A242377 Greatest n-digit prime in which every two-digit string is also a prime.

7, 97, 971, 9719, 97973, 979717, 9797371, 97973731, 979797979, 9797979713, 97979797171, 979797973117, 9797979797971, 97979797973173, 979797979797317, 9797979797979719, 97979797979797373, 979797979797971179, 9797979797979737971

Offset: 1

Author

Robert G. Wilson v, May 12 2014

Keywords

• nonn
• base

Comments

To stay parallel with A090534, a(1) exists.

The greatest potential candidate, gpc(n), is of the form floor(10^n*97/99). The following is gpc(n)-a(n): 2, 0, 8, 78, 6, 80, 608, 6066, 0, 84, 808, 6680, 8, 6624, 662, 78, 606, 8618, 60008, 86, 600, 6000, 660, 608060, 808, ... .

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A090534, A069488.

Programs

Mathematica

fQ[p_] := Block[{id = IntegerDigits@ p}, Union@ PrimeQ[ FromDigits@# & /@ Partition[id, 2, 1]] == {True}]; f[n_] := Block[{p = NextPrime[10^n*97/99, -1]}, While[ !fQ@ p, p = NextPrime[p, -1]]; p]; f[1] = 7; Array[f, 19]