娱乐娱乐：分解大数152414752935769

yangchuanju · 发表于 2025-7-13 20:48

重生888@ 发表于 2025-7-13 17:27
10^20+7 与 10^20+9是一对孪生素数对！

100000000000000000007 = 67 * 166909 * 8942221889969
100000000000000000009 = 557 * 72937 * 2461483384901

重生888@ · 发表于 2025-7-14 07:28

10^20+21 与 10^20+19是一对孪生素数对！

yangchuanju · 发表于 2025-7-14 14:39

本帖最后由 yangchuanju 于 2025-7-15 13:08 编辑

重生888@ 发表于 2025-7-14 07:28
10^20+21 与 10^20+19是一对孪生素数对！

继续懵下去，总有懵对的时候！
1 11 is prime 13 is prime
2 101 is prime 103 is prime
3 1001=7*11*13 1003=17*59
4 10001=73*137 10003=7*1429
5 100001=11*9091 100003 is prime
6 1000001=101*9901 1000003 is prime
7 10000001=11*909091 10000003=13*769231
8 100000001=17*5882353 100000003=643*155521
9 1000000001=7*11*13*19*52579 1000000003=23*307*141623
10 10000000001=101*3541*27961 10000000003=7*1428571429
11 100000000001=11*11*23*4093*8779 100000000003 is prime
12 1000000000001=73*137*99990001 1000000000003=61*14221*1152763
13 10000000000001=11*859*1058313049 10000000000003=13*29*547*48492137
14 100000000000001=29*101*281*121499449 100000000000003=19*31*613*276964579
15 1000000000000001=7*11*13*211*241*2161*9091 1000000000000003=14902357*67103479
16 10000000000000001=353*449*641*1409*69857 10000000000000003=7*1428571428571429
17 100000000000000001=11*103*4013*21993833369 100000000000000003 is prime
18 1000000000000000001=101*9901*999999000001 1000000000000000003 is prime
19 10000000000000000001=11*909090909090909091 10000000000000000003=13*17*43*18679*56335953419
20 100000000000000000001=73*137*1676321*5964848081 100000000000000000003=373*155773*1721071782307
21 1000000000000000000001=7*7*11*13*127*2689*459691*909091 1000000000000000000003=67*14925373134328358209
22 10000000000000000000001=89*101*1052788969*1056689261 10000000000000000000003=7*157*601*1031137*14682887281
23 100000000000000000000001=11*47*139*2531*549797184491917 100000000000000000000003=113*3049*290244589115247419
24 1000000000000000000000001=17*5882353*9999999900000001 1000000000000000000000003=3529*821461*838069*411605923
25 10000000000000000000000001=11*251*5051*9091*78875943472201 10000000000000000000000003=13*7668629*100308773475776339
26 100000000000000000000000001=101*521*1900381976777332243781 100000000000000000000000003=223*161377320703*2778770221987
27 1000000000000000000000000001=7*11*13*19*52579*70541929*14175966169 1000000000000000000000000003=813219713*1229679979486675331
28 10000000000000000000000000001=73*137*7841*127522001020150503761 10000000000000000000000000003=7*199*571*89779*140035456540965619
29 100000000000000000000000000001=11*59*154083204930662557781201849 100000000000000000000000000003=31*10928153*295183134022089846821
30 1000000000000000000000000000001=61*101*3541*9901*27961*4188901*39526741 1000000000000000000000000000003=1859827*537684419034673655130289

1 17 is prime 19 is prime
2 107 is prime 109 is prime
3 1007=19*53 1009 is prime
4 10007 is prime 10009 is prime
5 100007=97*1031 100009=7*7*13*157
6 1000007=29*34483 1000009=293*3413
7 10000007=941*10627 10000009=23*434783
8 100000007 is prime 100000009=149*671141
9 1000000007 is prime 1000000009 is prime
10 10000000007=23*2293*189613 10000000009=33889*295081
11 100000000007=353*283286119 100000000009=7*13*53*1979*10477
12 1000000000007=34519*28969553 1000000000009=29*66413*519217
13 10000000000007=167*619*6959*13901 10000000000009=47*69761*3049927
14 100000000000007=43*1103*2083*1012201 100000000000009=17*541*1249*8705453
15 1000000000000007=47*59*360620266859 1000000000000009=179*367*47207*322459
16 10000000000000007=53*113*277*1117*5396507 10000000000000009=197*11717*4332288241
17 100000000000000007=17*9920467*592951213 100000000000000009=7*13*13*84530853761623
18 1000000000000000007=1370531*729644203597 1000000000000000009 is prime
19 10000000000000000007=191*786407*66576239711 10000000000000000009=19*318007*1655044667173
20 100000000000000000007=67*166909*8942221889969 100000000000000000009=557*72937*2461483384901
21 1000000000000000000007=19*223*236016049091338211 1000000000000000000009=89*103*727*11971*12343*1015517
22 10000000000000000000007=947*1429*7389546599589289 10000000000000000000009 is prime
23 100000000000000000000007=80683*50048543*24764326603 100000000000000000000009=7*13*197419*5566339100598721
24 1000000000000000000000007 is prime 1000000000000000000000009=53*193*5189*82633*189169*1205257
25 10000000000000000000000007=544667*18359841885041686021 10000000000000000000000009=173*3739*336958757*45879817771
26 100000000000000000000000007=21267247*4702066045501799081 100000000000000000000000009=317*315457413249211356466877
27 1000000000000000000000000007=8325465851*120113398805171557 1000000000000000000000000009=115901179*8628039927014029771
28 10000000000000000000000000007=823*339943*51888587*688846121749 10000000000000000000000000009=461*7873*339341*11725297*692466289
29 100000000000000000000000000007=53*827*2281490269444000821336497 100000000000000000000000000009=7*13*23*6526241*12047047*607696954219
30 1000000000000000000000000000007=251897*387727*10238844796821566353 1000000000000000000000000000009=17*1021*57613642910641239845595437

1 29 is prime 31 is prime
2 119=7*17 121=11*11
3 1019 is prime 1021 is prime
4 10019=43*233 10021=11*911
5 100019 is prime 100021=29*3449
6 1000019=47*21277 1000021=11*90911
7 10000019 is prime 10000021=97*103093
8 100000019=7*14285717 100000021=11*19*23*71*293
9 1000000019=83*12048193 1000000021 is prime
10 10000000019 is prime 10000000021=11*909090911
11 100000000019 is prime 100000000021=33533*2982137
12 1000000000019=1601*2593*240883 1000000000021=11*17*12119*441257
13 10000000000019=211*47393364929 10000000000021=349*1453*19720093
14 100000000000019=7*7*2040816326531 100000000000021=11*9090909090911
15 1000000000000019=1151*868809730669 1000000000000021=47293*21144778297
16 10000000000000019=23*263*1653165812531 10000000000000021=11*31*1231*23822512751
17 100000000000000019 is prime 100000000000000021 is prime
18 1000000000000000019=17*6047*124987*77829863 1000000000000000021=11*694619*130876193869
19 10000000000000000019=157*8419*294793*25663901 10000000000000000021=3163*2918411*1083313997
20 100000000000000000019=7*14285714285714285717 100000000000000000021=11*307*29612081729345573
21 1000000000000000000019=1187*303567907*2775194491 1000000000000000000021=277*618347*5838321045059
22 10000000000000000000019=452869*22081440769847351 10000000000000000000021=11*457*773*316703*8125674917
23 100000000000000000000019=163*255917*2397249625915189 100000000000000000000021=313*4752817*67220938212301
24 1000000000000000000000019=6469*5055793*30575499776807 1000000000000000000000021=11*11*8264462809917355371901
25 10000000000000000000000019=43*4951*39791*1180466765018113 10000000000000000000000021=89*103703*2583089*419449135067
26 100000000000000000000000019=7*18731*20759*2078357*17677238389 100000000000000000000000021=11*19*407397573281*1174452011749
27 1000000000000000000000000019=8252776265081*121171344997099 1000000000000000000000000021=23633*184081*229864645860609077
28 10000000000000000000000000019=28813*3954211*87771128218603733 10000000000000000000000000021=11*17*12969373*107415439*38385986389
29 100000000000000000000000000019=29*58027*14731042673*4034023245341 100000000000000000000000000021=211*479843152933*987684509807467
30 1000000000000000000000000000019=2531*3323*26737*28409*156534074818411 1000000000000000000000000000021=11*23*677*5838359187533935462777541

yangchuanju · 发表于 2025-7-14 15:37

A088274-29 A088275-24
Numbers k such that 10^k + 7 is prime.
Numbers k such that 10^k + 9 is prime.
1 1 1 1
2 2 2 2
3 4 3 3
4 8 4 4
5 9 5 9
6 24 6 18
7 60 7 22
8 110 8 45
9 134 9 49
10 222 10 56
11 412 11 69
12 700 12 146
13 999 13 202
14 1383 14 272
15 5076 15 2730
16 5543 16 2841
17 6344 17 4562
18 14600 18 31810
19 15093 19 43186
20 21717 20 48109
21 23636 21 92691
22 30221 22 237670
23 50711 23 400310
24 221628 24 482706
25 350071
26 371696
27 487291
28 995256
29 1043372

yangchuanju · 发表于 2025-7-14 15:40

A108052-20 A108050-19
Integers n such that 10^n+19 is a prime number.
Integers k such that 10^k+21 is prime.
1 1 1 1
2 3 2 3
3 5 3 9
4 7 4 17
5 10 5 55
6 11 6 77
7 17 7 133
8 59 8 195
9 81 9 357
10 108 10 1537
11 574 11 2629
12 629 12 3409
13 1069 13 8007
14 1759 14 25671
15 2063 15 48003
16 2682 16 55811
17 9174 17 94983
18 40929 18 109615
19 42457 19 135669
20 66033

重生888@ · 发表于 2025-7-14 17:38

谢谢杨先生辛苦！，看来，人工智能对人的思维的理解还有不足。

重生888@ · 发表于 2025-7-15 10:53

10^20+8121 与 10^20+8119是一对孪生素数对！

谢谢时空伴随者！

yangchuanju · 发表于 2025-7-15 20:59

n位最小孪生小素数
1 3
2 11
3 101
4 1019
5 10007
6 100151
7 1000037
8 10000139
9 100000037
10 1000000007
11 10000000277
12 100000000817
13 1000000000061
14 10000000001267
15 100000000000097
16 1000000000002371
17 10000000000001549
18 100000000000000019
19 1000000000000000619
20 10000000000000000097
21 100000000000000000391
22 1000000000000000000409
23 10000000000000000000649
24 100000000000000000005527
25 1000000000000000000002731
26 10000000000000000000000559
27 100000000000000000000000949
28 1000000000000000000000000427
29 10000000000000000000000000601
30 100000000000000000000000002797
……

n位最小孪生小素数与10^n的差
0 2
1 1
2 1
3 19
4 7
5 151
6 37
7 139
8 37
9 7
10 277
11 817
12 61
13 1267
14 97
15 2371
16 1549
17 19
18 619
19 97
20 391
21 409
22 649
23 5527
24 2731
25 559
26 949
27 427
28 601
29 2797
……

yangchuanju · 发表于 2025-7-15 21:02

n位最大孪生小素数 n位最大孪生大素数
1 5 1 7
2 71 2 73
3 881 3 883
4 9929 4 9931
5 99989 5 99991
6 999959 6 999961
7 9999971 7 9999973
8 99999587 8 99999589
9 999999191 9 999999193
10 9999999701 10 9999999703
11 99999999761 11 99999999763
12 999999999959 12 999999999961
13 9999999998489 13 9999999998491
14 99999999999971 14 99999999999973
15 999999999997967 15 999999999997969
16 9999999999999641 16 9999999999999643
17 99999999999998807 17 99999999999998809
18 999999999999998927 18 999999999999998929
19 9999999999999998501 19 9999999999999998503
20 99999999999999997739 20 99999999999999997741
21 999999999999999994997 21 999999999999999994999
22 9999999999999999997571 22 9999999999999999997573
23 99999999999999999998207 23 99999999999999999998209
24 999999999999999999995669 24 999999999999999999995671
25 9999999999999999999999167 25 9999999999999999999999169
26 99999999999999999999994121 26 99999999999999999999994123
27 999999999999999999999999641 27 999999999999999999999999643
28 9999999999999999999999999221 28 9999999999999999999999999223
29 99999999999999999999999997187 29 99999999999999999999999997189
30 999999999999999999999999998939 30 999999999999999999999999998941
…………

n位最大孪生小素数与10^n的差
1 5
2 29
3 119
4 71
5 11
6 41
7 29
8 413
9 809
10 299
11 239
12 41
13 1511
14 29
15 2033
16 359
17 1193
18 1073
19 1499
20 2261
21 5003
22 2429
23 1793
24 4331
25 833
26 5879
27 359
28 779
29 2813
30 1061
……

yangchuanju · 发表于 2025-7-15 21:14

n位最小素数与10^n的差
1 2 0 1
2 11 1 1
3 101 2 1
4 1009 3 9
5 10007 4 7
6 100003 5 3
7 1000003 6 3
8 10000019 7 19
9 100000007 8 7
10 1000000007 9 7
11 10000000019 10 19
12 100000000003 11 3
13 1000000000039 12 39
14 10000000000037 13 37
15 100000000000031 14 31
16 1000000000000037 15 37
17 10000000000000061 16 61
18 100000000000000003 17 3
19 1000000000000000003 18 3
20 10000000000000000051 19 51
21 100000000000000000039 20 39
22 1000000000000000000117 21 117
23 10000000000000000000009 22 9
24 100000000000000000000117 23 117
25 1000000000000000000000007 24 7
26 10000000000000000000000013 25 13
27 100000000000000000000000067 26 67
28 1000000000000000000000000103 27 103
29 10000000000000000000000000331 28 331
30 100000000000000000000000000319 29 319
31 1000000000000000000000000000057 30 57
32 10000000000000000000000000000033 31 33
33 100000000000000000000000000000049 32 49
34 1000000000000000000000000000000061 33 61
35 10000000000000000000000000000000193 34 193
36 100000000000000000000000000000000069 35 69
37 1000000000000000000000000000000000067 36 67
38 10000000000000000000000000000000000043 37 43
39 100000000000000000000000000000000000133 38 133
40 1000000000000000000000000000000000000003 39 3
41 10000000000000000000000000000000000000121 40 121
42 100000000000000000000000000000000000000109 41 109
43 1000000000000000000000000000000000000000063 42 63
44 10000000000000000000000000000000000000000057 43 57
45 100000000000000000000000000000000000000000031 44 31
46 1000000000000000000000000000000000000000000009 45 9
47 10000000000000000000000000000000000000000000121 46 121
48 100000000000000000000000000000000000000000000033 47 33
49 1000000000000000000000000000000000000000000000193 48 193
50 10000000000000000000000000000000000000000000000009 49 9
……

n位最大素数与10^n的差
1 7 1 3
2 97 2 3
3 997 3 3
4 9973 4 27
5 99991 5 9
6 999983 6 17
7 9999991 7 9
8 99999989 8 11
9 999999937 9 63
10 9999999967 10 33
11 99999999977 11 23
12 999999999989 12 11
13 9999999999971 13 29
14 99999999999973 14 27
15 999999999999989 15 11
16 9999999999999937 16 63
17 99999999999999997 17 3
18 999999999999999989 18 11
19 9999999999999999961 19 39
20 99999999999999999989 20 11
21 999999999999999999899 21 101
22 9999999999999999999973 22 27
23 99999999999999999999977 23 23
24 999999999999999999999743 24 257
25 9999999999999999999999877 25 123
26 99999999999999999999999859 26 141
27 999999999999999999999999901 27 99
28 9999999999999999999999999791 28 209
29 99999999999999999999999999973 29 27
30 999999999999999999999999999989 30 11
31 9999999999999999999999999999973 31 27
32 99999999999999999999999999999979 32 21
33 999999999999999999999999999999991 33 9
34 9999999999999999999999999999999589 34 411
35 99999999999999999999999999999999977 35 23
36 999999999999999999999999999999999841 36 159
37 9999999999999999999999999999999999919 37 81
38 99999999999999999999999999999999999941 38 59
39 999999999999999999999999999999999999943 39 57
40 9999999999999999999999999999999999999983 40 17
41 99999999999999999999999999999999999999881 41 119
42 999999999999999999999999999999999999999917 42 83
43 9999999999999999999999999999999999999999919 43 81
44 99999999999999999999999999999999999999999947 44 53
45 999999999999999999999999999999999999999999991 45 9
46 9999999999999999999999999999999999999999999967 46 33
47 99999999999999999999999999999999999999999999959 47 41
48 999999999999999999999999999999999999999999999967 48 33
49 9999999999999999999999999999999999999999999999943 49 57
50 99999999999999999999999999999999999999999999999943 50 57
……

		自动登录	找回密码
密码			注册

娱乐娱乐：分解大数152414752935769

点评

点评

点评