[原创]k生素数群的数量公式

白新岭 · 发表于 2021-5-13 19:42

10的n次幂 12986/63倍最密四生素数的数量 5221/12倍最密五生素数的数量
2 1.9000000000000000E+02 0.0000000000000000E+00
3 7.5000000000000000E+02 4.8300000000000000E+02
4 2.4270000000000000E+03 1.5950000000000000E+03
5 8.3110000000000000E+03 4.4310000000000000E+03
6 3.5245000000000000E+04 1.5143000000000000E+04
7 1.7532600000000000E+05 6.2524000000000000E+04
8 9.7336100000000000E+05 2.9647900000000000E+05
9 5.8507570000000000E+06 1.5599780000000000E+06
10 3.7321898000000000E+07 8.8634730000000000E+06
11 2.4940216000000000E+08 5.3440374000000000E+07
12 1.7303471670000000E+09 3.3791591000000000E+08
13 1.2383171356000000E+10 2.2220652870000000E+09
14 9.0961962204000000E+10 1.5100054153000000E+10
15 6.8321853022300000E+11 1.0552733872600000E+11
16 5.2313898260650000E+12 7.5552861950100000E+11
17 4.0735328507577000E+13 5.5245335834510000E+12
18 3.2192344233147100E+14 4.1153095838136000E+13
19 2.5777418049116600E+15 3.1164672504106500E+14
20 2.0884574462723300E+16 2.3950435599752100E+15
21 1.7100049088143500E+17 1.8651302317494400E+16
22 1.4135623490409200E+18 1.4699333404398600E+17
23 1.1786894477886400E+19 1.1711243767185700E+18
24 9.9065274249944600E+19 9.4235009708831500E+18
25 8.3867442249341200E+20 7.6518168475661300E+19
26 7.1476337804624700E+21 6.2653124783138300E+20
27 6.1292104764644900E+22 5.1697142796147600E+21
28 5.2859312516023200E+23 4.2962258428269600E+22
29 4.5828536255027500E+24 3.5940356983198600E+23
30 3.9929065399791600E+25 3.0251956140854400E+24
31 3.4949270322683500E+26 2.5610697198218300E+25
32 3.0722311746953900E+27 2.1798402950459100E+26
33 2.7115624779181600E+28 1.8647343446724200E+27
34 2.4023101353564200E+29 1.6027482804644700E+28
35 2.1359223053028700E+30 1.3837210241830200E+29
36 1.9054618225354500E+31 1.1996536121295700E+30
37 1.7052669307207500E+32 1.0442050612817500E+31
38 1.5306901582563600E+33 9.1231553929731300E+31
39 1.3778958378830200E+34 7.9992234931659200E+32
40 1.2437019926018700E+35 7.0374418831516100E+33
41 1.1254560431821600E+36 6.2111605023219500E+34
42 1.0209364853793000E+37 5.4986199673856800E+35
43 9.2827464464070500E+37 4.8819645612594200E+36
44 8.4589205401771300E+38 4.3464716847215700E+37
45 7.7245006443308700E+39 3.8799466734158800E+38
46 7.0680908879895100E+40 3.4722447643152500E+39
47 6.4799547604647700E+41 3.1148914317553700E+40
48 5.9517446030793100E+42 2.8007792760813300E+41
49 5.4762797202880400E+43 2.5239248220267400E+42
50 5.0473635908061300E+44 2.2792724544891300E+43
51 4.6596326702597900E+45 2.0625356333131300E+44
52 4.3084308330494700E+46 1.8700677358940900E+45
53 3.9897047119502700E+47 1.6987565580829700E+46
54 3.6999161409850900E+48 1.5459377923367500E+47
55 3.4359686514572800E+49 1.4093237945750100E+48
56 3.1951455588794600E+50 1.2869447197057500E+49
57 2.9750576449176800E+51 1.1770997037909100E+50
58 2.7735988101151800E+52 1.0783162383850300E+51
59 2.5889083705677600E+53 9.8931624983474900E+51
60 2.4193389106964400E+54 9.0898768607145000E+52
61 2.2634287970380300E+55 8.3636064299903200E+53
62 2.1198786140750000E+56 7.7058724522023100E+54
63 1.9875309099905000E+57 7.1092464172896800E+55
64 1.8653527437053400E+58 6.5672059416785500E+56
65 1.7524206092328900E+59 6.0740122938728100E+57
66 1.6479073829167800E+60 5.6246060407473800E+58
67 1.5510709963895300E+61 5.2145179084553500E+59
68 1.4612445854132400E+62 4.8397924529729500E+60
69 1.3778279039823100E+63 4.4969225441374600E+61
70 1.3002798256660800E+64 4.1827930016266600E+62
71 1.2281117813387400E+65 3.8946319960017900E+63
72 1.1608820051528900E+66 3.6299690540884100E+64
73 1.0981904796419500E+67 3.3865986947075400E+65
74 1.0396744868250800E+68 3.1625488753920600E+66
75 9.8500468565360100E+68 2.9560535591021500E+67
76 9.3388164750758500E+69 2.7655288168222700E+68
77 8.8603279107289000E+70 2.5895519711133600E+69
78 8.4120966609061800E+71 2.4268433603173700E+70
79 7.9918554240951400E+72 2.2762503656961000E+71
80 7.5975326668329900E+73 2.1367333964002600E+72
81 7.2272335410214700E+74 2.0073535714963000E+73
82 6.8792228686562900E+75 1.8872618757154800E+74
83 6.5519099480624100E+76 1.7756895972737600E+75
84 6.2438349675223000E+77 1.6719398829818200E+76
85 5.9536568395482200E+78 1.5753802687016300E+77
86 5.6801422926412200E+79 1.4854360626534500E+78
87 5.4221560777579800E+80 1.4015844756703600E+79
88 5.1786521643385200E+81 1.3233494066832200E+80
89 4.9486658160317200E+82 1.2502968038690200E+81
90 4.7313064495248600E+83 1.1820305323204300E+82
91 4.5257511914236900E+84 1.1181886880563600E+83
92 4.3312390581818300E+85 1.0584403059096100E+84
93 4.1470656928482500E+86 1.0024824154840600E+85
94 3.9725786000645900E+87 9.5003740512449700E+85
95 3.8071728274502200E+88 9.0085065881904600E+86
96 3.6502870473894300E+89 8.5468843526802900E+87
97 3.5013999983933700E+90 8.1133596209796000E+88
98 3.3600272497423500E+91 7.7059572145554600E+89
99 3.2257182571034400E+92 7.3228590605177000E+90
100 3.0980536803343200E+93 6.9623902719864300E+91
101 2.9766429377870400E+94 6.6230065854024400E+92
102 2.8611219741661000E+95 6.3032830106786700E+93
103 2.7511512214212000E+96 6.0019035666251900E+94
104 2.6464137343026200E+97 5.7176519885786900E+95
105 2.5466134841128500E+98 5.4494033078979200E+96
106 2.4514737958795600E+99 5.1961162141783100E+97
107 2.3607359156788700E+100 4.9568261208913000E+98
108 2.2741576961763700E+101 4.7306388638368600E+99
109 2.1915123896457000E+102 4.5167249694605200E+100
110 2.1125875387883200E+103 4.3143144368557600E+101
111 2.0371839566276400E+104 4.1226919832607300E+102
112 1.9651147875998200E+105 3.9411927081612200E+103
113 1.8962046427231900E+106 3.7691981358124400E+104
114 1.8302888024085900E+107 3.6061326001649100E+105
115 1.7672124810830800E+108 3.4514599398867800E+106
116 1.7068301483470700E+109 3.3046804744718600E+107
117 1.6490049018766800E+110 3.1653282353588300E+108
118 1.5936078877257200E+111 3.0329684286033800E+109
119 1.5405177640794600E+112 2.9071951079796000E+110
120 1.4896202048714300E+113 2.7876290394720400E+111
121 1.4408074399975100E+114 2.6739157399833500E+112
122 1.3939778291537200E+115 2.5657236747504300E+113
123 1.3490354665876600E+116 2.4627425994554600E+114
124 1.3058898142918700E+117 2.3646820343574400E+115
125 1.2644553613830700E+118 2.2712698589714600E+116
126 1.2246513076066300E+119 2.1822510169017300E+117
127 1.1864012690823900E+120 2.0973863214049700E+118
128 1.1496330045687100E+121 2.0164513531327600E+119
129 1.1142781606673400E+122 1.9392354422879600E+120
130 1.0802720345238800E+123 1.8655407281379900E+121
131 1.0475533526992000E+124 1.7951812894667900E+122
132 1.0160640649966400E+125 1.7279823401236700E+123
133 9.8574915212933200E+125 1.6637794843483500E+124
134 9.5655644620315100E+126 1.6024180270222000E+125
135 9.2843646307332200E+127 1.5437523344220400E+126
136 9.0134224570850400E+128 1.4876452414384500E+127
137 8.7522921776510700E+129 1.4339675015704700E+128
138 8.5005504663763800E+130 1.3825972763255100E+129
139 8.2577951530858400E+131 1.3334196609409700E+130
140 8.0236440237403400E+132 1.2863262436056200E+131
141 7.7977336966960000E+133 1.2412146955962000E+132
142 7.5797185696537300E+134 1.1979883899606800E+133
143 7.3692698323927200E+135 1.1565560465762100E+134
144 7.1660745407531500E+136 1.1168314015889700E+135
145 6.9698347476748800E+137 1.0787328994060500E+136
146 6.7802666874128500E+138 1.0421834055584300E+137
147 6.5971000093375200E+139 1.0071099388898900E+138
148 6.4200770579944300E+140 9.7344342165058200E+138
149 6.2489521963400100E+141 9.4111844618724500E+139
150 6.0834911692959300E+142 9.1007305702574000E+140
151 5.9234705049704300E+143 8.8024854723609500E+141
152 5.7686769510859800E+144 8.5158926805712900E+142
153 5.6189069443282000E+145 8.2404245083706200E+143
154 5.4739661104928900E+146 7.9755804041930600E+144
155 5.3336687934580300E+147 7.7208853916938600E+145
156 5.1978376111453800E+148 7.4758886090016200E+146
157 5.0663030367643400E+149 7.2401619400872400E+147
158 4.9389030037487400E+150 7.0132987318999000E+148
159 4.8154825329062000E+151 6.7949125913947000E+149
160 4.6958933804011600E+152 6.5846362570129400E+150
161 4.5799937052860900E+153 6.3821205395776000E+151
162 4.4676477553820500E+154 6.1870333279360500E+152
163 4.3587255703902100E+155 5.9990586550223400E+153
164 4.2531027011905900E+156 5.8178958203252000E+154
165 4.1506599443531200E+157 5.6432585650368400E+155
166 4.0512830909505900E+158 5.4748742964245600E+156
167 3.9548626888225800E+159 5.3124833582132200E+157
168 3.8612938174945800E+160 5.1558383439939900E+158
169 3.7704758750084700E+161 5.0047034508846900E+159
170 3.6823123759678300E+162 4.8588538708611000E+160
171 3.5967107601464100E+163 4.7180752173581200E+161
172 3.5135822110494400E+164 4.5821629849056700E+162
173 3.4328414838559600E+165 4.4509220397177300E+163
174 3.3544067422063900E+166 4.3241661392952600E+164
175 3.2781994033328400E+167 4.2017174792356700E+165
176 3.2041439910611300E+168 4.0834062655633700E+166
177 3.1321679962424500E+169 3.9690703110094200E+167
178 3.0622017441996500E+170 3.8585546537732300E+168
179 2.9941782687987300E+171 3.7517111973968100E+169
180 2.9280331927795700E+172 3.6483983704724800E+170
181 2.8637046140021000E+173 3.5484808049892300E+171
182 2.8011329972849100E+174 3.4518290322007100E+172
183 2.7402610715322900E+175 3.3583191949707800E+173
184 2.6810337318640400E+176 3.2678327756197800E+174
185 2.6233979464792800E+177 3.1802563383577300E+175
186 2.5673026680010200E+178 3.0954812854490300E+176
187 2.5126987490633100E+179 3.0134036263075300E+177
188 2.4595388619166300E+180 2.9339237587719500E+178
189 2.4077774218400800E+181 2.8569462618583400E+179
190 2.3573705141610800E+182 2.7823796993307100E+180
191 2.3082758246948000E+183 2.7101364334718900E+181
192 2.2604525734262300E+184 2.6401324484750000E+182
193 2.2138614512677500E+185 2.5722871829114700E+183
194 2.1684645597345100E+186 2.5065233707654400E+184
195 2.1242253533889100E+187 2.4427668905547700E+185
196 2.0811085849136100E+188 2.3809466220888200E+186
197 2.0390802526802700E+189 2.3209943104396700E+187
198 1.9981075506888200E+190 2.2628444367293700E+188
199 1.9581588207586600E+191 2.2064340953593100E+189
200 1.9192035068598400E+192 2.1517028773302700E+190
201 1.8812121114782400E+193 2.0985927593222600E+191
202 1.8441561539147400E+194 2.0470479982231100E+192
203 1.8080081304234400E+195 1.9970150308126800E+193
204 1.7727414760993400E+196 1.9484423783268600E+194
205 1.7383305284305800E+197 1.9012805556416000E+195
206 1.7047504924348400E+198 1.8554819848319600E+196
207 1.6719774073037900E+199 1.8110009128757000E+197
208 1.6399881144833300E+200 1.7677933332835600E+198
209 1.6087602271215300E+201 1.7258169114514000E+199
210 1.5782721008191800E+202 1.6850309135405200E+200
211 1.5485028056217300E+203 1.6453961387036200E+201
212 1.5194320991942900E+204 1.6068748544841500E+202
213 1.4910404011243800E+205 1.5694307352262900E+203
214 1.4633087683000700E+206 1.5330288033419500E+204
215 1.4362188713137300E+207 1.4976353732897400E+205
216 1.4097529718440400E+208 1.4632179981287100E+206
217 1.3838939009715600E+209 1.4297454185173900E+207
218 1.3586250383851300E+210 1.3971875140354700E+208
219 1.3339302924386100E+211 1.3655152567125100E+209
220 1.3097940810196400E+212 1.3347006666538400E+210
221 1.2862013131936500E+213 1.3047167696602800E+211
222 1.2631373715885000E+214 1.2755375567433900E+212
223 1.2405880954867300E+215 1.2471379454434600E+213
224 1.2185397645937900E+216 1.2194937428623500E+214
225 1.1969790834525800E+217 1.1925816103279300E+215
226 1.1758931664756900E+218 1.1663790296112100E+216
227 1.1552695235682900E+219 1.1408642706214300E+217
228 1.1350960463158900E+220 1.1160163605084500E+218
229 1.1153609947124300E+221 1.0918150541049900E+219
230 1.0960529844053100E+222 1.0682408056454700E+220
231 1.0771609744350600E+223 1.0452747417006800E+221
232 1.0586742554484700E+224 1.0228986352713400E+222
233 1.0405824383649000E+225 1.0010948809859900E+223
234 1.0228754434765400E+226 9.7984647135176400E+223
235 1.0055434899642200E+227 9.5913697400905100E+224
236 9.8857708581122600E+227 9.3895050994353400E+225
237 9.7196701809842600E+228 9.1927173261152600E+226
238 9.5570434366475200E+229 9.0008580793661500E+227
239 9.3978038011780200E+230 8.8137839513782000E+228
240 9.2418669718005900E+231 8.6313562835134800E+229
241 9.0891510835685000E+232 8.4534409901001700E+230
242 8.9395766291281700E+233 8.2799083894608600E+231
243 8.7930663814425300E+234 8.1106330418497800E+232
244 8.6495453193523200E+235 7.9454935939893800E+233
245 8.5089405558600200E+236 7.7843726299120100E+234
246 8.3711812690261500E+237 7.6271565278262700E+235
247 8.2361986353727700E+238 7.4737353227417800E+236
248 8.1039257656933000E+239 7.3240025745982200E+237
249 7.9742976431727000E+240 7.1778552416573000E+238
250 7.8472510637257100E+241 7.0351935589273000E+239
251 7.7227245784653800E+242 6.8959209214012200E+240
252 7.6006584382175800E+243 6.7599437718994500E+241
253 7.4809945400010800E+244 6.6271714933183600E+242
254 7.3636763753959300E+245 6.4975163050948200E+243
255 7.2486489807266500E+246 6.3708931637061500E+244
256 7.1358588889894800E+247 6.2472196670330400E+245

白新岭 · 发表于 2021-5-13 19:51

本帖最后由白新岭于 2021-5-13 20:04 编辑

10的n次幂 \({25376}\over{35}\)倍最密六生素数的数量 \({4285}\over{12}\)倍最密七生素数的数量
2 0.0000000000000000E+00 0.0000000000000000E+00
3 1.1500000000000000E+02 0.0000000000000000E+00
4 5.2900000000000000E+02 8.2000000000000000E+01
5 1.2810000000000000E+03 1.9000000000000000E+02
6 3.6330000000000000E+03 4.6800000000000000E+02
7 1.2520000000000000E+04 1.3740000000000000E+03
8 5.0438000000000000E+04 4.6960000000000000E+03
9 2.3137400000000000E+05 1.8702000000000000E+04
10 1.1681950000000000E+06 8.3659000000000000E+04
11 6.3460650000000000E+06 4.0869800000000000E+05
12 3.6541113000000000E+07 2.1405980000000000E+06
13 2.2066683700000000E+08 1.1862995000000000E+07
14 1.3867002100000000E+09 6.8906329000000000E+07
15 9.0142800190000000E+09 4.1650811500000000E+08
16 6.0332436811000000E+10 2.6053647130000000E+09
17 4.1420224361200000E+11 1.6790499884000000E+10
18 2.9079454509150000E+12 1.1108075335500000E+11
19 2.0824382341447000E+13 7.5213876044700000E+11
20 1.5179192063265500E+14 5.1994494632590000E+12
21 1.1241804098568300E+15 3.6618533776978000E+13
22 8.4463310408874200E+15 2.6226905728531200E+14
23 6.4294123066252200E+16 1.9073176313094700E+15
24 4.9527670625584000E+17 1.4065192559314800E+16
25 3.8571221254305700E+18 1.0505240979612100E+17
26 3.0341422253666000E+19 7.9388397653394000E+17
27 2.4089526379747800E+20 6.0646258387047800E+18
28 1.9290386586643600E+21 4.6794694021600100E+19
29 1.5570654332344000E+22 3.6443698499362600E+20
30 1.2661548486319400E+23 2.8628708205639700E+21
31 1.0367299948769200E+24 2.2671643123866800E+22
32 8.5437630827330300E+24 1.8090025538466800E+23
33 7.0837225431936900E+25 1.4536663574964700E+24
34 5.9066725365182900E+26 1.1759068638926600E+25
35 4.9516235155073600E+27 9.5717989066523500E+25
36 4.1719837831439500E+28 7.8373845768444600E+26
37 3.5318798275263200E+29 6.4530231554260900E+27
38 3.0034852396130900E+30 5.3412006392246200E+28
39 2.5650639899041600E+31 4.4430138949381400E+29
40 2.1995246101204000E+32 3.7133712832577400E+30
41 1.8933431397840800E+33 3.1175123733517100E+31
42 1.6357545643988900E+34 2.6284628261464100E+32
43 1.4181413535235200E+35 2.2251582132340700E+33
44 1.2335678247496500E+36 1.8910504051045800E+34
45 1.0764232020988100E+37 1.6130648996663300E+35
46 9.4214626651234600E+37 1.3808153296784800E+36
47 8.2701166758346600E+38 1.1860078193371000E+37
48 7.2796313444479200E+39 1.0219864667630100E+38
49 6.4248257725365100E+40 8.8338443358072300E+38
50 5.6848681620220300E+41 7.6585456621099500E+39
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52 4.4831685083121000E+43 5.8051235152891500E+41
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255 3.0924316439067200E+242 8.1070893684787000E+239
256 3.0205346632839500E+243 7.8876190321375700E+240

白新岭 · 发表于 2021-5-13 20:17

10的n次幂 241/3倍最密八生素数的数量 6倍最密九生素数的数量
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105 1.2687997072137400E+90 1.3913629604564100E+87
106 1.1757611402918700E+91 1.2771194877690600E+88
107 1.0903277505493500E+92 1.1732040892932300E+89
108 1.0118150382798800E+93 1.0785989344536700E+90
109 9.3960566608264300E+93 9.9239464304792400E+90
110 8.7314233366065300E+94 9.1377787746073200E+91
111 8.1192146431959900E+95 8.4202045025951400E+92
112 7.5548760445348500E+96 7.7646975059705200E+93
113 7.0342845005450200E+97 7.1654031981274300E+94
114 6.5537042529404100E+98 6.6170642969240000E+95
115 6.1097474773997500E+99 6.1149553660973000E+96
116 5.6993392301503700E+100 5.6548250172755700E+97
117 5.3196861884341100E+101 5.2328448200262600E+98
118 4.9682487463143200E+102 4.8455640926788400E+99
119 4.6427160811492100E+103 4.4898698545933400E+100
120 4.3409838529233100E+104 4.1629513136367300E+101
121 4.0611342394537200E+105 3.8622683430236500E+102
122 3.8014180460922800E+106 3.5855234711939300E+103
123 3.5602386596325200E+107 3.3306369685832300E+104
124 3.3361376433047700E+108 3.0957246673112100E+105
125 3.1277817935240700E+109 2.8790781950853900E+106
126 2.9339514998897000E+110 2.6791473439552200E+107
127 2.7535302682073600E+111 2.4945243287687000E+108
128 2.5854952823478300E+112 2.3239297199820100E+109
129 2.4289088948556900E+113 2.1661998614521900E+110
130 2.2829109486265900E+114 2.0202756065164600E+111
131 2.1467118428971100E+115 1.8851922254736300E+112
132 2.0195862664222400E+116 1.7600703549103900E+113
133 1.9008675292152800E+117 1.6441078744877500E+114
134 1.7899424317320900E+118 1.5365726101005500E+115
135 1.6862466170198900E+119 1.4367957739905100E+116
136 1.5892603572245700E+120 1.3441660626397500E+117
137 1.4985047310549200E+121 1.2581243422801100E+118
138 1.4135381534148900E+122 1.1781588597801900E+119
139 1.3339532225097700E+123 1.1038009236541400E+120
140 1.2593738533683200E+124 1.0346210060918500E+121
141 1.1894526699558300E+125 9.7022522234222300E+121
142 1.1238686309289700E+126 9.1025214857923900E+122
143 1.0623248666451100E+127 8.5436994362202500E+123
144 1.0045467073210900E+128 8.0227374363353100E+124
145 9.5027988427283200E+128 7.5368330224621500E+125
146 8.9928888798475400E+129 7.0834085150945000E+126
147 8.5135546838187300E+130 6.6600916166709100E+127
148 8.0627726412948400E+131 6.2646978009432100E+128
149 7.6386654908452800E+132 5.8952143178510400E+129
150 7.2394908518628200E+133 5.5497856561556300E+130
151 6.8636307211664000E+134 5.2267003224095300E+131
152 6.5095818499542000E+135 4.9243788093795300E+132
153 6.1759469221540600E+136 4.6413626400019600E+133
154 5.8614264627564500E+137 4.3763043845139900E+134
155 5.5648114114906300E+138 4.1279585587291500E+135
156 5.2849763032983900E+139 3.8951733206506300E+136
157 5.0208730025450300E+140 3.6768828908644400E+137
158 4.7715249428473400E+141 3.4721006295361600E+138
159 4.5360218288510200E+142 3.2799127094439200E+139
160 4.3135147603059800E+143 3.0994723304036400E+140
161 4.1032117424121500E+144 2.9299944257533600E+141
162 3.9043735496817900E+145 2.7707508163297200E+142
163 3.7163099135217700E+146 2.6210657716492100E+143
164 3.5383760064144200E+147 2.4803119418526300E+144
165 3.3699691979950900E+148 2.3479066274291100E+145
166 3.2105260605162000E+149 2.2233083568474600E+146
167 3.0595196031721200E+150 2.1060137450239000E+147
168 2.9164567165588100E+151 1.9955546080792800E+148
169 2.7808758101744200E+152 1.8914953121139800E+149
170 2.6523446273478300E+153 1.7934303357814500E+150
171 2.5304582233278400E+154 1.7009820282939100E+151
172 2.4148370934874800E+155 1.6137985461670100E+152
173 2.3051254397091800E+156 1.5315519535227800E+153
174 2.2009895640276100E+157 1.4539364721375000E+154
175 2.1021163795265900E+158 1.3806668686586700E+155
176 2.0082120293244400E+159 1.3114769675354100E+156
177 1.9190006052457000E+160 1.2461182792214800E+157
178 1.8342229584726600E+161 1.1843587341301400E+158
179 1.7536355951053600E+162 1.1259815136538000E+159
180 1.6770096501377200E+163 1.0707839703189800E+160
181 1.6041299338865800E+164 1.0185766298338500E+161
182 1.5347940453936700E+165 9.6918226841030700E+161
183 1.4688115477621200E+166 9.2243505930969700E+162
184 1.4060032007932300E+167 8.7817978307755700E+163
185 1.3462002466585400E+168 8.3627109640213200E+164
186 1.2892437446809000E+169 7.9657285495889700E+165
187 1.2349839516075400E+170 7.5895748599256800E+166
188 1.1832797440426400E+171 7.2330540674292400E+167
189 1.1339980799666500E+172 6.8950448514413500E+168
190 1.0870134965084800E+173 6.5744953952239200E+169
191 1.0422076413558200E+174 6.2704187428589300E+170
192 9.9946883538949200E+174 5.9818884884711400E+171
193 9.5869166431294700E+175 5.7080347724190800E+172
194 9.1977659721705600E+176 5.4480405611528300E+173
195 8.8262963017681700E+177 5.2011381893139400E+174
196 8.4716195311966200E+178 4.9666061443706000E+175
197 8.1328963833719700E+179 4.7437660756526500E+176
198 7.8093334913355700E+180 #NUM!
199 7.5001806721544900E+181 #NUM!
200 7.2047283753193600E+182 #NUM!
201 6.9223052936702100E+183 #NUM!
202 6.6522761257556600E+184 #NUM!
203 6.3940394793388800E+185 #NUM!
204 6.1470259065083000E+186 #NUM!
205 5.9106960615393100E+187 #NUM!
206 5.6845389732879800E+188 #NUM!
207 5.4680704244847200E+189 #NUM!
208 5.2608314308383100E+190 2.9059124582842000E+187
209 5.0623868133618100E+191 2.7828897357720400E+188
210 4.8723238577959600E+192 2.6656267557722700E+189
211 4.6902510554344700E+193 2.5538282746680900E+190
212 4.5157969200528900E+194 2.4472154820772200E+191
213 4.3486088760107900E+195 2.3455250145415200E+192
214 4.1883522129370800E+196 2.2485080326741500E+193
215 4.0347091027245800E+197 2.1559293574101800E+194
216 3.8873776748521100E+198 2.0675666613233100E+195
217 3.7460711463241100E+199 1.9832097112647300E+196
218 3.6105170027690500E+200 1.9026596588498100E+197
219 3.4804562274720600E+201 1.8257283755687000E+198
220 3.3556425753334100E+202 1.7522378295270700E+199
221 3.2358418889463300E+203 1.6820195010368500E+200
222 3.1208314541744200E+204 1.6149138344737700E+201
223 3.0103993927827600E+205 1.5507697240010700E+202
224 2.9043440898384700E+206 1.4894440309273100E+203
225 2.8024736537464400E+207 1.4308011306227400E+204
226 2.7046054069261400E+208 1.3747124870628500E+205
227 2.6105654052648900E+209 1.3210562532023800E+206
228 2.5201879846043400E+210 1.2697168955064600E+207
229 2.4333153326296500E+211 1.2205848410812700E+208
230 2.3497970846352700E+212 1.1735561459529700E+209
231 2.2694899417397800E+213 1.1285321831426700E+210
232 2.1922573102126000E+214 1.0854193492771100E+211
233 2.1179689606607600E+215 1.0441287885599300E+212
234 2.0465007059031300E+216 1.0045761330074700E+213
235 1.9777340964330300E+217 9.6668125792666700E+213
236 1.9115561324395300E+218 9.3036805168072100E+214
237 1.8478589914218200E+219 8.9556419885191000E+215
238 1.7865397704911200E+220 8.6220097596961700E+216
239 1.7275002425108300E+221 8.3021305902675400E+217
240 1.6706466252778700E+222 7.9953834205865100E+218
241 1.6158893629973600E+223 7.7011776610600600E+219
242 1.5631429193482000E+224 7.4189515792769100E+220
243 1.5123255814804000E+225 7.1481707787034000E+221
244 1.4633592743245800E+226 6.8883267633999500E+222
245 1.4161693846318300E+227 6.6389355835675400E+223
246 1.3706845941969100E+228 6.3995365570667600E+224
247 1.3268367217509000E+229 6.1696910623618400E+225
248 1.2845605730397000E+230 5.9489813986313400E+226
249 1.2437937986339800E+231 5.7370097090570300E+227
250 1.2044767590427000E+232 5.5333969635539000E+228
251 1.1665523967279600E+233 5.3377819974392800E+229
252 1.1299661146423200E+234 5.1498206027582300E+230
253 1.0946656609320400E+235 4.9691846691870200E+231
254 1.0606010194704200E+236 4.7955613716276600E+232
255 1.0277243059051300E+237 4.6286524017853100E+233
256 9.9598966892139300E+237 4.4681732411869000E+234
所涉及数据全部给出（指计算跨度为30的二生相邻素数的数量有关数据），涉及到665种k生生素数的数量。

白新岭 · 发表于 2021-5-13 20:30

10的n次幂跨度为30的二生相邻素数的数量实际值实际-理论误差率
2 7.3000000000000000E+01
3 7.0000000000000000E+00
4 1.1000000000000000E+01 11 0 0.00%
5 1.4000000000000000E+02 146 6 4.11%
6 1.9170000000000000E+03 1914 -3 -0.16%
7 2.1703000000000000E+04 21741 38 0.17%
8 2.2296600000000000E+05 222847 -119 -0.05%
9 2.1780460000000000E+06
10 2.0709257000000000E+07
11 1.9402363700000000E+08
12 1.8033889570000000E+09
13 1.6694705852000000E+10
14 1.5429262686800000E+11
15 1.4256490896690000E+12
16 1.3181527166106000E+13
17 1.2202274352278700E+14
18 1.1313066148480200E+15
19 1.0506702477053400E+16
20 9.7755634904590200E+16
21 9.1122006703148700E+17
22 8.5096312681436800E+18
23 7.9614655497862100E+19
24 7.4619413550609700E+20
25 7.0059089677800400E+21
26 6.5887910548765600E+22
27 6.2065318088758000E+23
28 5.8555432121917300E+24
29 5.5326527028045300E+25
30 5.2350543990724200E+26
31 4.9602648173949100E+27
32 4.7060833249273400E+28
33 4.4705571935374300E+29
34 4.2519509310391000E+30
35 4.0487194837047900E+31
36 3.8594848835122100E+32
37 3.6830159266181200E+33
38 3.5182104995993900E+34
39 3.3640802073500200E+35
40 3.2197369956240400E+36
41 3.0843814990278400E+37
42 2.9572928802495800E+38
43 2.8378199578123100E+39
44 2.7253734475007600E+40
45 2.6194191669680000E+41
46 2.5194720741467000E+42
47 2.4250910283003000E+43
48 2.3358741781934100E+44
49 2.2514548952678100E+45
50 2.1714981811830500E+46
51 2.0956974888915500E+47
52 2.0237719048054400E+48
53 1.9554636467850800E+49
54 1.8905358388162800E+50
55 1.8287705284985300E+51
56 1.7699669179710300E+52
57 1.7139397827694900E+53
58 1.6605180564279100E+54
59 1.6095435614978100E+55
60 1.5608698701201000E+56
61 1.5143612794097300E+57
62 1.4698918887498800E+58
63 1.4273447676821400E+59
64 1.3866112044572100E+60
65 1.3475900265071700E+61
66 1.3101869851408100E+62
67 1.2743141976700100E+63
68 1.2398896409652700E+64
69 1.2068366911297200E+65
70 1.1750837045846500E+66
71 1.1445636363895300E+67
72 1.1152136920843100E+68
73 1.0869750097497300E+69
74 1.0597923693417200E+70
75 1.0336139266718400E+71
76 1.0083909696865200E+72
77 9.8407769494408000E+72
78 9.6063100240797100E+73
79 9.3801030686853900E+74
80 9.1617736447741600E+75
81 8.9509611303179700E+76
82 8.7473252478213600E+77
83 8.5505447065744700E+78
84 8.3603159491116300E+79
85 8.1763519928654900E+80
86 7.9983813588728800E+81
87 7.8261470801599500E+82
88 7.6594057831268200E+83
89 7.4979268358734700E+84
90 7.3414915579662000E+85
91 7.1898924866456300E+86
92 7.0429326949289300E+87
93 6.9004251574654700E+88
94 6.7621921603722800E+89
95 6.6280647516067000E+90
96 6.4978822287330300E+91
97 6.3714916612108100E+92
98 6.2487474445776900E+93
99 6.1295108841216600E+94
100 6.0136498058395400E+95
101 5.9010381926612600E+96
102 5.7915558440859400E+97
103 5.6850880575272300E+98
104 5.5815253298027500E+99
105 5.4807630773284800E+100
106 5.3827013736927600E+101
107 5.2872447033897700E+102
108 5.1943017305868600E+103
109 5.1037850818882700E+104
110 5.0156111421366400E+105
111 4.9296998623674100E+106
112 4.8459745790979100E+107
113 4.7643618441939000E+108
114 4.6847912646135500E+109
115 4.6071953513792900E+110
116 4.5315093771767100E+111
117 4.4576712420222800E+112
118 4.3856213464826300E+113
119 4.3153024719646900E+114
120 4.2466596676301400E+115
121 4.1796401435192200E+116
122 4.1141931694977300E+117
123 4.0502699796678600E+118
124 3.9878236819084100E+119
125 3.9268091722324800E+120
126 3.8671830536719300E+121
127 3.8089035594178300E+122
128 3.7519304799636600E+123
129 3.6962250940150500E+124
130 3.6417501029456400E+125
131 3.5884695685924400E+126
132 3.5363488541982900E+127
133 3.4853545683206000E+128
134 3.4354545115375900E+129
135 3.3866176257940500E+130
136 3.3388139462381000E+131
137 3.2920145554104400E+132
138 3.2461915396554300E+133
139 3.2013179476321100E+134
140 3.1573677508103100E+135
141 3.1143158058442100E+136
142 3.0721378187219400E+137
143 3.0308103105966000E+138
144 2.9903105852087000E+139
145 2.9506166978163400E+140
146 2.9117074255539300E+141
147 2.8735622391446100E+142
148 2.8361612758967800E+143
149 2.7994853139180800E+144
150 2.7635157474848600E+145
151 2.7282345635083100E+146
152 2.6936243190417900E+147
153 2.6596681197771700E+148
154 2.6263495994807200E+149
155 2.5936529003220800E+150
156 2.5615626540522200E+151
157 2.5300639639888300E+152
158 2.4991423877697500E+153
159 2.4687839208374200E+154
160 2.4389749806190000E+155
161 2.4097023913690500E+156
162 2.3809533696431500E+157
163 2.3527155103726900E+158
164 2.3249767735126300E+159
165 2.2977254712353700E+160
166 2.2709502556454000E+161
167 2.2446401069907300E+162
168 2.2187843223482400E+163
169 2.1933725047613000E+164
170 2.1683945528091700E+165
171 2.1438406505886900E+166
172 2.1197012580896900E+167
173 2.0959671019466100E+168
174 2.0726291665496000E+169
175 2.0496786854992500E+170
176 2.0271071333897900E+171
177 2.0049062179065600E+172
178 1.9830678722238300E+173
179 1.9615842476904400E+174
180 1.9404477067903300E+175
181 1.9196508163667600E+176
182 1.8991863410985000E+177
183 1.8790472372178200E+178
184 1.8592266464597000E+179
185 1.8397178902328500E+180
186 1.8205144640031300E+181
187 1.8016100318807000E+182
188 1.7829984214024600E+183
189 1.7646736185017000E+184
190 1.7466297626574600E+185
191 1.7288611422162200E+186
192 1.7113621898789300E+187
193 1.6941274783468000E+188
194 1.6771517161195500E+189
195 1.6604297434398700E+190
196 1.6439565283785700E+191
197 1.6277271630545600E+192
198 1.6117368599846700E+193
199 1.5959809485581000E+194
200 1.5804548716306300E+195
201 1.5651541822340300E+196
202 1.5500745403963100E+197
203 1.5352117100682900E+198
204 1.5205615561528800E+199
205 1.5061200416327000E+200
206 1.4918832247927600E+201
207 1.4778472565342300E+202
208 1.4640083777762900E+203
209 1.4503629169424500E+204
210 1.4369072875284100E+205
211 1.4236379857484200E+206
212 1.4105515882571200E+207
213 1.3976447499443900E+208
214 1.3849142018002500E+209
215 1.3723567488474100E+210
216 1.3599692681391700E+211
217 1.3477487068200000E+212
218 1.3356920802468600E+213
219 1.3237964701689800E+214
220 1.3120590229639900E+215
221 1.3004769479285000E+216
222 1.2890475156212000E+217
223 1.2777680562565500E+218
224 1.2666359581475000E+219
225 1.2556486661952600E+220
226 1.2448036804248000E+221
227 1.2340985545643200E+222
228 1.2235308946671700E+223
229 1.2130983577749200E+224
230 1.2027986506201000E+225
231 1.1926295283671700E+226
232 1.1825887933907100E+227
233 1.1726742940892200E+228
234 1.1628839237337100E+229
235 1.1532156193495900E+230
236 1.1436673606310900E+231
237 1.1342371688867900E+232
238 1.1249231060155700E+233
239 1.1157232735116900E+234
240 1.1066358114983500E+235
241 1.0976588977885300E+236
242 1.0887907469724000E+237
243 1.0800296095304300E+238
244 1.0713737709712600E+239
245 1.0628215509937300E+240
246 1.0543713026721300E+241
247 1.0460214116640100E+242
248 1.0377702954398800E+243
249 1.0296164025340600E+244
250 1.0215582118159400E+245
251 1.0135942317812000E+246
252 1.0057229998622600E+247
253 9.9794308175733800E+247
254 9.9025307077757700E+248
255 9.8265158721176900E+249
256 9.7513727770797300E+250
这楼是最终数据，而且与实际值做了比对，还有一组完全吻合，即在10^4时，实际与理论都是11组（理论解没有人为干预，都是用统一公式求得）。

白新岭 · 发表于 2021-5-13 20:33

10的n次幂 241/3倍最密八生素数的数量 6倍最密九生素数的数量
198 7.8093334913355700E+180 4.5319800110904000E+177
199 7.5001806721544900E+181 4.3306477662796800E+178
200 7.2047283753193600E+182 4.1392045317041400E+179
201 6.9223052936702100E+183 3.9571186250534300E+180
202 6.6522761257556600E+184 3.7838893965927500E+181
203 6.3940394793388800E+185 3.6190452764716900E+182
204 6.1470259065083000E+186 3.4621419537168800E+183
205 5.9106960615393100E+187 3.3127606774394100E+184
206 5.6845389732879800E+188 3.1705066715109000E+185
207 5.4680704244847200E+189 3.0350076546265100E+186
补充1783#的超范围的数值（#NUM！）。

蔡家雄 · 发表于 2021-5-13 20:48

目前为止，已经达到179页了，，，未来必超200页，，，，热度91. 继续升温，，，，，

白新岭 · 发表于 2021-5-13 20:53

二生相邻素数（P，P+30）的数量公式：
\(8\over 3\)*1.32032372118072*\(∫_1^n\)\(1\over{ln^2(n)}\)\(d_n\)-\({1207}\over {40}\)*2.85824917688516*\(∫_1^n\)\(1\over{ln^3(n)}\)\(d_n\)+\({12986}\over{63}\)*4.15118255134627*\(∫_1^n\)\(1\over{ln^4(n)}\)\(d_n\)-\({5221}\over{12}\)*10.1318018169296*\(∫_1^n\)\(1\over{ln^5(n)}\)\(d_n\)+\({25376}\over{35}\)*17.2986298980835*\(∫_1^n\)\(1\over{ln^6(n)}\)\(d_n\)-\({4285}\over{12}\)*53.9720251184226*\(∫_1^n\)\(1\over{ln^7(n)}\)\(d_n\)+\({241}\over 3\)*178.26229268981*\(∫_1^n\)\(1\over{ln^8(n)}\)\(d_n\)-6*630.065899972291*\(∫_1^n\)\(1\over{ln^9(n)}\)\(d_n\)

白新岭 · 发表于 2021-5-13 21:03

本帖最后由白新岭于 2021-5-13 21:04 编辑

yangchuanju 发表于 2021-5-11 11:05
跨距30的2-9生素数共665种：
2生 1
3生 14

从本楼（1750#）开始到1787楼给出跨度30的二生相邻素数（P，P+30）的数量公式截止，完成了一项重大工程，它涉及到665种k生素数（k值从2到9，跨度都是30）.重头戏是1787#，公式给出。

白新岭 · 发表于 2021-5-13 21:09

所以大跨度的二生相邻素数（P，P+2k）的数量公式的计算量是无法估量的，它比整数拆分要困难的多，不亲身操作你是不知道有多么的繁杂而艰难，深渊莫测。

白新岭 · 发表于 2021-5-13 21:15

截止2021年5月12日星期三四月初一22：28分，浏览量30802人次，回复2055，热度89°。
截止2021年5月13日星期四四月初二21：13分，浏览量31040人次，回复2073，热度91°。
浏览量 ↑238人次，回复 ↑ 18，热度↑2°。
晚安！

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[原创]k生素数群的数量公式

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