转载几组有趣的大素数

yangchuanju · 发表于 2025-8-31 10:56

计算确定长度为 L 的连续合数链位置
https://tieba.baidu.com/p/9819895080?pn=1

9楼2025-06-27 06:47 小月亮1379
100亿以内每一次最大两素数差分布情况
2 3 两素数差=1
3 5 两素数差=2
7 11 两素数差=4
23 29 两素数差=6
89 97 两素数差=8
113 127 两素数差=14
523 541 两素数差=18
887 907 两素数差=20
1129 1151 两素数差=22
1327 1361 两素数差=34
9551 9587 两素数差=36
15683 15727 两素数差=44
19609 19661 两素数差=52
31397 31469 两素数差=72
155921 156007 两素数差=86
360653 360749 两素数差=96
370261 370373 两素数差=112
492113 492227 两素数差=114
1349533 1349651 两素数差=118
1357201 1357333 两素数差=132
2010733 2010881 两素数差=148
4652353 4652507 两素数差=154
17051707 17051887 两素数差=180
20831323 20831533 两素数差=210
47326693 47326913 两素数差=220
122164747 122164969 两素数差=222
189695659 189695893 两素数差=234
191912783 191913031 两素数差=248
387096133 387096383 两素数差=250
436273009 436273291 两素数差=282
1294268491 1294268779 两素数差=288
1453168141 1453168433 两素数差=292
2300942549 2300942869 两素数差=320
3842610773 3842611109 两素数差=336
4302407359 4302407713 两素数差=354

yangchuanju · 发表于 2025-8-31 10:59

17楼2025-06-29 10:34 S云淡风清X
宁可相信人世间有鬼，也不相信某阿姨那张嘴。
2025-06-29 10:19:34
1146: [10^560-299, 10^560+847]
4386: [10^561-2597, 10^561+1789]
2048: [10^562-1841, 10^562+207]
1530: [10^563-399, 10^563+1131]
3960: [10^564-1269, 10^564+2691]
2240: [10^565-2069, 10^565+171]
1586: [10^566-977, 10^566+609]
4476: [10^567-1347, 10^567+3129]
1302: [10^568-801, 10^568+501]
3466: [10^569-2697, 10^569+769]
2086: [10^570-1419, 10^570+667]
2172: [10^571-303, 10^571+1869]
6270: [10^572-3309, 10^572+2961]
818: [10^573-269, 10^573+549]
4848: [10^574-4829, 10^574+19]
680: [10^575-497, 10^575+183]
3318: [10^576-201, 10^576+3117]
6342: [10^577-1551, 10^577+4791]
2982: [10^578-239, 10^578+2743]
3358: [10^579-477, 10^579+2881]
1656: [10^580-867, 10^580+789]
2432: [10^581-851, 10^581+1581]
2616: [10^582-2277, 10^582+339]
3734: [10^583-1457, 10^583+2277]
1906: [10^584-1077, 10^584+829]
5912: [10^585-1493, 10^585+4419]
5610: [10^586-561, 10^586+5049]
2198: [10^587-1631, 10^587+567]
2096: [10^588-1829, 10^588+267]
420: [10^589-323, 10^589+97]
1932: [10^590-1763, 10^590+169]
2588: [10^591-341, 10^591+2247]
1056: [10^592-117, 10^592+939]
2816: [10^593-1289, 10^593+1527]
800: [10^594-11, 10^594+789]
800: [10^595-503, 10^595+297]
5590: [10^596-4077, 10^596+1513]
5020: [10^597-381, 10^597+4639]
1404: [10^598-983, 10^598+421]
4500: [10^599-2339, 10^599+2161]
2334: [10^600-1791, 10^600+543]
2424: [10^601-981, 10^601+1443]
3014: [10^602-743, 10^602+2271]
930: [10^603-827, 10^603+103]
1850: [10^604-989, 10^604+861]
1850: [10^605-1571, 10^605+279]
2720: [10^606-899, 10^606+1821]
3840: [10^607-3159, 10^607+681]
1550: [10^608-983, 10^608+567]
4012: [10^609-3159, 10^609+853]
1936: [10^610-1833, 10^610+103]
3150: [10^611-2663, 10^611+487]
2008: [10^612-597, 10^612+1411]
610: [10^613-117, 10^613+493]
3790: [10^614-1161, 10^614+2629]
2746: [10^615-2427, 10^615+319]
3326: [10^616-449, 10^616+2877]
9060: [10^617-6453, 10^617+2607]
4514: [10^618-1661, 10^618+2853]
1862: [10^619-1241, 10^619+621]
2898: [10^620-2181, 10^620+717]
1450: [10^621-837, 10^621+613]
1088: [10^622-647, 10^622+441]
2482: [10^623-921, 10^623+1561]
600: [10^624-413, 10^624+187]
3232: [10^625-1029, 10^625+2203]
4966: [10^626-4113, 10^626+853]
4032: [10^627-1031, 10^627+3001]
4016: [10^628-1217, 10^628+2799]
628: [10^629-609, 10^629+19]
7156: [10^630-273, 10^630+6883]
2326: [10^631-1383, 10^631+943]
964: [10^632-927, 10^632+37]
272: [10^633-53, 10^633+219]
3670: [10^634-1323, 10^634+2347]
4730: [10^635-3851, 10^635+879]
3086: [10^636-347, 10^636+2739]
1196: [10^637-89, 10^637+1107]
2854: [10^638-531, 10^638+2323]
1286: [10^639-17, 10^639+1269]
2832: [10^640-849, 10^640+1983]
5592: [10^641-2589, 10^641+3003]
1054: [10^642-51, 10^642+1003]
1818: [10^643-77, 10^643+1741]
2810: [10^644-1901, 10^644+909]
3400: [10^645-3291, 10^645+109]
1122: [10^646-401, 10^646+721]
6762: [10^647-1133, 10^647+5629]
1074: [10^648-831, 10^648+243]
1652: [10^649-1043, 10^649+609]
2898: [10^650-899, 10^650+1999]
340: [10^651-93, 10^651+247]
9962: [10^652-3713, 10^652+6249]
3684: [10^653-1721, 10^653+1963]
2900: [10^654-1811, 10^654+1089]
1394: [10^655-551, 10^655+843]
4298: [10^656-1139, 10^656+3159]
2082: [10^657-291, 10^657+1791]
632: [10^658-581, 10^658+51]
3300: [10^659-2363, 10^659+937]
用时 117.57673 秒
【附注】各行第一个数字为间隙

25楼 S云淡风清X
2025-06-30 12:45:44
1 (23112): [10^3125 + 21481, 10^3125 + 44593]
2 (21658): [10^3125 + 122451, 10^3125 + 144109]
3 (24942): [10^3125 + 144109, 10^3125 + 169051]
4 (23218): [10^3125 + 174591, 10^3125 + 197809]
5 (25076): [10^3125 + 357517, 10^3125 + 382593]
6 (21750): [10^3125 + 394191, 10^3125 + 415941]
7 (25828): [10^3125 + 418113, 10^3125 + 443941]
8 (21388): [10^3125 + 466383, 10^3125 + 487771]
9 (24588): [10^3125 + 490101, 10^3125 + 514689]
10 (23076): [10^3125 + 518557, 10^3125 + 541633]
11 (37374): [10^3125 + 584517, 10^3125 + 621891]
12 (21360): [10^3125 + 711337, 10^3125 + 732697]
13 (23192): [10^3125 + 858049, 10^3125 + 881241]
14 (35106): [10^3125 + 929037, 10^3125 + 964143]
15 (29626): [10^3125 + 969891, 10^3125 + 999517]
16 (30410): [10^3125 + 1016119, 10^3125 + 1046529]
17 (23620): [10^3125 + 1105947, 10^3125 + 1129567]
18 (25934): [10^3125 + 1132867, 10^3125 + 1158801]
19 (23884): [10^3125 + 1181727, 10^3125 + 1205611]
20 (34092): [10^3125 + 1440321, 10^3125 + 1474413]
21 (21192): [10^3125 + 1537551, 10^3125 + 1558743]
22 (20772): [10^3125 + 1582119, 10^3125 + 1602891]
23 (22692): [10^3125 + 1777077, 10^3125 + 1799769]
24 (20952): [10^3125 + 1926537, 10^3125 + 1947489]
25 (23152): [10^3125 + 1947489, 10^3125 + 1970641]
26 (33412): [10^3125 + 2038281, 10^3125 + 2071693]
27 (40242): [10^3125 + 2230117, 10^3125 + 2270359]
28 (24720): [10^3125 + 2341951, 10^3125 + 2366671]
29 (28996): [10^3125 + 2425377, 10^3125 + 2454373]
30 (23124): [10^3125 + 2458599, 10^3125 + 2481723]
用时 33181.58728 秒

yangchuanju · 发表于 2025-8-31 11:00

22楼2025-06-30 15:58 H云淡风清Z
云端漫步，高处不胜寒。在2^5000后面寻找较大素数间隔。
2025-06-30 15:10:42
5490: [2^5000+3147, 2^5000+8637]
5014: [2^5000+8637, 2^5000+13651]
8312: [2^5000+15901, 2^5000+24213]
11528: [2^5000+32437, 2^5000+43965]
4692: [2^5000+43965, 2^5000+48657]
5340: [2^5000+48657, 2^5000+53997]
5084: [2^5000+60613, 2^5000+65697]
4230: [2^5000+84585, 2^5000+88815]
12056: [2^5000+95275, 2^5000+107331]
18066: [2^5000+107331, 2^5000+125397]
9638: [2^5000+133453, 2^5000+143091]
9142: [2^5000+151071, 2^5000+160213]
5868: [2^5000+163933, 2^5000+169801]
5712: [2^5000+169801, 2^5000+175513]
4234: [2^5000+177261, 2^5000+181495]
8486: [2^5000+181495, 2^5000+189981]
7438: [2^5000+191877, 2^5000+199315]
6636: [2^5000+201201, 2^5000+207837]
6168: [2^5000+207837, 2^5000+214005]
8562: [2^5000+214005, 2^5000+222567]
5786: [2^5000+225715, 2^5000+231501]
4242: [2^5000+236595, 2^5000+240837]
13920: [2^5000+247465, 2^5000+261385]
6366: [2^5000+261385, 2^5000+267751]
8900: [2^5000+267751, 2^5000+276651]
4784: [2^5000+278623, 2^5000+283407]
7568: [2^5000+290833, 2^5000+298401]
4172: [2^5000+302545, 2^5000+306717]
4742: [2^5000+309595, 2^5000+314337]
6630: [2^5000+316275, 2^5000+322905]
用时 2762.24599 秒

yangchuanju · 发表于 2025-8-31 11:01

16楼小月亮1379
看看这两个素数之间有多少合数。
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997661 ——599位
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002161——600位

yangchuanju · 发表于 2025-8-31 11:35

本帖最后由 yangchuanju 于 2025-8-31 11:42 编辑

A033874 A033873
最大的n位素数与10^n之差和最小的n+1位素数与10^n之差
最大的n位素数与10^n之差最小的n+1位素数与10^n之差
1 3 1 1 ——1位最大素数7与10的差是3，2位最小素数11与10的差是1
2 3 2 1 ——2位最大素数97与100的差是3，3位最小素数101与100的差是1
3 3 3 9 ——3位最大素数997与1000的差是3，4位最小素数1009与1000的差是9
4 27 4 7 ——4位最大素数9973与10的差是27，5位最小素数10007与10000的差是7
5 9 5 3
6 17 6 3
7 9 7 19
8 11 8 7
9 63 9 7
10 33 10 19
11 23 11 3
12 11 12 39
13 29 13 37
14 27 14 31
15 11 15 37
16 63 16 61
17 3 17 3
18 11 18 3
19 39 19 51
20 11 20 39
21 101 21 117
22 27 22 9
23 23 23 117
24 257 24 7
25 123 25 13
26 141 26 67
27 99 27 103
28 209 28 331
29 27 29 319
30 11 30 57
…………
990 3 990 1197
991 1061 991 547
992 671 992 421
993 6107 993 7443
994 4437 994 831
995 317 995 2013
996 2259 996 8823
997 2361 997 2437
998 173 998 837
999 6101 999 7
1000 1769 1000 453
…………

yangchuanju · 发表于 2025-9-5 13:28

本帖最后由 yangchuanju 于 2025-9-5 14:53 编辑

转载时空伴随者《管窥10^1500邻域的孪生素数》贴
http://www.mathchina.com/bbs/for ... ead&tid=2053569
1楼时空伴随者发表于 2022-9-3 09:30
1: 10^1500-93103162±1
2: 10^1500-89788630±1
3: 10^1500-87650062±1
4: 10^1500-84157378±1
5: 10^1500-80885260±1
6: 10^1500-69385168±1
7: 10^1500-63494182±1
8: 10^1500-57223912±1
9: 10^1500-53182420±1
10: 10^1500-49575928±1
11: 10^1500-47846278±1
12: 10^1500-46866868±1
13: 10^1500-35924158±1
14: 10^1500-30949582±1
15: 10^1500-6564268±1
16: 10^1500+1306208±1
17: 10^1500+27552188±1
18: 10^1500+30167708±1
19: 10^1500+43668698±1
20: 10^1500+47038832±1
用时 723359.2656624317 秒

7楼
又用了7天半时间，向前进了10组。
2022-09-03 12:13:16
21: 10^1500+55316972±1
22: 10^1500+58622348±1
23: 10^1500+67531472±1
24: 10^1500+85198472±1
25: 10^1500+92955998±1
26: 10^1500+100326038±1
27: 10^1500+157067210±1
28: 10^1500+169338698±1
29: 10^1500+183436772±1
30: 10^1500+209334170±1
用时 654179.7366158962 秒
总结：
30对孪生素数，用了半月有余，恰逢月半，天意乎？
跨度第1亿，有15对孪生素数；第2亿有10对，第3亿连5对都没达到！

8楼
2022/9/11 11:15:22
31: 10^1500+210287060±1
用时 3617.9761638641357 秒
32: 10^1500+228633332±1
用时 76773.85360074043 秒
33: 10^1500+236525132±1
用时 106222.47982764244 秒
34: 10^1500+253772732±1
用时 182391.8937664032 秒
35: 10^1500+254873378±1
用时 186468.98708724976 秒
36: 10^1500+254933480±1
用时 186696.52765655518 秒
------------------------------------
偷窥暂告结束，取义六六大顺！

重生888@ · 发表于 2025-9-5 16:12

距离任意大还很远！

不很远！因为K!-2， K可以任意大！找到比K大的间隔就行！

谁有这大精力玩？

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