10
2 6 18 16
10 2 28 18
2 6 30 24
4 4 34 28
2 6 36 34
10 2 46 36
2 12 48 48
10 10 58 58
2 2 60 60
4 4 64 64
2 2 66 66
4 4 70 70
14 6 84 76
4 2 88 78
2 6 90 84
4 10 94 94
12 6 106 100
2 6 108 106
6 2 114 108
4 6 118 114
8 6 126 120
4 6 130 126
6 4 136 130
8 6 144 136
4 8 148 144
2 4 150 148
6 6 156 154
4 2 160 156
8 4 168 160
6 8 174 168
4 6 178 174
6 4 184 178
6 8 190 186
6 4 196 190
2 6 198 196
6 2 204 198
6 12 210 210
10 4 220 214
6 2 226 216
2 4 228 220
6 14 234 234
4 4 238 238
2 2 240 240
4 4 244 244
2 2 246 246
10 10 256 256
12 2 268 258
2 10 270 268
6 2 276 270
4 4 280 274
6 2 286 276
2 10 288 286
6 2 294 288
4 10 298 298
2 2 300 300
4 4 304 304
这是最密60生素数的两种表示形式，至23的素数式中，预选为6组，其余4组未通过素数29的关卡。

独舟星海 · 发表于 2019-8-9 20:10

最密60生素数的最终系数C60(L304)=3.48602297493483E+32

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