[原创]k生素数群的数量公式

独舟星海 · 发表于 2019-8-9 20:14

n(10的次幂）最密60生素数的数量
113 5.000000000000000000E+00
114 3.200000000000000000E+01
115 1.900000000000000000E+02
116 1.129000000000000000E+03
117 6.733000000000000000E+03
118 4.031100000000000000E+04
119 2.423710000000000000E+05
120 1.463517000000000000E+06
121 8.874507000000000000E+06
122 5.403674500000000000E+07
123 3.303720100000000000E+08
124 2.027951590000000000E+09
125 1.249752553300000000E+10
126 7.731702089000000000E+10
127 4.801578091710000000E+11
128 2.993122551903000000E+12
129 1.872712239756300000E+13
130 1.175976579844080000E+14
131 7.411105162207870000E+14
132 4.687055818626680000E+15
133 2.974588077356370000E+16
134 1.894263261349010000E+17
135 1.210370656582580000E+18
136 7.759598135081440000E+18
137 4.990931346105650000E+19
138 3.220510210866760000E+20
139 2.084721926487920000E+21
140 1.353729984541870000E+22
141 8.817732969314890000E+22
142 5.761077967390990000E+23
143 3.775320430025040000E+24
144 2.481354828141780000E+25
145 1.635652448703880000E+26
146 1.081291460233030000E+27
147 7.168477946486380000E+27
148 4.765700740917080000E+28
149 3.177062476860920000E+29
150 2.123771501623560000E+30
151 1.423498664384130000E+31
152 9.566610487450530000E+31
153 6.446079971961890000E+32
154 4.354667223894130000E+33
155 2.949316283227450000E+34
156 2.002536806697550000E+35
157 1.363070799983270000E+36
158 9.300821400922020000E+36
159 6.361736484212160000E+37
160 4.361825422013880000E+38
161 2.997685843445410000E+39
162 2.064982772543500000E+40
163 1.425760924619390000E+41
164 9.866534853128880000E+41
165 6.843183870747680000E+42
166 4.756806988680120000E+43
167 3.313790037234010000E+44
168 2.313530153740860000E+45
169 1.618657055045370000E+46
170 1.134888024782700000E+47
171 7.973680884734250000E+47
172 5.613861920713950000E+48

白新岭 · 发表于 2019-8-10 17:48

素数式61 素数式61 素数式61 素数式61
0 0 0 0
6 4 6 4
4 2 10 6
2 4 12 10
10 6 22 16
2 2 24 18
10 6 34 24
2 4 36 28
4 6 40 34
2 2 42 36
10 12 52 48
2 10 54 58
10 2 64 60
2 4 66 64
4 2 70 66
2 4 72 70
4 6 76 76
14 2 90 78
4 6 94 84
2 10 96 94
4 6 100 100
12 6 112 106
2 2 114 108
6 6 120 114
4 6 124 120
8 6 132 126
4 4 136 130
6 6 142 136
8 8 150 144
4 4 154 148
2 6 156 154
6 2 162 156
4 4 166 160
8 8 174 168
6 6 180 174
4 4 184 178
6 8 190 186
6 4 196 190
6 6 202 196
2 2 204 198
6 12 210 210
6 4 216 214
10 2 226 216
6 4 232 220
2 14 234 234
6 4 240 238
4 2 244 240
2 4 246 244
4 2 250 246
2 10 252 256
10 2 262 258
12 10 274 268
2 2 276 270
6 4 282 274
4 2 286 276
6 10 292 286
2 2 294 288
6 10 300 298
4 2 304 300
2 4 306 304
4 6 310 310
这是最密61生素数的两种表示形式，只有这两组通过检验，另外4组没有通过素数29的关卡。

白新岭 · 发表于 2019-8-10 17:52

最密61生素数的最终系数C61(L310)=7.14164106413128E+32

白新岭 · 发表于 2019-8-10 17:55

n(10的次幂）最密61生素数的数量
115 1.000000000000000000E+00
116 8.000000000000000000E+00
117 5.100000000000000000E+01
118 3.050000000000000000E+02
119 1.820000000000000000E+03
120 1.090100000000000000E+04
121 6.555600000000000000E+04
122 3.958820000000000000E+05
123 2.400567000000000000E+06
124 1.461609700000000000E+07
125 8.934899400000000000E+07
126 5.483536670000000000E+08
127 3.378449141000000000E+09
128 2.089454620100000000E+10
129 1.297123789410000000E+11
130 8.082345942360000000E+11
131 5.054476378617000000E+12
132 3.172293771498200000E+13
133 1.998045787862910000E+14
134 1.262842359572590000E+15
135 8.009066298001150000E+15
136 5.096611864161670000E+16
137 3.254067286052090000E+17
138 2.084469954161510000E+18
139 1.339578601890180000E+19
140 8.636225468489670000E+19
141 5.585256766309630000E+20
142 3.623316994799580000E+21
143 2.357732671309170000E+22
144 1.538825098671020000E+23
145 1.007331103973880000E+24
146 6.613413879664340000E+24
147 4.354438843761180000E+25
148 2.875243559237450000E+26
149 1.903865647472910000E+27
150 1.264156297836820000E+28
151 8.416896653296170000E+28
152 5.619196445885380000E+29
153 3.761421450102930000E+30
154 2.524469954286050000E+31
155 1.698689511642610000E+32
156 1.145958378853910000E+33
157 7.750334631029070000E+33
158 5.254783636540430000E+34
159 3.571562620846390000E+35
160 2.433421132651300000E+36
161 1.661952629926130000E+37
162 1.137756687736070000E+38
163 7.807227132400110000E+38
164 5.369679926475700000E+39
165 3.701620460854990000E+40
166 2.557497610686060000E+41
167 1.770951325955450000E+42
168 1.229007241126950000E+43
169 8.547660900204430000E+43
170 5.957635851470070000E+44
171 4.161246561053680000E+45
172 2.912627606340230000E+46
173 2.042903591869100000E+47
174 1.435825778356710000E+48

白新岭 · 发表于 2019-8-10 18:16

素数式62 素数式62 素数式62 素数式62 素数式62 素数式62 素数式62 素数式62
0 0 0 0 0 0 0 0
2 8 2 6 2 8 2 8
6 4 4 2 4 4 4 4
4 2 2 4 6 2 2 2
6 10 4 6 2 18 4 6
2 8 6 8 6 6 6 4
22 6 8 6 4 4 2 8
2 4 4 4 6 6 6 6
4 6 2 2 14 2 4 4
2 2 4 10 10 4 2 6
4 4 6 14 2 6 4 2
6 6 6 4 4 8 6 4
2 8 8 2 2 6 6 6
6 6 6 10 4 4 2 8
4 4 6 2 6 2 6 6
2 2 4 10 2 10 6 4
4 10 6 2 6 14 6 2
6 2 8 4 4 4 4 10
6 12 4 6 6 2 6 2
2 4 2 8 6 10 8 6
6 2 4 6 6 2 4 6
6 10 2 4 2 10 6 4
6 2 12 2 6 2 2 2
4 10 6 4 6 4 4 10
6 2 4 6 6 6 8 2
8 4 12 6 4 8 6 10
4 6 6 2 6 6 4 2
6 8 2 6 8 4 8 4
2 6 6 4 4 2 4 6
4 4 6 8 6 4 6 8
8 6 6 4 2 6 2 6
6 6 4 6 4 6 6 4
4 6 6 8 8 2 6 6
8 2 8 4 6 6 4 6
4 6 6 2 4 4 2 6
6 4 4 6 8 8 4 2
2 8 2 4 4 4 6 6
6 4 10 8 6 6 8 12
6 6 2 6 2 8 6 4
4 8 10 4 6 4 4 6
2 4 2 6 6 2 2 12
4 2 4 6 4 6 10 2
6 6 6 6 2 4 2 4
8 4 6 2 4 8 10 2
6 8 2 6 14 6 2 4
4 6 10 6 4 4 4 8
2 4 2 4 2 6 14 6
10 6 4 2 4 6 10 4
2 6 6 4 2 6 2 6
10 6 8 6 10 2 4 6
2 2 6 2 2 6 6 8
4 6 4 6 10 6 8 6
14 6 2 4 2 4 6 6
10 4 6 2 4 2 4 4
2 2 4 4 12 4 2 2
4 4 6 2 2 6 6 4
6 8 8 22 10 2 4 8
8 6 4 2 2 6 6 6
6 4 6 6 4 4 18 4
4 2 2 4 6 2 2 2
2 4 4 6 8 4 4 4
6 2 8 2 6 2 8 2

白新岭 · 发表于 2019-8-10 18:16

素数式62 素数式62 素数式62 素数式62 素数式62 素数式62 素数式62 素数式62
0 0 0 0 0 0 0 0
2 8 2 6 2 8 2 8
6 4 4 2 4 4 4 4
4 2 2 4 6 2 2 2
6 10 4 6 2 18 4 6
2 8 6 8 6 6 6 4
22 6 8 6 4 4 2 8
2 4 4 4 6 6 6 6
4 6 2 2 14 2 4 4
2 2 4 10 10 4 2 6
4 4 6 14 2 6 4 2
6 6 6 4 4 8 6 4
2 8 8 2 2 6 6 6
6 6 6 10 4 4 2 8
4 4 6 2 6 2 6 6
2 2 4 10 2 10 6 4
4 10 6 2 6 14 6 2
6 2 8 4 4 4 4 10
6 12 4 6 6 2 6 2
2 4 2 8 6 10 8 6
6 2 4 6 6 2 4 6
6 10 2 4 2 10 6 4
6 2 12 2 6 2 2 2
4 10 6 4 6 4 4 10
6 2 4 6 6 6 8 2
8 4 12 6 4 8 6 10
4 6 6 2 6 6 4 2
6 8 2 6 8 4 8 4
2 6 6 4 4 2 4 6
4 4 6 8 6 4 6 8
8 6 6 4 2 6 2 6
6 6 4 6 4 6 6 4
4 6 6 8 8 2 6 6
8 2 8 4 6 6 4 6
4 6 6 2 4 4 2 6
6 4 4 6 8 8 4 2
2 8 2 4 4 4 6 6
6 4 10 8 6 6 8 12
6 6 2 6 2 8 6 4
4 8 10 4 6 4 4 6
2 4 2 6 6 2 2 12
4 2 4 6 4 6 10 2
6 6 6 6 2 4 2 4
8 4 6 2 4 8 10 2
6 8 2 6 14 6 2 4
4 6 10 6 4 4 4 8
2 4 2 4 2 6 14 6
10 6 4 2 4 6 10 4
2 6 6 4 2 6 2 6
10 6 8 6 10 2 4 6
2 2 6 2 2 6 6 8
4 6 4 6 10 6 8 6
14 6 2 4 2 4 6 6
10 4 6 2 4 2 4 4
2 2 4 4 12 4 2 2
4 4 6 2 2 6 6 4
6 8 8 22 10 2 4 8
8 6 4 2 2 6 6 6
6 4 6 6 4 4 18 4
4 2 2 4 6 2 2 2
2 4 4 6 8 4 4 4
6 2 8 2 6 2 8 2

白新岭 · 发表于 2019-8-10 18:21

上楼第二列和第五列所表示的最密62生素数没有，未通过素数29的关卡，还有两组未列出，也没有通过素数29的关卡，只有6种最密62生素数。

白新岭 · 发表于 2019-8-10 18:22

素数式62 素数式62 素数式62 素数式62 素数式62 素数式62
0 0 0 0 0 0
2 2 6 8 2 8
8 6 8 12 6 12
12 8 12 14 8 14
18 12 18 32 12 20
20 18 26 38 18 24
42 26 32 42 20 32
44 30 36 48 26 38
48 32 38 50 30 42
50 36 48 54 32 48
54 42 62 60 36 50
60 48 66 68 42 54
62 56 68 74 48 60
68 62 78 78 50 68
72 68 80 80 56 74
74 72 90 90 62 78
78 78 92 104 68 80
84 86 96 108 72 90
90 90 102 110 78 92
92 92 110 120 86 98
98 96 116 122 90 104
104 98 120 132 96 108
110 110 122 134 98 110
114 116 126 138 102 120
120 120 132 144 110 122
128 132 138 152 116 132
132 138 140 158 120 134
138 140 146 162 128 138
140 146 150 164 132 144
144 152 158 168 138 152
152 158 162 174 140 158
158 162 168 180 146 162
162 168 176 182 152 168
170 176 180 188 156 174
174 182 182 192 158 180
180 186 188 200 162 182
182 188 192 204 168 188
188 198 200 210 176 200
194 200 206 218 182 204
198 210 210 222 186 210
200 212 216 224 188 222
204 216 222 230 198 224
210 222 228 234 200 228
218 228 230 242 210 230
224 230 236 248 212 234
228 240 242 252 216 242
230 242 246 258 230 248
240 246 248 264 240 252
242 252 252 270 242 258
252 260 258 272 246 264
254 266 260 278 252 272
258 270 266 284 260 278
272 272 270 288 266 284
282 278 272 290 270 288
284 282 276 294 272 290
288 288 278 300 278 294
294 296 300 302 282 302
302 300 302 308 288 308
308 306 308 312 306 312
312 308 312 314 308 314
314 312 318 318 312 318
320 320 320 320 320 320

白新岭 · 发表于 2019-8-10 18:29

最密62生素数的最终系数C62(L320)=3.75448716201756E+33

白新岭 · 发表于 2019-8-10 18:32

n(10的次幂）最密62生素数的数量
117 1.000000000000000000E+00
118 5.000000000000000000E+00
119 3.500000000000000000E+01
120 2.080000000000000000E+02
121 1.242000000000000000E+03
122 7.442000000000000000E+03
123 4.476200000000000000E+04
124 2.703320000000000000E+05
125 1.639263000000000000E+06
126 9.980210000000000000E+06
127 6.100197700000000000E+07
128 3.743125280000000000E+08
129 2.305603457000000000E+09
130 1.425505367600000000E+10
131 8.846304299400000000E+10
132 5.509840565150000000E+11
133 3.444104005710000000E+12
134 2.160478878304900000E+13
135 1.359995073809860000E+14
136 8.590445854719670000E+14
137 5.444564502674890000E+15
138 3.462247896391290000E+16
139 2.208918587790480000E+17
140 1.413862640328300000E+18
141 9.078634933738690000E+18
142 5.847900931716740000E+19
143 3.778559748542980000E+20
144 2.448953470573220000E+21
145 1.592004314441720000E+22
146 1.038004680576290000E+23
147 6.787784088027160000E+23
148 4.451567853271330000E+24
149 2.927771869334270000E+25
150 1.931007938284590000E+26
151 1.277135978443250000E+27
152 8.469942587114520000E+27
153 5.632463005609330000E+28
154 3.755566018822060000E+29
155 2.510709943787810000E+30
156 1.682856108971390000E+31
157 1.130868792202680000E+32
158 7.618650010064040000E+32
159 5.145533849480060000E+33
160 3.483820551411850000E+34
161 2.364506982013700000E+35
162 1.608687651997710000E+36
163 1.097074753340660000E+37
164 7.499311251661690000E+37
165 5.138244140931320000E+38
166 3.528613176974490000E+39
167 2.428719215263860000E+40
168 1.675416183133020000E+41
169 1.158320261369990000E+42
170 8.025715601621400000E+42
171 5.572843695727210000E+43
172 3.877903128690850000E+44
173 2.704165409976770000E+45
174 1.889622918361130000E+46
175 1.323159551517550000E+47
176 9.283980399181930000E+47

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