数论小猜想

白新岭 · 发表于 2019-7-19 10:08

等比数列8生素数首项6公比10的最终系数=5072.67454173891

白新岭 · 发表于 2019-7-19 10:10

n(10的次幂）等比数列8生素数首项6公比10的数量
4 1.000000000000000000E+00
5 4.000000000000000000E+00
6 1.000000000000000000E+01
7 2.600000000000000000E+01
8 7.500000000000000000E+01
9 2.610000000000000000E+02
10 1.034000000000000000E+03
11 4.531000000000000000E+03
12 2.155500000000000000E+04
13 1.095300000000000000E+05
14 5.877140000000000000E+05
15 3.301968000000000000E+06
16 1.929820800000000000E+07
17 1.167213990000000000E+08
18 7.275340060000000000E+08
19 4.657225163000000000E+09
20 3.052967911000000000E+10
21 2.044482056590000000E+11
22 1.395761496482000000E+12
23 9.696899496619000000E+12
24 6.845081081720800000E+13
25 4.903024817961670000E+14
26 3.559398231527820000E+15
27 2.616154703447770000E+16
28 1.945015273678930000E+17
29 1.461495099195190000E+18
30 1.109087835865770000E+19
31 8.494554933301500000E+19
32 6.562381256019630000E+20
33 5.110849019677200000E+21
34 4.010713179890970000E+22
35 3.169949330868880000E+23
36 2.522360812678760000E+24
37 2.019869052180300000E+25
38 1.627236104648590000E+26
39 1.318412783501180000E+27
40 1.073985703021750000E+28
41 8.793752238679660000E+28
42 7.235517449379770000E+29
43 5.981132725201610000E+30
44 4.966171053053050000E+31
45 4.140918194174140000E+32
46 3.466782415046290000E+33
47 2.913634304021260000E+34
48 2.457822294347520000E+35
49 2.080682620060980000E+36
50 1.767413550221110000E+37
51 1.506219774752780000E+38
52 1.287658399126530000E+39
53 1.104136304419020000E+40
54 9.495218090409630000E+40
55 8.188431241241900000E+41
56 7.080530670246920000E+42
57 6.138446162202420000E+43
58 5.335056710518790000E+44
59 4.648041872241240000E+45
60 4.058969554469030000E+46
61 3.552568643926260000E+47
62 3.116146765750320000E+48
63 2.739122460786130000E+49
64 2.412647929352380000E+50
65 2.129303738330450000E+51
66 1.882850923134880000E+52
67 1.668029030801910000E+53
68 1.480391064838150000E+54
69 1.316168171558970000E+55
70 1.172158375792170000E+56
71 1.045634825219540000E+57
72 9.342699089166820000E+57
73 8.360723315375300000E+58
74 7.493347920241650000E+59
75 6.725903669909790000E+60
76 6.045760589840040000E+61
77 5.442022579949350000E+62
78 4.905270959710160000E+63
79 4.427348603629670000E+64
80 4.001177832055120000E+65
81 3.620606440706760000E+66
82 3.280277241839430000E+67
83 2.975517295653420000E+68
84 2.702243668366060000E+69
85 2.456883091745130000E+70
86 2.236303340661400000E+71
87 2.037754508565530000E+72
88 1.858818660356160000E+73
89 1.697366589650580000E+74
90 1.551520612489590000E+75
91 1.419622499683620000E+76
92 1.300205791563260000E+77
93 1.191971856894410000E+78
94 1.093769156280350000E+79
95 1.004575252864470000E+80
96 9.234811823266570000E+80
97 8.496778522906340000E+81
98 7.824441901890670000E+82
99 7.211367998973460000E+83
100 6.651809223093710000E+84
101 6.140625245345360000E+85
102 5.673213674104290000E+86
103 5.245449222699340000E+87
104 4.853630259726810000E+88
105 4.494431786081040000E+89
106 4.164864014172130000E+90
107 3.862235837109710000E+91
108 3.584122571769940000E+92
109 3.328337442083180000E+93
110 3.092906339642090000E+94
111 2.876045459572860000E+95
112 2.676141461998270000E+96
113 2.491733854590240000E+97
114 2.321499330707820000E+98
115 2.164237831332350000E+99
116 2.018860128199200000E+100
117 1.884376750825250000E+101
118 1.759888102088810000E+102
119 1.644575626100100000E+103
120 1.537693908701100000E+104
121 1.438563605395600000E+105
122 1.346565104121750000E+106
123 1.261132841291820000E+107
124 1.181750199149800000E+108
125 1.107944920921390000E+109
126 1.039284987610970000E+110
127 9.753749067726270000E+110
128 9.158523692651750000E+111
129 8.603852349955930000E+112
130 8.086688130494100000E+113
131 7.604234054767180000E+114
132 7.153920874141360000E+115
133 6.733386992337350000E+116
134 6.340460290693210000E+117
135 5.973141664217830000E+118
136 5.629590096260410000E+119
137 5.308109118054430000E+120
138 5.007134515736420000E+121
139 4.725223161943200000E+122
140 4.461042861971920000E+123
141 4.213363115938870000E+124
142 3.981046708561080000E+125
143 3.763042047258100000E+126
144 3.558376177357030000E+127
145 3.366148410396610000E+128
146 3.185524507964960000E+129
147 3.015731369257650000E+130
148 2.856052175686350000E+131
149 2.705821950470530000E+132
150 2.564423495265980000E+133
151 2.431283669577320000E+134
152 2.305869982014560000E+135
153 2.187687465426140000E+136
154 2.076275810611550000E+137
155 1.971206735716610000E+138
156 1.872081570572740000E+139
157 1.778529037184990000E+140
158 1.690203209323320000E+141
159 1.606781635748840000E+142
160 1.527963613029350000E+143
161 1.453468595182410000E+144
162 1.383034728543470000E+145
163 1.316417501304370000E+146
164 1.253388498115120000E+147
165 1.193734250998820000E+148
166 1.137255178605960000E+149
167 1.083764606537570000E+150
168 1.033087862103620000E+151
169 9.850614374618760000E+151
170 9.395322156064420000E+152
171 8.963567541522860000E+153
172 8.554006222945400000E+154
173 8.165377867152720000E+155
174 7.796500425682940000E+156
175 7.446264859985740000E+157
176 7.113630249495000000E+158
177 6.797619252817240000E+159
178 6.497313894737810000E+160
179 6.211851653995480000E+161
180 5.940421828828410000E+162
181 5.682262159167880000E+163
182 5.436655686068160000E+164
183 5.202927830525480000E+165
184 4.980443675269710000E+166
185 4.768605434421840000E+167
186 4.566850097108240000E+168
187 4.374647232220600000E+169
188 4.191496942515600000E+170
189 4.016927957170770000E+171
190 3.850495852757790000E+172
191 3.691781393370890000E+173
192 3.540388981359690000E+174
193 3.395945210770120000E+175
194 3.258097516197960000E+176
195 3.126512910311830000E+177
196 3.000876803810680000E+178
197 2.880891902048080000E+179
198 2.766277172985910000E+180
199 2.656766881536100000E+181
200 2.552109685714200000E+182
201 2.452067790364590000E+183
202 2.356416154527660000E+184
203 2.264941748804840000E+185
204 2.177442859341740000E+186
205 2.093728435292830000E+187
206 2.013617476856650000E+188
207 1.936938461177760000E+189
208 1.863528803604200000E+190
209 1.793234351966780000E+191
210 1.725908911710530000E+192
211 1.661413799860980000E+193
212 1.599617425948340000E+194
213 1.540394898143250000E+195
214 1.483627652978020000E+196
215 1.429203107139510000E+197
216 1.377014329923220000E+198
217 1.326959735034350000E+199
218 1.278942790510720000E+200
219 1.232871745625250000E+201
220 1.188659373702440000E+202
221 1.146222729854630000E+203
222 1.105482922710050000E+204
223 1.066364899266380000E+205
224 1.028797242060490000E+206
225 9.927119778985580000E+206
226 9.580443974399300000E+207
227 9.247328849745300000E+208
228 8.927187577760960000E+209
229 8.619461144537200000E+210
230 8.323616917611870000E+211
231 8.039147293583160000E+212
232 7.765568420507340000E+213
233 7.502418990646200000E+214
234 7.249259099410270000E+215
235 7.005669166605070000E+216
236 6.771248916332730000E+217
237 6.545616412128310000E+218
238 6.328407144123460000E+219
239 6.119273165228920000E+220
240 5.917882273512360000E+221
241 5.723917238122530000E+222
242 5.537075066271690000E+223
243 5.357066308941030000E+224
244 5.183614403114710000E+225
245 5.016455048481420000E+226
246 4.855335616665940000E+227
247 4.700014591169990000E+228
248 4.550261036309910000E+229
249 4.405854093540800000E+230
250 4.266582503652340000E+231
251 4.132244153410660000E+232
252 4.002645645304680000E+233
253 3.877601889133750000E+234
254 3.756935714247290000E+235
255 3.640477501316110000E+236
256 3.528064832580020000E+237

白新岭 · 发表于 2019-7-19 10:26

蔡家雄发表于 2019-7-18 14:47
素数差为等比10的8生素数是存在的，

p,p+6*1,p+6*11,p+6*111,p+6*1111,p+6*11111,p+6*111111,p+6*111111 ...

蔡家雄先生给出10^9内有223组，我的公式预测为261组，误差有点大。

蔡家雄 · 发表于 2019-7-19 20:29

素数差为等比4的8生素数是存在的，

p,p+6*1,p+6*5,p+6*21,p+6*85,p+6*341,p+6*1365,p+6*5461,

当 p<=10^9 时，就有871组解。

白新岭 · 发表于 2019-7-20 10:00

等比数列8生素数首项6公比4的最终系数(153#)=16906.7709342074

白新岭 · 发表于 2019-7-20 10:04

n(10的次幂）等比数列8生素数首项6公比4的数量
4 6.000000000000000000E+00
5 1.400000000000000000E+01
6 3.300000000000000000E+01
7 8.600000000000000000E+01
8 2.520000000000000000E+02
9 8.720000000000000000E+02
10 3.446000000000000000E+03
11 1.510200000000000000E+04
12 7.184200000000000000E+04
13 3.650540000000000000E+05
14 1.958801000000000000E+06
15 1.100516500000000000E+07
16 6.431920200000000000E+07
17 3.890219920000000000E+08
18 2.424805829000000000E+09
19 1.552211528400000000E+10
20 1.017526922280000000E+11
21 6.814075991970000000E+11
22 4.651948337244000000E+12
23 3.231889947056800000E+13
24 2.281404354300640000E+14
25 1.634134356539970000E+15
26 1.186315622437610000E+16
27 8.719409837099170000E+16
28 6.482562093240840000E+17
29 4.871032560880500000E+18
30 3.696490644651240000E+19
31 2.831159248709430000E+20
32 2.187183028707120000E+21
33 1.703400305775980000E+22
34 1.336734861605740000E+23
35 1.056515784110850000E+24
36 8.406803180943360000E+24
37 6.732043047768750000E+25
38 5.423432520812750000E+26
39 4.394151989049990000E+27
40 3.579498372741650000E+28
41 2.930879036851540000E+29
42 2.411533306554100000E+30
43 1.993458087642480000E+31
44 1.655180432397250000E+32
45 1.380131029305000000E+33
46 1.155447598454320000E+34
47 9.710882761906900000E+34
48 8.191702066751760000E+35
49 6.934729234984310000E+36
50 5.890631420118550000E+37
51 5.020095907747550000E+38
52 4.291650374257550000E+39
53 3.679987632826830000E+40
54 3.164671336668630000E+41
55 2.729130957783220000E+42
56 2.359877598089680000E+43
57 2.045889250382400000E+44
58 1.778126725528650000E+45
59 1.549150819355520000E+46
60 1.352818280015370000E+47
61 1.184039381921790000E+48
62 1.038583869956930000E+49
63 9.129250383443420000E+49
64 8.041139945175290000E+50
65 7.096779077209180000E+51
66 6.275373868119290000E+52
67 5.559391698271380000E+53
68 4.934011125753420000E+54
69 4.386670898033620000E+55
70 3.906699118003610000E+56
71 3.485007430568720000E+57
72 3.113838116521960000E+58
73 2.786554366424650000E+59
74 2.497465898421630000E+60
75 2.241683587958490000E+61
76 2.014997977387390000E+62
77 1.813777493922330000E+63
78 1.634882975512370000E+64
79 1.475595725125920000E+65
80 1.333556815383530000E+66
81 1.206715771577210000E+67
82 1.093287090905340000E+68
83 9.917133242918370000E+68
84 9.006336663935880000E+69
85 8.188571788408690000E+70
86 7.453399189888570000E+71
87 6.791653675588610000E+72
88 6.195276483891860000E+73
89 5.657171160198650000E+74
90 5.171079551669920000E+75
91 4.731474928602530000E+76
92 4.333469711966640000E+77
93 3.972735679909700000E+78
94 3.645434854528260000E+79
95 3.348159545148130000E+80
96 3.077880254918870000E+81
97 2.831900351253890000E+82
98 2.607816563724040000E+83
99 2.403484510542310000E+84
100 2.216988570970730000E+85
101 2.046615519320830000E+86
102 1.890831419593000000E+87
103 1.748261350604870000E+88
104 1.617671591688770000E+89
105 1.497953950356230000E+90
106 1.388111957121420000E+91
107 1.287248690106510000E+92
108 1.194556024094240000E+93
109 1.109305126162430000E+94
110 1.030838043620310000E+95
111 9.585602502441880000E+95
112 8.919340342704060000E+96
113 8.304726266575290000E+97
114 7.737349811276960000E+98
115 7.213211287341670000E+99
116 6.728680394301020000E+100
117 6.280459315457550000E+101
118 5.865549773996130000E+102
119 5.481223596285300000E+103
120 5.124996383549490000E+104
121 4.794603941291600000E+105
122 4.487981157880350000E+106
123 4.203243060418750000E+107
124 3.938667808092930000E+108
125 3.692681411276840000E+109
126 3.463843989264890000E+110
127 3.250837401077540000E+111
128 3.052454102724580000E+112
129 2.867587100957250000E+113
130 2.695220888185940000E+114
131 2.534423256138500000E+115
132 2.384337897205040000E+116
133 2.244177712449800000E+117
134 2.113218754133620000E+118
135 1.990794738427730000E+119
136 1.876292070934450000E+120
137 1.769145333774170000E+121
138 1.668833188444610000E+122
139 1.574874653491950000E+123
140 1.486825720326730000E+124
141 1.404276274333930000E+125
142 1.326847291822310000E+126
143 1.254188286382250000E+127
144 1.185974980915940000E+128
145 1.121907184008160000E+129
146 1.061706851451290000E+130
147 1.005116315655930000E+131
148 9.518966673923680000E+131
149 9.018262758421260000E+132
150 8.546994343125940000E+133
151 8.103251201984700000E+134
152 7.685258588780120000E+135
153 7.291366822228150000E+136
154 6.920041732898560000E+137
155 6.569855895644180000E+138
156 6.239480578419810000E+139
157 5.927678344847120000E+140
158 5.633296253714680000E+141
159 5.355259603858680000E+142
160 5.092566177611630000E+143
161 4.844280940284710000E+144
162 4.609531157014180000E+145
163 4.387501891793990000E+146
164 4.177431856674660000E+147
165 3.978609581965450000E+148
166 3.790369880863870000E+149
167 3.612090584280020000E+150
168 3.443189523747490000E+151
169 3.283121742239740000E+152
170 3.131376914459270000E+153
171 2.987476959755320000E+154
172 2.850973832268510000E+155
173 2.721447474212980000E+156
174 2.598503919399620000E+157
175 2.481773535190400000E+158
176 2.370909392062690000E+159
177 2.265585750863940000E+160
178 2.165496658658480000E+161
179 2.070354644817750000E+162
180 1.979889509689280000E+163
181 1.893847198804000000E+164
182 1.811988756152330000E+165
183 1.734089350580590000E+166
184 1.659937369836510000E+167
185 1.589333577228660000E+168
186 1.522090326264140000E+169
187 1.458030828994680000E+170
188 1.396988474136360000E+171
189 1.338806191335490000E+172
190 1.283335858234960000E+173
191 1.230437747253830000E+174
192 1.179980009230420000E+175
193 1.131838191297160000E+176
194 1.085894786555460000E+177
195 1.042038813303490000E+178
196 1.000165421738480000E+179
197 9.601755262115320000E+179
198 9.219754612557360000E+180
199 8.854766597409550000E+181
200 8.505953516298510000E+182
201 8.172522819220920000E+183
202 7.853724464768860000E+184
203 7.548848444994050000E+185
204 7.257222465645640000E+186
205 6.978209771328610000E+187
206 6.711207105879480000E+188
207 6.455642798948970000E+189
208 6.210974970421320000E+190
209 5.976689844892230000E+191
210 5.752300168974470000E+192
211 5.537343724707350000E+193
212 5.331381932814540000E+194
213 5.133998539989560000E+195
214 4.944798384789860000E+196
215 4.763406237093640000E+197
216 4.589465706418530000E+198
217 4.422638214722080000E+199
218 4.262602029600830000E+200
219 4.109051354080620000E+201
220 3.961695469446900000E+202
221 3.820257927801340000E+203
222 3.684475791251910000E+204
223 3.554098914848880000E+205
224 3.428889270569790000E+206
225 3.308620309833930000E+207
226 3.193076362191610000E+208
227 3.082052067987340000E+209
228 2.975351842938610000E+210
229 2.872789372705090000E+211
230 2.774187135646930000E+212
231 2.679375952086450000E+213
232 2.588194558494700000E+214
233 2.500489205124950000E+215
234 2.416113275708680000E+216
235 2.334926927916600000E+217
236 2.256796753368960000E+218
237 2.181595456055140000E+219
238 2.109201548093410000E+220
239 2.039499061828290000E+221
240 1.972377277324440000E+222
241 1.907730464374030000E+223
242 1.845457638188550000E+224
243 1.785462327996670000E+225
244 1.727652357816680000E+226
245 1.671939638716700000E+227
246 1.618239971916860000E+228
247 1.566472862126570000E+229
248 1.516561340546190000E+230
249 1.468431796996380000E+231
250 1.422013820670220000E+232
251 1.377240049033050000E+233
252 1.334046024422680000E+234
253 1.292370057929270000E+235
254 1.252153100158250000E+236
255 1.213338618502980000E+237
256 1.175872480575420000E+238

白新岭 · 发表于 2019-7-20 10:06

蔡家雄发表于 2019-7-19 12:29
素数差为等比4的8生素数是存在的，

p,p+6*1,p+6*5,p+6*21,p+6*85,p+6*341,p+6*1365,p+6*5461,

这回公式计算值与蔡家雄先生提供的实际数据高度吻合，先生提供的871组，公式计算值872组，差了1组。

蔡家雄 · 发表于 2019-7-20 17:48

本帖最后由蔡家雄于 2019-7-22 03:00 编辑

素数差为等比3的8生素数是存在的，(p,p+6*1,......),当 p<=10^9 时，有66组解。

素数差为等比4的8生素数是存在的，(p,p+6*1,......),当 p<=10^9 时，有871组解。

素数差为等比5的8生素数是存在的，(p,p+6*1,......),当 p<=10^9 时，有219组解。

素数差为等比7的8生素数是存在的，(p,p+6*1,......),当 p<=10^9 时，有120组解。

素数差为等比9的8生素数是存在的，(p,p+6*1,......),当 p<=10^9 时，有922组解。

素数差为等比10的8生素数是存在的，(p,p+6*1,......),当 p<=10^9 时，有223组解。

素数差为等比12的8生素数是存在的，(p,p+6*1,......),当 p<=10^9 时，有46组解。

白新岭 · 发表于 2019-7-20 18:12

一切素数差为等比的数列都存在，且公比可以是任意大于等于2的自然数，且可任意长。
有数列的性质，最少为4生素数，它可以形成3个素数差值，具备数列的最小项条件。首项是素数的连乘积（如2,6,30，......,∏P）。

白新岭 · 发表于 2019-7-20 18:41

等比数列8生素数首项6公比5的最终系数=4092.26389661153

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