与2^n相关的孪生素数

yangchuanju

A356256给出29个
The lesser of the 2^n-th twin prime pair (A001359).
第2^n对孪生素数之孪小素

0 3
1 5
2 17
3 71
4 227
5 821
6 2087
7 5021
8 13757
9 33149
10 81197
11 186647
12 435401
13 1002719
14 2241779
15 5060171
16 11296421
17 25121207
18 55559507
19 121831601
20 266187827
21 578653919
22 1253242691
23 2705496551
24 5820833729
25 12491149637
26 26733605159
27 57077657321
28 121575837179
29 258438193379

yangchuanju

A071406给出300个最小的a(n)使得a(n)*n!±1是一对孪生素数
a(n) is the smallest multiplier of n! such that -1+a(n)*n! and 1+a(n)*n! are both primes.

例：n=7， a(7)=7，7!=5040， 7*7!=35280 and {35279,35281} are primes.

1 4
2 2
3 1
4 3
5 2
6 17
7 7
8 6
9 3
10 14
11 29
12 30
13 48
14 27
15 9
16 24
17 12
18 97
19 78
20 47
21 71
22 80
23 55
24 13
25 57
26 20
27 81
28 259
29 108
30 163
31 81
32 118
33 63
34 215
35 173
36 513
37 420
38 561
39 537
40 1162
41 158
42 33
43 122
44 286
45 459
46 391
47 305
48 288
49 114
50 307
51 15
52 680
53 355
54 365
55 338
56 70
57 23
58 371
59 329
60 169
61 828
62 208
63 813
64 701
65 106
66 431
67 1604
68 275
69 2246
70 331
71 532
72 266
73 1713
74 331
75 3419
76 489
77 223
78 1429
79 858
80 1716
81 1395
82 1104
83 255
84 489
85 711
86 1896
87 33
88 2350
89 306
90 257
91 2120
92 943
93 1445
94 747
95 462
96 137
97 1394
98 1628
99 1759
100 494
……
300……

yangchuanju

yangchuanju 发表于 2025-10-16 05:08
A060256给出500个第n个素数阶乘q(n)#的最小倍数a(n)，使得a(n)*q(n)#±1是一对孪生素数
Smallest multiple ...

A100804给出25个最小的p#使得n*p#±1是一对孪生素数
Smallest prime P such that n*P# -1 and n*P# +1 are twin primes, where P#=primorial P, or 0 if no such prime exists.
       
1 3        1*3#±1=6±1是孪生素数
2 2        2*2#±1=4±1是孪生素数
3 2        3*2#±1=6±1是孪生素数
4 11        4*11#±1=9240±1是孪生素数
5 3
6 2
7 3
8 5
9 2
10 3
11 7
12 3
13 7
14 5
15 2
16 7
17 3
18 3
19 5
20 5
21 2
22 5
23 3
24 11
25 3

No solutions found yet for n = {26, 39, 46, 59, 63, 68, 76, 81, 82, 84, 89} through prime(1700) = 14519. - Ray Chandler, Jan 23 2005

a(26)=?, 5, 7, 7, 2, 19, 3, 3, 5, 5, 2, 19, 3, a(39)=?, 3, 5, 7, 5, 5, 3, a(46)=?, 3, 11, 17, 7, 2, 3, 43, 2, 7, 37, 7, 3, a(59)=?, 151, 31, 13, a(63)=?.