相邻孪生素数对间隙规律

yangchuanju

A033843-53
Number of twin primes < 2^n.
小于2^n的孪生素数的数量。
1 0
2 1
3 2
4 3
5 5
6 7
7 10
8 17
9 24
10 36
11 62
12 107
13 177
14 290
15 505
16 860
17 1526
18 2679
19 4750
20 8535
21 15500
22 27995
23 50638
24 92246
25 168617
26 309561
27 571313
28 1056281
29 1961080
30 3650557
31 6810670
32 12739574
33 23878645
34 44849427
35 84384508
36 159082253
37 300424743
38 568237005
39 1076431099
40 2042054332
41 3879202049
42 7378928530
43 14053179903
44 26795709320
45 51149458583
46 97741674629
47 186965900951
48 357988002871
49 686087457349
50 1316068371494
51 2526674510802
52 4854867527889
53 9335730886225

yangchuanju

A092245-1000
Lesser of the first twin prime pair with n digits.
n位最小孪小素
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
……
1000……

yangchuanju

A092250-1000
Lesser of the greatest twin prime pair with n digits.
n位最大孪小素
1 5
2 71
3 881
4 9929
5 99989
6 999959
7 9999971
8 99999587
9 999999191
10 9999999701
11 99999999761
12 999999999959
13 9999999998489
14 99999999999971
15 999999999997967
16 9999999999999641
17 99999999999998807
18 999999999999998927
19 9999999999999998501
20 99999999999999997739
21 999999999999999994997
22 9999999999999999997571
23 99999999999999999998207
24 999999999999999999995669
25 9999999999999999999999167
26 99999999999999999999994121
27 999999999999999999999999641
28 9999999999999999999999999221
29 99999999999999999999999997187
30 999999999999999999999999998939
……
1000……

yangchuanju

A124001-1250
Difference between first twin prime > 10^n and 10^n.
a(0) = 2 because 3 and 5 are twin primes and 3 - 10^0 = 2,
最小n位孪小素减10^n之差
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
30 1681
……
1250……

yangchuanju

A327133-1250
The difference between 10^n and the lesser of the twin primes immediately before.
10^n减最大n位孪小素之差
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
……
1250……

yangchuanju

A146214-10
a(n) = (10^n)-th lower twin prime.
第10^n个孪生素数对之孪小素
0 3
1 107
2 3821
3 79559
4 1260989
5 18409199
6 252427601
7 3285916169
8 41375648687
9 507575862527
10 6100479510551

A147797-13
The 10^n-th twin prime, A001097(10^n).
第10^n个孪生素数
0 3——第一个孪生素数
1 41——第10个孪生素数，第6对孪生素数之小素
2 1607——第100个孪生素数，第51对孪生素数之小素
3 32441
4 557729
5 8265137
6 115438691
7 1523976761
8 19358094101
9 239211161009
10 2891512532927
11 34338035342339
12 401888325140039
13 4646528385435887