[原创]k生素数群的数量公式

白新岭 · 发表于 2020-9-12 18:23

素数式形态统计
素数式间0 188
素数式间1 1276
素数式间2 1314
素数式间3 192
2970
当总间距为12时，复杂度剧增。即要是分析相邻二生素数L12（P，P+12），就得涉及到从2生素数到5生素数各种情况，排列顺序，种类，嵌套关系，从外向里，或从里向外，一层一层像绳结那样慢慢解开。
素数式间1：5种形式（0,2,10）（0,10,2）（0,4,8）（0,8,4）（0,6，6）
素数式间2：6种形式 246 264 426 462 624 642
素数式间3：2种形式 4242 2424
这就14种形式了，再加普通型的4种，总共需分析18种k生素数才能获得结果。

白新岭 · 发表于 2020-9-13 14:36

一般二生素数L12（0,12）的最终系数: 2.640647020607380 .有一楼的公式可以获得：一般二生素数L12（P，P+12）的数量为：2.640647020607380*∫(1/(ln（N）)^2)dN(2,N)

白新岭 · 发表于 2020-9-13 18:10

今天温习一下导数及不定积分知识，从新核对一边求解公式，以前或许因为换电脑或者复制文件，又或者长时间没有运用。个别数据可能有误。为了保证数据准确无误，今天着重温习了一边微积分知识。

白新岭 · 发表于 2020-9-13 18:12

同时把公式求解的工作表核对了一边，这样可以保证以后的数据是理论值。

白新岭 · 发表于 2020-9-13 18:36

一般二生素数L12(P,P+12的数量
2 4.000000000000000E+00
3 1.400000000000000E+01
4 5.600000000000000E+01
5 2.490000000000000E+02
6 1.327000000000000E+03
7 7.929000000000000E+03
8 5.125800000000000E+04
9 3.508790000000000E+05
10 2.508566000000000E+06
11 1.856019800000000E+07
12 1.411954010000000E+08
13 1.099185137000000E+09
14 8.724916754000000E+09
15 7.041523748000000E+10
16 5.765174710860000E+11
17 4.779808330774000E+12
18 4.006947565440500E+13
19 3.392221651310340E+14
20 2.897144967776390E+15
21 2.493952377539500E+16
22 2.162268981265960E+17
23 1.886912229082970E+18
24 1.656410785566260E+19
25 1.461987432698870E+20
26 1.296848588483030E+21
27 1.155680213334580E+22
28 1.034285009932210E+23
29 9.293178650504400E+23
30 8.380905816521650E+24
31 7.584261300870990E+25
32 6.885487235805270E+26
33 6.270001063526450E+27
34 5.725752253564470E+28
35 5.242723779665330E+29
36 4.812542708912990E+30
37 4.428173750257290E+31
38 4.083676394372050E+32
39 3.774011174194000E+33
40 3.494884144231800E+34
41 3.242621300591550E+35
42 3.014066609156470E+36
43 2.806498763427280E+37
44 2.617562888558620E+38
45 2.445214238710450E+39
46 2.287671569146360E+40
47 2.143378352086650E+41
48 2.010970382432980E+42
49 1.889248612875390E+43
50 1.777156287445840E+44
51 1.673759623154770E+45
52 1.578231432123550E+46
53 1.489837190076270E+47
54 1.407923147628510E+48
55 1.331906153451530E+49
56 1.261264916902170E+50
57 1.195532485037490E+51
58 1.134289747371430E+52
59 1.077159813069140E+53
60 1.023803130920230E+54
61 9.739132434955300E+54
62 9.272130842509130E+55
63 8.834517406965610E+56
64 8.424016186590960E+57
65 8.038559525744750E+58
66 7.676266150223480E+59
67 7.335421856383120E+60
68 7.014462453549270E+61
69 6.711958668174250E+62
70 6.426602759518540E+63
71 6.157196631601330E+64
72 5.902641255830810E+65
73 5.661927243954890E+66
74 5.434126432480190E+67
75 5.218384358083770E+68
76 5.013913519278160E+69
77 4.819987333094510E+70
78 4.635934707161980E+71
79 4.461135157569500E+72
80 4.295014411536840E+73
81 4.137040441398170E+74
82 3.986719882880550E+75
83 3.843594796286950E+76
84 3.707239734087860E+77
85 3.577259082691130E+78
86 3.453284649883210E+79
87 3.334973472690420E+80
88 3.222005823260380E+81
89 3.114083392864610E+82
90 3.010927636320720E+83
91 2.912278261065910E+84
92 2.817891846816980E+85
93 2.727540583255380E+86
94 2.641011114504210E+87
95 2.558103480339500E+88
96 2.478630145119790E+89
97 2.402415106342060E+90
98 2.329293075553190E+91
99 2.259108725076100E+92
100 2.191715994660740E+93
101 2.126977452749260E+94
102 2.064763707563180E+95
103 2.004952863682750E+96
104 1.947430020202760E+97
105 1.892086806920260E+98
106 1.838820955341920E+99
107 1.787535901597810E+100
108 1.738140418616350E+101
109 1.690548275156870E+102
110 1.644677919513440E+103
111 1.600452185899770E+104
112 1.557798021701720E+105
113 1.516646233943520E+106
114 1.476931253458420E+107
115 1.438590915384810E+108
116 1.401566254727480E+109
117 1.365801315830540E+110
118 1.331242974706060E+111
119 1.297840773250740E+112
120 1.265546764463150E+113
121 1.234315367847050E+114
122 1.204103234252970E+115
123 1.174869119470380E+116
124 1.146573765938410E+117
125 1.119179791993020E+118
126 1.092651588114840E+119
127 1.066955219683650E+120
128 1.042058335784160E+121
129 1.017930083642500E+122
130 9.945410283055460E+122
131 9.718630772042640E+123
132 9.498694092695080E+124
133 9.285344082935730E+125
134 9.078336002534770E+126
135 8.877435943329740E+127
136 8.682420273995440E+128
137 8.493075117103040E+129
138 8.309195856371360E+130
139 8.130586672163180E+131
140 7.957060103418080E+132
141 7.788436634341290E+133
142 7.624544304285420E+134
143 7.465218339371400E+135
144 7.310300804494970E+136
145 7.159640274458580E+137
146 7.013091523053960E+138
147 6.870515229000820E+139
148 6.731777697720330E+140
149 6.596750597990690E+141
150 6.465310712595050E+142
151 6.337339702131020E+143
152 6.212723881205280E+144
153 6.091354006287470E+145
154 5.973125074544400E+146
155 5.857936133019410E+147
156 5.745690097562120E+148
157 5.636293580951670E+149
158 5.529656729691590E+150
159 5.425693068987290E+151
160 5.324319355447330E+152
161 5.225455437078440E+153
162 5.129024120170320E+154
163 5.034951042691120E+155
164 4.943164553837680E+156
165 4.853595599405780E+157
166 4.766177612666040E+158
167 4.680846410449650E+159
168 4.597540094166000E+160
169 4.516198955490050E+161
170 4.436765386473450E+162
171 4.359183793847070E+163
172 4.283400517296400E+164
173 4.209363751503920E+165
174 4.137023471764070E+166
175 4.066331362987790E+167
176 3.997240751923770E+168
177 3.929706542433490E+169
178 3.863685153665920E+170
179 3.799134460986850E+171
180 3.736013739525220E+172
181 3.674283610206980E+173
182 3.613905988153730E+174
183 3.554844033330180E+175
184 3.497062103330920E+176
185 3.440525708202480E+177
186 3.385201467202790E+178
187 3.331057067404860E+179
188 3.278061224056740E+180
189 3.226183642614390E+181
190 3.175394982368410E+182
191 3.125666821589820E+183
192 3.076971624123720E+184
193 3.029282707363820E+185
194 2.982574211543560E+186
195 2.936821070283640E+187
196 2.891998982338110E+188
197 2.848084384484600E+189
198 2.805054425506790E+190
199 2.762886941219800E+191
200 2.721560430491820E+192
201 2.681054032217400E+193
202 2.641347503200100E+194
203 2.602421196904450E+195
204 2.564256043038760E+196
205 2.526833527932580E+197
206 2.490135675674070E+198
207 2.454145029974420E+199
208 2.418844636727880E+200
209 2.384218027237550E+201
210 2.350249202078480E+202
211 2.316922615570990E+203
212 2.284223160838240E+204
213 2.252136155423720E+205
214 2.220647327444790E+206
215 2.189742802260240E+207
216 2.159409089630270E+208
217 2.129633071348610E+209
218 2.100401989327410E+210
219 2.071703434116190E+211
220 2.043525333837210E+212
221 2.015855943520410E+213
222 1.988683834821650E+214
223 1.961997886108910E+215
224 1.935787272901620E+216
225 1.910041458649080E+217
226 1.884750185834570E+218
227 1.859903467392070E+219
228 1.835491578423500E+220
229 1.811505048204570E+221
230 1.787934652467980E+222
231 1.764771405953300E+223
232 1.742006555213010E+224
233 1.719631571665010E+225
234 1.697638144882120E+226
235 1.676018176109400E+227
236 1.654763772000720E+228
237 1.633867238566270E+229
238 1.613321075323030E+230
239 1.593117969640540E+231
240 1.573250791274770E+232
241 1.553712587082950E+233
242 1.534496575912730E+234
243 1.515596143659270E+235
244 1.497004838483860E+236
245 1.478716366188530E+237
246 1.460724585740510E+238
247 1.443023504941470E+239
248 1.425607276236120E+240
249 1.408470192655080E+241
250 1.391606683887390E+242
251 1.375011312477890E+243
252 1.358678770144980E+244
253 1.342603874214680E+245
254 1.326781564166620E+246
255 1.311206898288270E+247
256 1.295875050433390E+248
这是一般二生素数L12（P，P+12）的数量列表，第一列是范围值，以10为底，数字是次方数，比如最后一行数字表示10^256次方时，有1.295875050433390E+248这么多的二生素数（本楼中的二生素数，非它），一般k生素数是指在k个固定位置（相对固定），都是素数，在k生素数段中是否有或无其它素数不做限制。本二生素数，可能是相邻二生素数，也可能不是，在不是的二生素数中，中间可能夹着一个其它素数，也可能是2个，或许3个，再无其它情况。

白新岭 · 发表于 2020-9-13 18:36

一般二生素数L12(P,P+12的数量
2 4.000000000000000E+00
3 1.400000000000000E+01
4 5.600000000000000E+01
5 2.490000000000000E+02
6 1.327000000000000E+03
7 7.929000000000000E+03
8 5.125800000000000E+04
9 3.508790000000000E+05
10 2.508566000000000E+06
11 1.856019800000000E+07
12 1.411954010000000E+08
13 1.099185137000000E+09
14 8.724916754000000E+09
15 7.041523748000000E+10
16 5.765174710860000E+11
17 4.779808330774000E+12
18 4.006947565440500E+13
19 3.392221651310340E+14
20 2.897144967776390E+15
21 2.493952377539500E+16
22 2.162268981265960E+17
23 1.886912229082970E+18
24 1.656410785566260E+19
25 1.461987432698870E+20
26 1.296848588483030E+21
27 1.155680213334580E+22
28 1.034285009932210E+23
29 9.293178650504400E+23
30 8.380905816521650E+24
31 7.584261300870990E+25
32 6.885487235805270E+26
33 6.270001063526450E+27
34 5.725752253564470E+28
35 5.242723779665330E+29
36 4.812542708912990E+30
37 4.428173750257290E+31
38 4.083676394372050E+32
39 3.774011174194000E+33
40 3.494884144231800E+34
41 3.242621300591550E+35
42 3.014066609156470E+36
43 2.806498763427280E+37
44 2.617562888558620E+38
45 2.445214238710450E+39
46 2.287671569146360E+40
47 2.143378352086650E+41
48 2.010970382432980E+42
49 1.889248612875390E+43
50 1.777156287445840E+44
51 1.673759623154770E+45
52 1.578231432123550E+46
53 1.489837190076270E+47
54 1.407923147628510E+48
55 1.331906153451530E+49
56 1.261264916902170E+50
57 1.195532485037490E+51
58 1.134289747371430E+52
59 1.077159813069140E+53
60 1.023803130920230E+54
61 9.739132434955300E+54
62 9.272130842509130E+55
63 8.834517406965610E+56
64 8.424016186590960E+57
65 8.038559525744750E+58
66 7.676266150223480E+59
67 7.335421856383120E+60
68 7.014462453549270E+61
69 6.711958668174250E+62
70 6.426602759518540E+63
71 6.157196631601330E+64
72 5.902641255830810E+65
73 5.661927243954890E+66
74 5.434126432480190E+67
75 5.218384358083770E+68
76 5.013913519278160E+69
77 4.819987333094510E+70
78 4.635934707161980E+71
79 4.461135157569500E+72
80 4.295014411536840E+73
81 4.137040441398170E+74
82 3.986719882880550E+75
83 3.843594796286950E+76
84 3.707239734087860E+77
85 3.577259082691130E+78
86 3.453284649883210E+79
87 3.334973472690420E+80
88 3.222005823260380E+81
89 3.114083392864610E+82
90 3.010927636320720E+83
91 2.912278261065910E+84
92 2.817891846816980E+85
93 2.727540583255380E+86
94 2.641011114504210E+87
95 2.558103480339500E+88
96 2.478630145119790E+89
97 2.402415106342060E+90
98 2.329293075553190E+91
99 2.259108725076100E+92
100 2.191715994660740E+93
101 2.126977452749260E+94
102 2.064763707563180E+95
103 2.004952863682750E+96
104 1.947430020202760E+97
105 1.892086806920260E+98
106 1.838820955341920E+99
107 1.787535901597810E+100
108 1.738140418616350E+101
109 1.690548275156870E+102
110 1.644677919513440E+103
111 1.600452185899770E+104
112 1.557798021701720E+105
113 1.516646233943520E+106
114 1.476931253458420E+107
115 1.438590915384810E+108
116 1.401566254727480E+109
117 1.365801315830540E+110
118 1.331242974706060E+111
119 1.297840773250740E+112
120 1.265546764463150E+113
121 1.234315367847050E+114
122 1.204103234252970E+115
123 1.174869119470380E+116
124 1.146573765938410E+117
125 1.119179791993020E+118
126 1.092651588114840E+119
127 1.066955219683650E+120
128 1.042058335784160E+121
129 1.017930083642500E+122
130 9.945410283055460E+122
131 9.718630772042640E+123
132 9.498694092695080E+124
133 9.285344082935730E+125
134 9.078336002534770E+126
135 8.877435943329740E+127
136 8.682420273995440E+128
137 8.493075117103040E+129
138 8.309195856371360E+130
139 8.130586672163180E+131
140 7.957060103418080E+132
141 7.788436634341290E+133
142 7.624544304285420E+134
143 7.465218339371400E+135
144 7.310300804494970E+136
145 7.159640274458580E+137
146 7.013091523053960E+138
147 6.870515229000820E+139
148 6.731777697720330E+140
149 6.596750597990690E+141
150 6.465310712595050E+142
151 6.337339702131020E+143
152 6.212723881205280E+144
153 6.091354006287470E+145
154 5.973125074544400E+146
155 5.857936133019410E+147
156 5.745690097562120E+148
157 5.636293580951670E+149
158 5.529656729691590E+150
159 5.425693068987290E+151
160 5.324319355447330E+152
161 5.225455437078440E+153
162 5.129024120170320E+154
163 5.034951042691120E+155
164 4.943164553837680E+156
165 4.853595599405780E+157
166 4.766177612666040E+158
167 4.680846410449650E+159
168 4.597540094166000E+160
169 4.516198955490050E+161
170 4.436765386473450E+162
171 4.359183793847070E+163
172 4.283400517296400E+164
173 4.209363751503920E+165
174 4.137023471764070E+166
175 4.066331362987790E+167
176 3.997240751923770E+168
177 3.929706542433490E+169
178 3.863685153665920E+170
179 3.799134460986850E+171
180 3.736013739525220E+172
181 3.674283610206980E+173
182 3.613905988153730E+174
183 3.554844033330180E+175
184 3.497062103330920E+176
185 3.440525708202480E+177
186 3.385201467202790E+178
187 3.331057067404860E+179
188 3.278061224056740E+180
189 3.226183642614390E+181
190 3.175394982368410E+182
191 3.125666821589820E+183
192 3.076971624123720E+184
193 3.029282707363820E+185
194 2.982574211543560E+186
195 2.936821070283640E+187
196 2.891998982338110E+188
197 2.848084384484600E+189
198 2.805054425506790E+190
199 2.762886941219800E+191
200 2.721560430491820E+192
201 2.681054032217400E+193
202 2.641347503200100E+194
203 2.602421196904450E+195
204 2.564256043038760E+196
205 2.526833527932580E+197
206 2.490135675674070E+198
207 2.454145029974420E+199
208 2.418844636727880E+200
209 2.384218027237550E+201
210 2.350249202078480E+202
211 2.316922615570990E+203
212 2.284223160838240E+204
213 2.252136155423720E+205
214 2.220647327444790E+206
215 2.189742802260240E+207
216 2.159409089630270E+208
217 2.129633071348610E+209
218 2.100401989327410E+210
219 2.071703434116190E+211
220 2.043525333837210E+212
221 2.015855943520410E+213
222 1.988683834821650E+214
223 1.961997886108910E+215
224 1.935787272901620E+216
225 1.910041458649080E+217
226 1.884750185834570E+218
227 1.859903467392070E+219
228 1.835491578423500E+220
229 1.811505048204570E+221
230 1.787934652467980E+222
231 1.764771405953300E+223
232 1.742006555213010E+224
233 1.719631571665010E+225
234 1.697638144882120E+226
235 1.676018176109400E+227
236 1.654763772000720E+228
237 1.633867238566270E+229
238 1.613321075323030E+230
239 1.593117969640540E+231
240 1.573250791274770E+232
241 1.553712587082950E+233
242 1.534496575912730E+234
243 1.515596143659270E+235
244 1.497004838483860E+236
245 1.478716366188530E+237
246 1.460724585740510E+238
247 1.443023504941470E+239
248 1.425607276236120E+240
249 1.408470192655080E+241
250 1.391606683887390E+242
251 1.375011312477890E+243
252 1.358678770144980E+244
253 1.342603874214680E+245
254 1.326781564166620E+246
255 1.311206898288270E+247
256 1.295875050433390E+248
这是一般二生素数L12（P，P+12）的数量列表，第一列是范围值，以10为底，数字是次方数，比如最后一行数字表示10^256次方时，有1.295875050433390E+248这么多的二生素数（本楼中的二生素数，非它），一般k生素数是指在k个固定位置（相对固定），都是素数，在k生素数段中是否有或无其它素数不做限制。本二生素数，可能是相邻二生素数，也可能不是，在不是的二生素数中，中间可能夹着一个其它素数，也可能是2个，或许3个，再无其它情况。

白新岭 · 发表于 2020-9-13 18:43

要想求出相邻二生素数L12（P，P+12）的数量还有许多工作要做，虽然已经做了简单的素数式分析。

白新岭 · 发表于 2020-9-13 18:55

如果这样分析下去，不用说找出相邻二生素数L100（P，P+100）的理论公式，即便是相邻二生素数L50（P，P+50）也难说。

白新岭 · 发表于 2020-9-13 19:02

这种分析有点类似容斥原理，但实际上与它大相径庭。似是而非。不过有一点可以保证，它是相邻二生素数就不是相邻三生素数，相邻几生素数是不混淆的，但是在不同相邻k生素数之间还是非常难分（这里的k是同一个值）。

白新岭 · 发表于 2020-9-18 08:41

在分析哥德巴赫猜想问题时，我获得一种数学工具，可以一网打尽哥德巴赫猜想，孪生素数猜想，拉曼扭扬系数的猜测（或感应到的神秘化，宗教化，上帝万能化的种种说法）。可以说是一箭三雕。

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