白新岭
发表于 2019-7-18 19:38
素数式 素数式序列
0 0
6 6
12 18
24 42
48 90
96 186
192 378
384 762
768 1530
1536 3066
恭喜蔡家雄先生找到了新型素数差为等比数列的实际例子,在我发的帖子中:存在任意长的素数差为等比数列的k生素数中,我已经否认了,除公比为2或0.5以外的任何素数差为等比数列的k生素数,不过此例并没有推翻我的结论,只是首相变成6,公比仍然是2,这与我的结论不矛盾。
白新岭
发表于 2019-7-18 19:43
等比数列10生素数首先6公比2的最终系数=6785.80175128480
白新岭
发表于 2019-7-18 19:48
n(10的次幂) 等比数列10生素数首项6公比2的数量 取对数 对数比值
9 1.000000000000000000E+00 0 0.00%
10 3.000000000000000000E+00 0.477121255 4.77%
11 1.000000000000000000E+01 1 9.09%
12 4.200000000000000000E+01 1.62324929 13.53%
13 1.820000000000000000E+02 2.260071388 17.39%
14 8.310000000000000000E+02 2.919601024 20.85%
15 4.030000000000000000E+03 3.605305046 24.04%
16 2.054100000000000000E+04 4.312621583 26.95%
17 1.093440000000000000E+05 5.038794957 29.64%
18 6.046320000000000000E+05 5.781491128 32.12%
19 3.457720000000000000E+06 6.538789822 34.41%
20 2.037478000000000000E+07 7.309092928 36.55%
21 1.233265580000000000E+08 8.091056611 38.53%
22 7.647847300000000000E+08 8.883539208 40.38%
23 4.847987542000000000E+09 9.685561495 42.11%
24 3.135282810500000000E+10 10.49627672 43.73%
25 2.065129807900000000E+11 11.31494736 45.26%
26 1.383333276150000000E+12 12.14092682 46.70%
27 9.411199386369000000E+12 12.97364497 48.05%
28 6.495257404068400000E+13 13.81259637 49.33%
29 4.542874627857270000E+14 14.65733075 50.54%
30 3.216957003018850000E+15 15.50744526 51.69%
31 2.304506392115050000E+16 16.36257792 52.78%
32 1.668792302386630000E+17 17.22240229 53.82%
33 1.220739267358260000E+18 18.08662291 54.81%
34 9.015120037395220000E+18 18.95497151 55.75%
35 6.717438880290630000E+19 19.82720372 56.65%
36 5.047732494307620000E+20 20.70309633 57.51%
37 3.823357349571900000E+21 21.58244489 58.33%
38 2.917841325608870000E+22 22.46506167 59.12%
39 2.242713887245570000E+23 23.35077387 59.87%
40 1.735489870306980000E+24 24.23942208 60.60%
41 1.351633433813610000E+25 25.13085893 61.29%
42 1.059126593116500000E+26 26.02494787 61.96%
43 8.347611011738190000E+26 26.9215622 62.61%
44 6.615826169133000000E+27 27.82058409 63.23%
45 5.271130417968080000E+28 28.72190376 63.83%
46 4.221033751557130000E+29 29.62541882 64.40%
47 3.396515310208750000E+30 30.53103358 64.96%
48 2.745733939605480000E+31 31.43865845 65.50%
49 2.229510416313990000E+32 32.34820951 66.02%
50 1.818058906889470000E+33 33.25960795 66.52%
51 1.488605925328560000E+34 34.17277974 67.01%
52 1.223644351813800000E+35 35.08765521 67.48%
53 1.009645022349820000E+36 36.00416871 67.93%
54 8.361001931443140000E+36 36.92225832 68.37%
55 6.948092466279610000E+37 37.84186559 68.80%
56 5.793422969217330000E+38 38.76293524 69.22%
57 4.846352119104280000E+39 39.68541497 69.62%
58 4.066822646022580000E+40 40.60925523 70.02%
59 3.423017090574550000E+41 41.53440907 70.40%
60 2.889561141326890000E+42 42.46083189 70.77%
61 2.446140225251380000E+43 43.38848135 71.13%
62 2.076429503917260000E+44 44.31731719 71.48%
63 1.767262676285330000E+45 45.24730111 71.82%
64 1.507983576855590000E+46 46.17839661 72.15%
65 1.289938313156020000E+47 47.11056894 72.48%
66 1.106075916364400000E+48 48.04378494 72.79%
67 9.506331235051290000E+48 48.97801294 73.10%
68 8.188846491301280000E+49 49.91322273 73.40%
69 7.069446329724020000E+50 50.8493854 73.69%
70 6.116082288823940000E+51 51.78647332 73.98%
71 5.302247945549270000E+52 52.72446003 74.26%
72 4.605960467028030000E+53 53.66332021 74.53%
73 4.008940073618640000E+54 54.60302956 74.80%
74 3.495946917980610000E+55 55.54356483 75.06%
75 3.054243576749330000E+56 56.48490367 75.31%
76 2.673158092699540000E+57 57.42702464 75.56%
77 2.343727752335500000E+58 58.36990716 75.81%
78 2.058407881983170000E+59 59.31353144 76.04%
79 1.810833157017070000E+60 60.25787844 76.28%
80 1.595621443870320000E+61 61.20292986 76.50%
81 1.408212186037010000E+62 62.1486681 76.73%
82 1.244732920959220000E+63 63.09507618 76.95%
83 1.101888765104670000E+64 64.04213776 77.16%
84 9.768706997552320000E+64 64.98983708 77.37%
85 8.672792843981590000E+65 65.93815897 77.57%
86 7.710610604473090000E+66 66.88708877 77.78%
87 6.864554183506060000E+67 67.83661234 77.97%
88 6.119501118269050000E+68 68.78671602 78.17%
89 5.462439343345330000E+69 69.73738663 78.36%
90 4.882153409069440000E+70 70.68861142 78.54%
91 4.368960158374490000E+71 71.64037808 78.73%
92 3.914485633670100000E+72 72.5926747 78.91%
93 3.511476424780520000E+73 73.54548976 79.08%
94 3.153639844555320000E+74 74.49881209 79.25%
95 2.835508280992360000E+75 75.45263092 79.42%
96 2.552323864048920000E+76 76.40693578 79.59%
97 2.299940234225840000E+77 77.36171655 79.75%
98 2.074738734603360000E+78 78.31696342 79.92%
99 1.873556789334730000E+79 79.27266686 80.07%
100 1.693626596676700000E+80 80.22881767 80.23%
101 1.532522567226720000E+81 81.18540688 80.38%
102 1.388116189328050000E+82 82.14242582 80.53%
103 1.258537212689360000E+83 83.09986606 80.68%
104 1.142140215557910000E+84 84.05771942 80.82%
105 1.037475766340260000E+85 85.01597796 80.97%
106 9.432655123375300000E+85 85.97463396 81.11%
107 8.583806303179230000E+86 86.93367991 81.25%
108 7.818231593276790000E+87 87.89310853 81.38%
109 7.127098081916630000E+88 88.85291274 81.52%
110 6.502578908452400000E+89 89.81308563 81.65%
111 5.937730938434430000E+90 90.77362051 81.78%
112 5.426388236634750000E+91 91.73451086 81.91%
113 4.963069180388230000E+92 92.69575033 82.03%
114 4.542895366067060000E+93 93.65733273 82.16%
115 4.161520725046440000E+94 94.61925206 82.28%
116 3.815069489581240000E+95 95.58150245 82.40%
117 3.500081839787540000E+96 96.5440782 82.52%
118 3.213466225585920000E+97 97.50697374 82.63%
119 2.952457496352910000E+98 98.47018365 82.75%
120 2.714580089779950000E+99 99.43370266 82.86%
121 2.497615633113010000E+100 100.3975256 82.97%
122 2.299574397113190000E+101 101.3616475 83.08%
123 2.118670117905770000E+102 102.3260633 83.19%
124 1.953297766202510000E+103 103.2907685 83.30%
125 1.802013898735770000E+104 104.2557581 83.40%
126 1.663519274440560000E+105 105.2210278 83.51%
127 1.536643459072810000E+106 106.1865731 83.61%
128 1.420331177498160000E+107 107.1523896 83.71%
129 1.313630203626810000E+108 108.1184731 83.81%
130 1.215680604586210000E+109 109.0848195 83.91%
131 1.125705178794610000E+110 110.0514247 84.01%
132 1.043000947619570000E+111 111.0182847 84.10%
133 9.669315776988780000E+111 111.9853957 84.20%
134 8.969206261284410000E+112 112.952754 84.29%
135 8.324455138918610000E+113 113.9203558 84.39%
136 7.730321443851460000E+114 114.8881976 84.48%
137 7.182500939047920000E+115 115.8562757 84.57%
138 6.677083097140350000E+116 116.8245868 84.66%
139 6.210512589488560000E+117 117.7931274 84.74%
140 5.779554783171620000E+118 118.7618944 84.83%
141 5.381264804064870000E+119 119.7308844 84.92%
142 5.012959775555220000E+120 120.7000942 85.00%
143 4.672193887559460000E+121 121.6695209 85.08%
144 4.356735990140500000E+122 122.6391612 85.17%
145 4.064549440863920000E+123 123.6090124 85.25%
146 3.793773965706380000E+124 124.5790715 85.33%
147 3.542709320344750000E+125 125.5493355 85.41%
148 3.309800562474800000E+126 126.5198018 85.49%
149 3.093624766829170000E+127 127.4904676 85.56%
150 2.892879033130070000E+128 128.4613303 85.64%
151 2.706369653623690000E+129 129.4323871 85.72%
152 2.533002321363180000E+130 130.4036356 85.79%
153 2.371773273263430000E+131 131.3750732 85.87%
154 2.221761273343810000E+132 132.3466974 85.94%
155 2.082120351679740000E+133 133.3185058 86.01%
156 1.952073223552060000E+134 134.2904961 86.08%
157 1.830905321250310000E+135 135.2626659 86.15%
158 1.717959378068130000E+136 136.2350129 86.22%
159 1.612630510329620000E+137 137.2075349 86.29%
160 1.514361748895800000E+138 138.1802296 86.36%
161 1.422639976598020000E+139 139.153095 86.43%
162 1.336992232502500000E+140 140.1261289 86.50%
163 1.256982347886630000E+141 141.0993292 86.56%
164 1.182207882358780000E+142 142.0726939 86.63%
165 1.112297331726530000E+143 143.0462209 86.69%
166 1.046907582055600000E+144 144.0199083 86.76%
167 9.857215869005830000E+144 144.9937543 86.82%
168 9.284462469622510000E+145 145.9677568 86.89%
169 8.748104734631230000E+146 146.941914 86.95%
170 8.245634183594690000E+147 147.9162241 87.01%
171 7.774728561468160000E+148 148.8906852 87.07%
172 7.333237034872020000E+149 149.8652957 87.13%
173 6.919166642082670000E+150 150.8400538 87.19%
174 6.530669884124280000E+151 151.8149577 87.25%
175 6.166033355032540000E+152 152.7900059 87.31%
176 5.823667318980850000E+153 153.7651966 87.37%
177 5.502096150624260000E+154 154.7405282 87.42%
178 5.199949562823470000E+155 155.7159991 87.48%
179 4.915954552951870000E+156 156.6916079 87.54%
180 4.648928005340640000E+157 157.6673528 87.59%
181 4.397769893151100000E+158 158.6432325 87.65%
182 4.161457028143620000E+159 159.6192454 87.70%
183 3.939037311493770000E+160 160.5953901 87.76%
184 3.729624443040180000E+161 161.5716651 87.81%
185 3.532393050179120000E+162 162.548069 87.86%
186 3.346574201089100000E+163 163.5246005 87.92%
187 3.171451270109850000E+164 164.501258 87.97%
188 3.006356125947440000E+165 165.4780404 88.02%
189 2.850665615958850000E+166 166.4549463 88.07%
190 2.703798322111690000E+167 167.4319743 88.12%
191 2.565211566341030000E+168 168.4091232 88.17%
192 2.434398644956470000E+169 169.3863917 88.22%
193 2.310886273507110000E+170 170.3637786 88.27%
194 2.194232225107840000E+171 171.3412826 88.32%
195 2.084023146681060000E+172 172.3189025 88.37%
196 1.979872538888830000E+173 173.2966372 88.42%
197 1.881418886732820000E+174 174.2744855 88.46%
198 1.788323928894610000E+175 175.2524462 88.51%
199 1.700271054887420000E+176 176.2305182 88.56%
200 1.616963820000250000E+177 177.2087003 88.60%
201 1.538124568846180000E+178 178.1869915 88.65%
202 1.463493159083960000E+179 179.1653907 88.70%
203 1.392825777574430000E+180 180.1438968 88.74%
204 1.325893841865150000E+181 181.1225088 88.79%
205 1.262482980474510000E+182 182.1012255 88.83%
206 1.202392085974720000E+183 183.0800461 88.87%
207 1.145432435356320000E+184 184.0589695 88.92%
208 1.091426872599050000E+185 185.0379946 88.96%
209 1.040209048778800000E+186 186.0171206 89.00%
210 9.916227154109660000E+186 186.9963465 89.05%
211 9.455210670706520000E+187 187.9756712 89.09%
212 9.017661296413650000E+188 188.9550939 89.13%
213 8.602281908296050000E+189 189.9346137 89.17%
214 8.207852698448630000E+190 190.9142296 89.21%
215 7.833226233850760000E+191 191.8939407 89.25%
216 7.477322852884240000E+192 192.8737461 89.29%
217 7.139126374153410000E+193 193.8536451 89.33%
218 6.817680095110020000E+194 194.8336366 89.37%
219 6.512083059699930000E+195 195.8137199 89.41%
220 6.221486575825210000E+196 196.7938942 89.45%
221 5.945090964865600000E+197 197.7741585 89.49%
222 5.682142526838260000E+198 198.7545121 89.53%
223 5.431930706003810000E+199 199.7349542 89.57%
224 5.193785442859210000E+200 200.715484 89.61%
225 4.967074699500600000E+201 201.6961007 89.64%
226 4.751202146301630000E+202 202.6768035 89.68%
227 4.545604998738850000E+203 203.6575917 89.72%
228 4.349751994014160000E+204 204.6384645 89.75%
229 4.163141497878880000E+205 205.6194212 89.79%
230 3.985299732760830000E+206 206.600461 89.83%
231 3.815779118939440000E+207 207.5815832 89.86%
232 3.654156721107750000E+208 208.5627872 89.90%
233 3.500032793210110000E+209 209.5440721 89.93%
234 3.353029414951690000E+210 210.5254374 89.97%
235 3.212789213845260000E+211 211.5068822 90.00%
236 3.078974167095700000E+212 212.488406 90.04%
237 2.951264478023810000E+213 213.4700081 90.07%
238 2.829357522103480000E+214 214.4516878 90.11%
239 2.712966858030660000E+215 215.4334445 90.14%
240 2.601821299561510000E+216 216.4152775 90.17%
241 2.495664044152920000E+217 217.3971861 90.21%
242 2.394251854712430000E+218 218.3791698 90.24%
243 2.297354291018800000E+219 219.361228 90.27%
244 2.204752987610040000E+220 220.3433599 90.30%
245 2.116240975154210000E+221 221.3255651 90.34%
246 2.031622042521340000E+222 222.3078429 90.37%
247 1.950710136962990000E+223 223.2901927 90.40%
248 1.873328799981010000E+224 224.272614 90.43%
249 1.799310636629320000E+225 225.2551061 90.46%
250 1.728496816143570000E+226 226.2376686 90.50%
251 1.660736601933860000E+227 227.2203008 90.53%
252 1.595886909105990000E+228 228.2030021 90.56%
253 1.533811887798210000E+229 229.1857721 90.59%
254 1.474382530732990000E+230 230.1686102 90.62%
255 1.417476303488690000E+231 231.1515158 90.65%
256 1.362976796093320000E+232 232.1344885 90.68%
白新岭
发表于 2019-7-18 19:52
从公式给出的数量来看,在有效数字15位内仅有831组解,所以找到一组实例还是比较困难的。
不过对于蔡家雄先生来说不是难事,能给出上几千位的素数,对于此实例就是小菜一碟。
蔡家雄
发表于 2019-7-18 21:11
素数差为等比2的8生素数:
p,p+6*1,p+6*3,p+6*7,p+6*15,p+6*31,p+6*63,p+6*127,
1------p = 11
2------p = 3761
3------p = 361961
4------p = 1231691
5------p = 4874561
6------p = 4963481
7------p = 5561441
8------p = 6809611
9------p = 10179791
10------p = 14019451
11------p = 15257311
12------p = 16758121
13------p = 29467661
14------p = 38681411
15------p = 46477811
16------p = 49517071
17------p = 52683971
18------p = 54979931
19------p = 60033691
20------p = 69791321
21------p = 72124561
22------p = 79964891
23------p = 112573361
24------p = 129403181
25------p = 149024761
26------p = 168351941
27------p = 177300881
28------p = 182159581
29------p = 186551731
30------p = 191204071
31------p = 203438311
32------p = 211988611
33------p = 223321321
34------p = 223630721
35------p = 228341761
36------p = 243621601
37------p = 250231361
38------p = 279476251
39------p = 304278721
40------p = 311396161
41------p = 332047081
42------p = 367996661
43------p = 392428651
44------p = 452330071
45------p = 465739181
46------p = 472225991
47------p = 499657351
48------p = 521941331
49------p = 530338841
50------p = 548947501
51------p = 552722081
52------p = 608406061
53------p = 631455281
54------p = 642188381
55------p = 697511891
56------p = 711640661
57------p = 738109441
58------p = 789391111
59------p = 793842151
60------p = 825734531
61------p = 834861701
62------p = 874538851
63------p = 886804441
64------p = 900471791
65------p = 925363471
66------p = 930014231
67------p = 985960421
蔡家雄
发表于 2019-7-18 21:57
白新岭 发表于 2019-7-18 19:52
从公式给出的数量来看,在有效数字15位内仅有831组解,所以找到一组实例还是比较困难的。
不过对于蔡家雄 ...
素数差为等比3的8生素数是存在的,
p,p+6*1,p+6*4,p+6*13,p+6*40,p+6*121,p+6*364,p+6*1093,
1------p = 1543
2------p = 9103
3------p = 31643
4------p = 2110853
5------p = 8098933
6------p = 9742393
7------p = 13390583
8------p = 48809603
9------p = 53560433
10------p = 92371093
11------p = 101109053
12------p = 105744943
13------p = 117757223
14------p = 121637743
15------p = 138445513
16------p = 144649963
17------p = 161784983
18------p = 170415703
19------p = 174952333
20------p = 178264313
21------p = 183810553
22------p = 195245053
23------p = 200065883
24------p = 202367413
25------p = 245406913
26------p = 259388993
27------p = 269864983
28------p = 275901083
29------p = 276595133
30------p = 382095913
31------p = 390340583
32------p = 399291413
33------p = 410075053
34------p = 422332123
35------p = 423995183
36------p = 501574013
37------p = 518650513
38------p = 524097283
39------p = 544036853
40------p = 575187553
41------p = 589322023
42------p = 592610483
43------p = 596238163
44------p = 599821043
45------p = 624678533
46------p = 650661413
47------p = 672285533
48------p = 672574283
49------p = 676456553
50------p = 729148493
51------p = 745008743
52------p = 770894603
53------p = 781381373
54------p = 809115233
55------p = 824695763
56------p = 835468063
57------p = 856179523
58------p = 858686503
59------p = 863126743
60------p = 872520463
61------p = 919758143
62------p = 940356973
63------p = 947851033
64------p = 963870043
65------p = 967122523
66------p = 987584573
蔡家雄
发表于 2019-7-18 22:47
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*1111111,
当 p<=10^9 时,就有223组解。
白新岭
发表于 2019-7-19 09:42
等比数列8生素数首项6公比3的最终系数=1189.50527870379
白新岭
发表于 2019-7-19 09:46
n(10的次幂) 等比数列8生素数首项6公比3的数量 取对数 对数比值
5 1.000000000000000000E+00 0 0.00%
6 2.000000000000000000E+00 0.301029996 5.02%
7 6.000000000000000000E+00 0.77815125 11.12%
8 1.700000000000000000E+01 1.230448921 15.38%
9 6.100000000000000000E+01 1.785329835 19.84%
10 2.420000000000000000E+02 2.383815366 23.84%
11 1.062000000000000000E+03 3.026124517 27.51%
12 5.054000000000000000E+03 3.703635238 30.86%
13 2.568400000000000000E+04 4.409662661 33.92%
14 1.378140000000000000E+05 5.139293338 36.71%
15 7.742870000000000000E+05 5.888901968 39.26%
16 4.525289000000000000E+06 6.65564632 41.60%
17 2.737031800000000000E+07 7.437279843 43.75%
18 1.706014320000000000E+08 8.231982672 45.73%
19 1.092085421000000000E+09 9.038256609 47.57%
20 7.158987662000000000E+09 9.854851614 49.27%
21 4.794161696200000000E+10 10.68071268 50.86%
22 3.272959174130000000E+11 11.51494059 52.34%
23 2.273852391550000000E+12 12.35676227 53.73%
24 1.605121718901200000E+13 13.20550797 55.02%
25 1.149723652600390000E+14 14.06059347 56.24%
26 8.346529923364430000E+14 14.92150595 57.39%
27 6.134692466570310000E+15 15.7877928 58.47%
28 4.560919326015900000E+16 16.65905239 59.50%
29 3.427099690682010000E+17 17.53492674 60.47%
30 2.600730294154160000E+18 18.41509532 61.38%
31 1.991911337946330000E+19 19.29927 62.26%
32 1.538830666283250000E+20 20.18719083 63.08%
33 1.198456916078850000E+21 21.07862243 63.87%
34 9.404830646225040000E+21 21.97335098 64.63%
35 7.433300581904670000E+22 22.87118169 65.35%
36 5.914752615783710000E+23 23.77193659 66.03%
37 4.736445991339430000E+24 24.67545259 66.69%
38 3.815750291587540000E+25 25.58157995 67.32%
39 3.091582068948610000E+26 26.49018078 67.92%
40 2.518418346150870000E+27 27.40112787 68.50%
41 2.062070929537100000E+28 28.3143036 69.06%
42 1.696676206875330000E+29 29.22959897 69.59%
43 1.402532114117540000E+30 30.14691281 70.11%
44 1.164530985370010000E+31 31.06615105 70.60%
45 9.710151932913460000E+31 31.98722603 71.08%
46 8.129352571082590000E+32 32.91005596 71.54%
47 6.832260489666000000E+33 33.83456442 71.99%
48 5.763414485172210000E+34 34.76067985 72.42%
49 4.879049384117080000E+35 35.68833521 72.83%
50 4.144456204201770000E+36 36.61746755 73.23%
51 3.531975801353660000E+37 37.54801772 73.62%
52 3.019465274827640000E+38 38.47993004 74.00%
53 2.589119313112280000E+39 39.41315206 74.36%
54 2.226559568931890000E+40 40.34763432 74.72%
55 1.920127559064990000E+41 41.28333008 75.06%
56 1.660332934624980000E+42 42.22019518 75.39%
57 1.439420970712580000E+43 43.15818783 75.72%
58 1.251031988575150000E+44 44.09726841 76.03%
59 1.089932006710590000E+45 45.03739941 76.33%
60 9.517988334185110000E+45 45.97854517 76.63%
61 8.330515037259320000E+46 46.92067185 76.92%
62 7.307137480586530000E+47 47.86374728 77.20%
63 6.423042912199730000E+48 48.80774082 77.47%
64 5.657483885482310000E+49 49.75262333 77.74%
65 4.993062369500110000E+50 50.69836699 78.00%
66 4.415148446155750000E+51 51.64494531 78.25%
67 3.911406735922540000E+52 52.59233298 78.50%
68 3.471409355521650000E+53 53.54050583 78.74%
69 3.086318617229140000E+54 54.48944076 78.97%
70 2.748626122194860000E+55 55.43911567 79.20%
71 2.451937600098410000E+56 56.38950941 79.42%
72 2.190794972644830000E+57 57.34060174 79.64%
73 1.960528797105040000E+58 58.29237323 79.85%
74 1.757135576696390000E+59 59.24480527 80.06%
75 1.577175482791430000E+60 60.19788002 80.26%
76 1.417686878237770000E+61 61.15158032 80.46%
77 1.276114706829960000E+62 62.10588971 80.66%
78 1.150250356500780000E+63 63.06079238 80.85%
79 1.038181040661450000E+64 64.01627309 81.03%
80 9.382470949201910000E+64 64.97231723 81.22%
81 8.490058721278180000E+65 65.92891069 81.39%
82 7.692011507291260000E+66 66.88603993 81.57%
83 6.977371603345280000E+67 67.84369185 81.74%
84 6.336564826734270000E+68 68.80185388 81.91%
85 5.761212123392200000E+69 69.76051387 82.07%
86 5.243968653245740000E+70 70.71966009 82.23%
87 4.778386085479530000E+71 71.67928124 82.39%
88 4.358794538174350000E+72 72.6393664 82.54%
89 3.980201177252540000E+73 73.59990502 82.70%
90 3.638202970422480000E+74 74.56088692 82.85%
91 3.328911490863110000E+75 75.52230225 82.99%
92 3.048887997327650000E+76 76.48414147 83.13%
93 2.795087294041580000E+77 77.44639538 83.28%
94 2.564809104888620000E+78 78.40905505 83.41%
95 2.355655889817540000E+79 79.37211185 83.55%
96 2.165496193620600000E+80 80.33555742 83.68%
97 1.992432753533090000E+81 81.29938367 83.81%
98 1.834774706839280000E+82 82.26358274 83.94%
99 1.691013336431000000E+83 83.22814703 84.07%
100 1.559800874015500000E+84 84.19306916 84.19%
101 1.439931949857780000E+85 85.15834197 84.32%
102 1.330327336602250000E+86 86.12395852 84.44%
103 1.230019684534040000E+87 87.08991206 84.55%
104 1.138140988016620000E+88 88.05619606 84.67%
105 1.053911558947530000E+89 89.02280417 84.78%
106 9.766303138862380000E+89 89.9897302 84.90%
107 9.056662078435000000E+90 90.95696816 85.01%
108 8.404506702652130000E+91 91.92451223 85.12%
109 7.804709180708130000E+92 92.89235673 85.22%
110 7.252640371994990000E+93 93.86049614 85.33%
111 6.744117383847070000E+94 94.82892512 85.43%
112 6.275357051615200000E+95 95.79763844 85.53%
113 5.842934627034040000E+96 96.76663103 85.63%
114 5.443747052294920000E+97 97.73589794 85.73%
115 5.074980276297750000E+98 98.70543436 85.83%
116 4.734080137998260000E+99 99.67523561 85.93%
117 4.418726401092840000E+100 100.6452971 86.02%
118 4.126809575772670000E+101 101.6156144 86.11%
119 3.856410208022250000E+102 102.5861832 86.21%
120 3.605780355866480000E+103 103.5569993 86.30%
121 3.373327005880870000E+104 104.5280584 86.39%
122 3.157597212854230000E+105 105.4993567 86.47%
123 2.957264771315460000E+106 106.4708902 86.56%
124 2.771118250208230000E+107 107.4426551 86.65%
125 2.598050241751310000E+108 108.4146475 86.73%
126 2.437047692827290000E+109 109.386864 86.81%
127 2.287183202420740000E+110 110.359301 86.90%
128 2.147607181951890000E+111 111.3319548 86.98%
129 2.017540787064230000E+112 112.3048223 87.06%
130 1.896269539728160000E+113 113.2779001 87.14%
131 1.783137568597880000E+114 114.2511849 87.21%
132 1.677542403558830000E+115 115.2246735 87.29%
133 1.578930267463030000E+116 116.198363 87.37%
134 1.486791814285400000E+117 117.1722502 87.44%
135 1.400658268448070000E+118 118.1463322 87.52%
136 1.320097924938980000E+119 119.1206061 87.59%
137 1.244712974173390000E+120 120.0950692 87.66%
138 1.174136619379230000E+121 121.0697186 87.73%
139 1.108030457687920000E+122 122.0445517 87.80%
140 1.046082099132740000E+123 123.0195658 87.87%
141 9.880030004422650000E+123 123.9947583 87.94%
142 9.335264929053440000E+124 124.9701266 88.01%
143 8.824059857117110000E+125 125.9456684 88.07%
144 8.344133280683570000E+126 126.9213812 88.14%
145 7.893373150832090000E+127 127.8972626 88.21%
146 7.469823239173700000E+128 128.8733103 88.27%
147 7.071670680561490000E+129 129.849522 88.33%
148 6.697234587551050000E+130 130.8258955 88.40%
149 6.344955637965990000E+131 131.8024286 88.46%
150 6.013386546587370000E+132 132.7791191 88.52%
151 5.701183340646880000E+133 133.755965 88.58%
152 5.407097366571220000E+134 134.7329642 88.64%
153 5.129967962396510000E+135 135.7101147 88.70%
154 4.868715736532950000E+136 136.6874144 88.76%
155 4.622336399187940000E+137 137.6648615 88.82%
156 4.389895097817550000E+138 138.6424541 88.87%
157 4.170521212532380000E+139 139.6201903 88.93%
158 3.963403571487510000E+140 140.5980683 88.99%
159 3.767786049984530000E+141 141.5760862 89.04%
160 3.582963520349720000E+142 142.5542424 89.10%
161 3.408278122662670000E+143 143.532535 89.15%
162 3.243115829128600000E+144 144.5109625 89.20%
163 3.086903277344530000E+145 145.489523 89.26%
164 2.939104849930840000E+146 146.4682151 89.31%
165 2.799219980010480000E+147 147.447037 89.36%
166 2.666780663837500000E+148 148.4259873 89.41%
167 2.541349163525980000E+149 149.4050643 89.46%
168 2.422515884324440000E+150 150.3842666 89.51%
169 2.309897412237240000E+151 151.3635927 89.56%
170 2.203134699024130000E+152 152.3430411 89.61%
171 2.101891382726950000E+153 153.3226103 89.66%
172 2.005852232887510000E+154 154.3022989 89.71%
173 1.914721710543590000E+155 155.2821057 89.76%
174 1.828222633929730000E+156 156.2620291 89.81%
175 1.746094941573620000E+157 157.2420679 89.85%
176 1.668094545174700000E+158 158.2222207 89.90%
177 1.593992265285920000E+159 159.2024862 89.94%
178 1.523572843397270000E+160 160.1828632 89.99%
179 1.456634024547440000E+161 161.1633505 90.04%
180 1.392985705070750000E+162 162.1439467 90.08%
181 1.332449140526170000E+163 163.1246506 90.12%
182 1.274856209256470000E+164 164.1054612 90.17%
183 1.220048727392510000E+165 165.0863772 90.21%
184 1.167877811453170000E+166 166.0673974 90.25%
185 1.118203284998430000E+167 167.0485208 90.30%
186 1.070893126074080000E+168 168.0297461 90.34%
187 1.025822952443840000E+169 169.0110724 90.38%
188 9.828755418406880000E+169 169.9924985 90.42%
189 9.419403846850200000E+170 170.9740234 90.46%
190 9.029132669158690000E+171 171.955646 90.50%
191 8.656958807630760000E+172 172.9373654 90.54%
192 8.301954614554160000E+173 173.9191804 90.58%
193 7.963244480130140000E+174 174.90109 90.62%
194 7.640001664133270000E+175 175.8830935 90.66%
195 7.331445335494750000E+176 176.8651896 90.70%
196 7.036837805188500000E+177 177.8473775 90.74%
197 6.755481938895440000E+178 178.8296563 90.78%
198 6.486718736929950000E+179 179.8120251 90.81%
199 6.229925069841510000E+180 180.7944828 90.85%
200 5.984511558960480000E+181 181.7770287 90.89%
201 5.749920591945480000E+182 182.7596618 90.93%
202 5.525624464116870000E+183 183.7423814 90.96%
203 5.311123637031910000E+184 184.7251864 91.00%
204 5.105945106375760000E+185 185.7080761 91.03%
205 4.909640871813750000E+186 186.6910497 91.07%
206 4.721786501978340000E+187 187.6741063 91.10%
207 4.541979788250970000E+188 188.6572452 91.14%
208 4.369839481450110000E+189 189.6404655 91.17%
209 4.205004105952840000E+190 190.6237664 91.21%
210 4.047130846162730000E+191 191.6071472 91.24%
211 3.895894500593160000E+192 192.5906072 91.28%
212 3.750986499165100000E+193 193.5741455 91.31%
213 3.612113979623990000E+194 194.5577614 91.34%
214 3.478998919263020000E+195 195.5414543 91.37%
215 3.351377318402790000E+196 196.5252233 91.41%
216 3.228998432319970000E+197 197.5090678 91.44%
217 3.111624048543150000E+198 198.4929871 91.47%
218 2.999027806643290000E+199 199.4769805 91.50%
219 2.890994557839840000E+200 200.4610473 91.53%
220 2.787319761924070000E+201 201.4451868 91.57%
221 2.687808919168240000E+202 202.4293984 91.60%
222 2.592277035044560000E+203 203.4136814 91.63%
223 2.500548115722330000E+204 204.3980352 91.66%
224 2.412454692445840000E+205 205.3824592 91.69%
225 2.327837373020240000E+206 206.3669526 91.72%
226 2.246544418749040000E+207 207.351515 91.75%
227 2.168431345274350000E+208 208.3361457 91.78%
228 2.093360545872000000E+209 209.320844 91.81%
229 2.021200935846860000E+210 210.3056095 91.84%
230 1.951827616761200000E+211 211.2904415 91.87%
231 1.885121559309890000E+212 212.2753394 91.89%
232 1.820969303731920000E+213 213.2603026 91.92%
233 1.759262676718470000E+214 214.2453307 91.95%
234 1.699898523843400000E+215 215.230423 91.98%
235 1.642778456603380000E+216 216.215579 92.01%
236 1.587808613212160000E+217 217.2007982 92.03%
237 1.534899432347130000E+218 218.1860799 92.06%
238 1.483965439095790000E+219 219.1714238 92.09%
239 1.434925042396870000E+220 220.1568292 92.12%
240 1.387700343313860000E+221 221.1422957 92.14%
241 1.342216953519820000E+222 222.1278227 92.17%
242 1.298403823410190000E+223 223.1134098 92.20%
243 1.256193079295640000E+224 224.0990564 92.22%
244 1.215519869160830000E+225 225.0847621 92.25%
245 1.176322216505420000E+226 226.0705263 92.27%
246 1.138540881813170000E+227 227.0563486 92.30%
247 1.102119231222170000E+228 228.0422286 92.32%
248 1.067003111994520000E+229 229.0281657 92.35%
249 1.033140734408110000E+230 230.0141595 92.38%
250 1.000482559714930000E+231 231.0002095 92.40%
251 9.689811938319000000E+231 231.9863153 92.42%
252 9.385912864495600000E+232 232.9724765 92.45%
253 9.092694352623000000E+233 233.9586926 92.47%
254 8.809740950413910000E+234 234.9449631 92.50%
255 8.536654912880420000E+235 235.9312877 92.52%
256 8.273055382190020000E+236 236.9176659 92.55%
白新岭
发表于 2019-7-19 09:52
蔡家雄 发表于 2019-7-18 13:57
素数差为等比3的8生素数是存在的,
p,p+6*1,p+6*4,p+6*13,p+6*40,p+6*121,p+6*364,p+6*1093,
蔡家雄先生给出10^9内66组解,我的公式给出61组解,在小范围内误差有点大。