转载几组有趣的大素数

yangchuanju

看看10个连续素数的跨度
转引自《百度贴吧  哥德巴赫猜想吧》
https://tieba.baidu.com/p/9372790386?pn=1

1楼  小月亮1379 发表于 2024-12-30 12:08
看看10个连续素数的跨度——标题是10个连续素数的跨度，实际给出的是20个445位连续大素数，此处仅给出第一个素数的全部数字，后19个已简化——
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000079

10^444+79
10^444+1263
10^444+3753
10^444+5007
10^444+5887
10^444+6001
10^444+7651
10^444+8869
10^444+14259
10^444+14961
10^444+15373
10^444+15411
10^444+17869
10^444+18529
10^444+19891
10^444+20673
10^444+22101
10^444+23259
10^444+24301
10^444+24711

小月亮1379——445位。最大间隔5000多，平均2000多。常见的间隔2、4、8啥的小间距的很少见了。大的某个具体数字间距也是同样稀少了。

yangchuanju

5楼2024-12-31 21:14   S云淡风清X
计算大数素数还是很费时间的。
26198: 10^908 + 54727123
26199: 10^908 + 54727369
26200: 10^908 + 54729723
26201: 10^908 + 54731607
26202: 10^908 + 54731673
26203: 10^908 + 54731931
26204: 10^908 + 54735303
26205: 10^908 + 54737623
26206: 10^908 + 54740659
26207: 10^908 + 54741051
26208: 10^908 + 54741817
26209: 10^908 + 54744567
26210: 10^908 + 54746091
26211: 10^908 + 54746611
26212: 10^908 + 54750207
26213: 10^908 + 54756787
26214: 10^908 + 54760869
26215: 10^908 + 54775953
26216: 10^908 + 54781897
26217: 10^908 + 54783639
26218: 10^908 + 54791227
26219: 10^908 + 54798373
26220: 10^908 + 54798691
26221: 10^908 + 54798951
26222: 10^908 + 54800901
26223: 10^908 + 54802317
26224: 10^908 + 54802917
26225: 10^908 + 54802981
26226: 10^908 + 54806023
26227: 10^908 + 54806293
26228: 10^908 + 54807057
26229: 10^908 + 54807837


7楼2025-01-01 10:28  S云淡风清X
新年好！善始善终，见仁见智。
47701: 10^908 + 99963033
47702: 10^908 + 99965341
47703: 10^908 + 99965697
47704: 10^908 + 99965781
47705: 10^908 + 99965893
47706: 10^908 + 99967459
47707: 10^908 + 99970773
47708: 10^908 + 99976363
47709: 10^908 + 99978913
47710: 10^908 + 99984549
47711: 10^908 + 99986253
47712: 10^908 + 99987297
47713: 10^908 + 99989919
47714: 10^908 + 99990639
47715: 10^908 + 99991531
47716: 10^908 + 99992077
47717: 10^908 + 99992929
47718: 10^908 + 99994749
47719: 10^908 + 99994887
47720: 10^908 + 99996091
47721: 10^908 + 99999939
47722: 10^908 + 100000599
47723: 10^908 + 100000903
47724: 10^908 + 100002567
47725: 10^908 + 100003821
47726: 10^908 + 100005361
47727: 10^908 + 100005783
47728: 10^908 + 100006117
47729: 10^908 + 100007127
47730: 10^908 + 100009129
47731: 10^908 + 100010787
47732: 10^908 + 100011859
47733: 10^908 + 100014667
47734: 10^908 + 100016379
47735: 10^908 + 100016613
47736: 10^908 + 100018309
47737: 10^908 + 100018711
47738: 10^908 + 100018941
47739: 10^908 + 100019541
47740: 10^908 + 100022217
47741: 10^908 + 100024641
47742: 10^908 + 100028043
47743: 10^908 + 100028229
47744: 10^908 + 100034301
47745: 10^908 + 100035523
47746: 10^908 + 100037121
47747: 10^908 + 100037581
47748: 10^908 + 100037899
47749: 10^908 + 100037973
47750: 10^908 + 100038373
47751: 10^908 + 100039953
47752: 10^908 + 100040469
47753: 10^908 + 100046883
47754: 10^908 + 100047873
47755: 10^908 + 100051051
47756: 10^908 + 100054383
47757: 10^908 + 100055607
47758: 10^908 + 100055671
47759: 10^908 + 100058401
47760: 10^908 + 100059177
47761: 10^908 + 100061721
47762: 10^908 + 100061781
47763: 10^908 + 100066939
47764: 10^908 + 100067691
47765: 10^908 + 100072057
47766: 10^908 + 100073299
47767: 10^908 + 100073403
47768: 10^908 + 100084743
47769: 10^908 + 100084851
47770: 10^908 + 100095523
47771: 10^908 + 100096173
47772: 10^908 + 100096867
47773: 10^908 + 100098813
47774: 10^908 + 100099981
47775: 10^908 + 100105569
47776: 10^908 + 100106013
47777: 10^908 + 100108287
47778: 10^908 + 100108899
47779: 10^908 + 100115907
47780: 10^908 + 100116237
47781: 10^908 + 100116537
47782: 10^908 + 100117623
47783: 10^908 + 100122691
47784: 10^908 + 100124047
47785: 10^908 + 100127203
47786: 10^908 + 100127407
47787: 10^908 + 100128057
47788: 10^908 + 100130197
47789: 10^908 + 100135017
47790: 10^908 + 100135519
47791: 10^908 + 100135879
47792: 10^908 + 100137529
47793: 10^908 + 100140159
47794: 10^908 + 100140951
47795: 10^908 + 100147251
47796: 10^908 + 100147977
47797: 10^908 + 100151191
47798: 10^908 + 100157073
47799: 10^908 + 100166613
47800: 10^908 + 100169419

yangchuanju

8楼2025-01-01 20:47  老白山黑水
10^909 + 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001113: 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000008019
这是10^909 +1000....1113与10^909 +1000....8019两个素数，其间隔为8019-1113=6806.
铁证如山，自己去思考吧！10080可不是凭空捏造的！

yangchuanju

素数越来越稀疏，而自然数中的很多区间反而是后面的素数数量
https://tieba.baidu.com/p/7266675992
1楼  小月亮1379  2021-03-18 23:17
素数越来越稀疏，而自然数中的很多区间反而是后面的素数数量多？素数真的是越来越稀疏吗？
1、在自然数77350000000-77400000000有素数1994702个；
2、在自然数77400000000-77450000000有素数1993993个；
3、在自然数77450000000-77500000000有素数1994087个；
4、在自然数77500000000-77550000000有素数1994310个；
第2区间比第一区间少，似乎素数越来越稀疏是正确的。而第3、4两个区间都比前一区间的素数数量多，似乎素数越来越稀疏又不正确了。

yangchuanju

9楼2025-07-10 17:49  S云淡风清X
区间长度至少以亿为单位，才能反映素数分布的情况。
由于对数函数的特性，相同长度内的素数个数在缓慢的减少，略有波动。
2025-07-10 17:43:29
在区间[77600000000, 77700000000]中有3988446个素数
在区间[77700000000, 77800000000]中有3985760个素数
在区间[77800000000, 77900000000]中有3987051个素数
在区间[77900000000, 78000000000]中有3985917个素数
在区间[78000000000, 78100000000]中有3987154个素数
在区间[78100000000, 78200000000]中有3986590个素数
在区间[78200000000, 78300000000]中有3987239个素数
在区间[78300000000, 78400000000]中有3987636个素数
在区间[78400000000, 78500000000]中有3986649个素数
在区间[78500000000, 78600000000]中有3985532个素数
在区间[78600000000, 78700000000]中有3987358个素数
在区间[78700000000, 78800000000]中有3985080个素数
在区间[78800000000, 78900000000]中有3985479个素数
在区间[78900000000, 79000000000]中有3986661个素数
在区间[79000000000, 79100000000]中有3986288个素数
在区间[79100000000, 79200000000]中有3983952个素数
在区间[79200000000, 79300000000]中有3983724个素数
在区间[79300000000, 79400000000]中有3985182个素数
在区间[79400000000, 79500000000]中有3983236个素数
在区间[79500000000, 79600000000]中有3984179个素数
在区间[79600000000, 79700000000]中有3983414个素数
在区间[79700000000, 79800000000]中有3983718个素数
在区间[79800000000, 79900000000]中有3983776个素数
在区间[79900000000, 80000000000]中有3982881个素数
用时 106.82859 秒

10楼2025-07-13 16:52  S云淡风清X
2025-07-13 16:45:56
在区间[7760000000000000, 7760000200000000]中有5464697个素数
在区间[7760000200000000, 7760000400000000]中有5465691个素数
在区间[7760000400000000, 7760000600000000]中有5467948个素数
在区间[7760000600000000, 7760000800000000]中有5466486个素数
在区间[7760000800000000, 7760001000000000]中有5467621个素数
在区间[7760001000000000, 7760001200000000]中有5464964个素数
在区间[7760001200000000, 7760001400000000]中有5468144个素数
在区间[7760001400000000, 7760001600000000]中有5465977个素数
在区间[7760001600000000, 7760001800000000]中有5467316个素数
在区间[7760001800000000, 7760002000000000]中有5465052个素数
在区间[7760002000000000, 7760002200000000]中有5467923个素数
在区间[7760002200000000, 7760002400000000]中有5466416个素数
在区间[7760002400000000, 7760002600000000]中有5463882个素数
在区间[7760002600000000, 7760002800000000]中有5470797个素数
在区间[7760002800000000, 7760003000000000]中有5466036个素数
在区间[7760003000000000, 7760003200000000]中有5468358个素数
在区间[7760003200000000, 7760003400000000]中有5466122个素数
在区间[7760003400000000, 7760003600000000]中有5466120个素数
在区间[7760003600000000, 7760003800000000]中有5468074个素数
在区间[7760003800000000, 7760004000000000]中有5463467个素数
在区间[7760004000000000, 7760004200000000]中有5467844个素数
在区间[7760004200000000, 7760004400000000]中有5464644个素数
在区间[7760004400000000, 7760004600000000]中有5466324个素数
在区间[7760004600000000, 7760004800000000]中有5467812个素数
在区间[7760004800000000, 7760005000000000]中有5466419个素数
用时 333.18103 秒

yangchuanju

445位最小的孪生素数对是10^444+815347，10^444+815349

重生888@

谁在验证这些数字？他们真的可靠吗？

白新岭

素数越来越希这个趋势是对的，但是特别区间，比开始时的素数都稠密的多。在30的跨度内可以出现9个素数，趋向无穷大时也会出现，永远不会消失。还有一个很重要的问题，越是大范围内，素数的增速，会越来越接近自然数的增长，增长的速度会越来越快，直至变化率接近1.

重生888@

白新岭 发表于 2025-8-30 23:03
素数越来越希这个趋势是对的，但是特别区间，比开始时的素数都稠密的多。在30的跨度内可以出现9个素数，趋 ...

有例子吗？

yangchuanju

素数越来越稀疏，而自然数中的很多区间反而是后面的素数数量
https://tieba.baidu.com/p/7266675992

15楼2025-08-26 11:23  S云淡风清X
素数分布，就是相邻素数间隔的变化，让大家看看一组数据。
2025-08-23 01:24:25
27010: 10^1957+6669, 10^1957+33679
【附注】各行第一个是相邻两素数的间距
用时 139.15373 秒

2025-08-23 01:35:32
10212: 10^920+10459, 10^920+20671
13398: 10^920+397039, 10^920+410437
10266: 10^920+498913, 10^920+509179
10306: 10^920+635181, 10^920+645487
10076: 10^920+807397, 10^920+817473
14508: 10^920+1002669, 10^920+1017177
10634: 10^920+1076629, 10^920+1087263
10876: 10^920+1133313, 10^920+1144189
11500: 10^920+1352271, 10^920+1363771
11762: 10^920+1599829, 10^920+1611591
14290: 10^920+1629141, 10^920+1643431
11044: 10^920+1817013, 10^920+1828057
10970: 10^920+2116219, 10^920+2127189
14646: 10^920+2319361, 10^920+2334007
13902: 10^920+2440687, 10^920+2454589
15738: 10^920+2500953, 10^920+2516691
10576: 10^920+2540721, 10^920+2551297
10496: 10^920+2829751, 10^920+2840247
10350: 10^920+2965353, 10^920+2975703
14138: 10^920+3191533, 10^920+3205671
13958: 10^920+3276703, 10^920+3290661
12708: 10^920+3762363, 10^920+3775071
13380: 10^920+5133793, 10^920+5147173
10004: 10^920+5355853, 10^920+5365857
10982: 10^920+6091789, 10^920+6102771
11304: 10^920+6384637, 10^920+6395941
12504: 10^920+6444739, 10^920+6457243
10668: 10^920+6606459, 10^920+6617127
13824: 10^920+7159383, 10^920+7173207
19698: 10^920+7228921, 10^920+7248619
11778: 10^920+7317019, 10^920+7328797
12842: 10^920+7673101, 10^920+7685943
13234: 10^920+8315247, 10^920+8328481
10452: 10^920+8500989, 10^920+8511441
19536: 10^920+8554801, 10^920+8574337
11642: 10^920+8673049, 10^920+8684691
12550: 10^920+8819133, 10^920+8831683
14330: 10^920+8975233, 10^920+8989563
10240: 10^920+9166353, 10^920+9176593
15980: 10^920+9548203, 10^920+9564183
10532: 10^920+9601777, 10^920+9612309
10248: 10^920+9651489, 10^920+9661737
11466: 10^920+9862647, 10^920+9874113
11382: 10^920+9925957, 10^920+9937339
10468: 10^920+10406103, 10^920+10416571
10320: 10^920+10492981, 10^920+10503301
11790: 10^920+10612057, 10^920+10623847
12210: 10^920+10825219, 10^920+10837429
13568: 10^920+10965529, 10^920+10979097
10462: 10^920+11114481, 10^920+11124943
11780: 10^920+11377789, 10^920+11389569
11418: 10^920+11709901, 10^920+11721319
14826: 10^920+11781753, 10^920+11796579
11430: 10^920+12024499, 10^920+12035929
17996: 10^920+12242947, 10^920+12260943
10092: 10^920+12358551, 10^920+12368643
10926: 10^920+12384001, 10^920+12394927
10366: 10^920+12669177, 10^920+12679543
17386: 10^920+12681897, 10^920+12699283
18430: 10^920+12943071, 10^920+12961501
12648: 10^920+12968551, 10^920+12981199
10158: 10^920+13185049, 10^920+13195207
11292: 10^920+13362079, 10^920+13373371
13764: 10^920+13579299, 10^920+13593063
11602: 10^920+13682721, 10^920+13694323
11730: 10^920+13889857, 10^920+13901587
11150: 10^920+14262223, 10^920+14273373
10704: 10^920+14540427, 10^920+14551131
18354: 10^920+15094869, 10^920+15113223
14610: 10^920+15479053, 10^920+15493663
10698: 10^920+15771693, 10^920+15782391
16798: 10^920+15869673, 10^920+15886471
10160: 10^920+16061557, 10^920+16071717
11382: 10^920+16360479, 10^920+16371861
11388: 10^920+16385799, 10^920+16397187
10012: 10^920+16769067, 10^920+16779079
24612: 10^920+16831419, 10^920+16856031
用时 10005.94764 秒

2025-08-23 05:17:27
11868: 10^981+74353, 10^981+86221
11648: 10^981+168601, 10^981+180249
14034: 10^981+564969, 10^981+579003
10928: 10^981+715189, 10^981+726117
12572: 10^981+831049, 10^981+843621
11324: 10^981+868597, 10^981+879921
10074: 10^981+953347, 10^981+963421
14122: 10^981+1074387, 10^981+1088509
11844: 10^981+1109287, 10^981+1121131
15518: 10^981+1321393, 10^981+1336911
10618: 10^981+1603311, 10^981+1613929
11204: 10^981+1613929, 10^981+1625133
10484: 10^981+1628269, 10^981+1638753
10194: 10^981+1681117, 10^981+1691311
10190: 10^981+1849567, 10^981+1859757
10404: 10^981+1988917, 10^981+1999321
14532: 10^981+2137527, 10^981+2152059
10488: 10^981+2223253, 10^981+2233741
17906: 10^981+2274751, 10^981+2292657
10620: 10^981+2452993, 10^981+2463613
10150: 10^981+2709951, 10^981+2720101
10672: 10^981+2889729, 10^981+2900401
16510: 10^981+2903493, 10^981+2920003
15796: 10^981+2929821, 10^981+2945617
12222: 10^981+3058689, 10^981+3070911
15006: 10^981+3533073, 10^981+3548079
11396: 10^981+3756703, 10^981+3768099
17120: 10^981+4000357, 10^981+4017477
12026: 10^981+4132933, 10^981+4144959
13986: 10^981+4159293, 10^981+4173279
12414: 10^981+4607407, 10^981+4619821
14418: 10^981+4772473, 10^981+4786891
10470: 10^981+4874119, 10^981+4884589
10228: 10^981+5255793, 10^981+5266021
13128: 10^981+5266083, 10^981+5279211
20048: 10^981+5333449, 10^981+5353497
用时 3814.17405 秒

2025-08-23 09:34:14
10950: 10^928+541869, 10^928+552819
10298: 10^928+998233, 10^928+1008531
12762: 10^928+1173151, 10^928+1185913
11880: 10^928+1397431, 10^928+1409311
10578: 10^928+1483909, 10^928+1494487
23002: 10^928+1603539, 10^928+1626541
用时 1031.17925 秒

2025-08-23 11:11:43
10250: 10^992+88741, 10^992+98991
13044: 10^992+123217, 10^992+136261
10062: 10^992+259221, 10^992+269283
10212: 10^992+382539, 10^992+392751
10974: 10^992+468099, 10^992+479073
10214: 10^992+595657, 10^992+605871
16698: 10^992+1100301, 10^992+1116999
10374: 10^992+1148769, 10^992+1159143
11812: 10^992+1164411, 10^992+1176223
11410: 10^992+1200669, 10^992+1212079
10294: 10^992+1551987, 10^992+1562281
10016: 10^992+1598857, 10^992+1608873
10342: 10^992+1614057, 10^992+1624399
11430: 10^992+1662339, 10^992+1673769
14246: 10^992+2104987, 10^992+2119233
10776: 10^992+2132367, 10^992+2143143
13300: 10^992+2197587, 10^992+2210887
13206: 10^992+2809593, 10^992+2822799
12470: 10^992+2827411, 10^992+2839881
11838: 10^992+3019681, 10^992+3031519
12000: 10^992+3145213, 10^992+3157213
10268: 10^992+3261853, 10^992+3272121
15966: 10^992+3588963, 10^992+3604929
15334: 10^992+3787737, 10^992+3803071
13248: 10^992+4000951, 10^992+4014199
13536: 10^992+4276201, 10^992+4289737
12264: 10^992+4407613, 10^992+4419877
11104: 10^992+4560369, 10^992+4571473
10570: 10^992+4732581, 10^992+4743151
13290: 10^992+4754283, 10^992+4767573
20678: 10^992+5064031, 10^992+5084709
用时 3737.61178 秒

老白山黑水: 祝贺你，不枉花费大量时间，终于找到5个超过20000的间隔，为你点赞！看来你的计算能力之强是我估计不到的，请再接再厉，距离任意大还很远！

老白山黑水: 10^1957+6669——10^992+5084709区间之大普通计算机难以企及！