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A262839 (5,7)-primes (defined in Comments).

%I A262839 #6 Nov 24 2015 01:42:23
%S A262839 2,3,5,7,13,17,23,31,41,43,53,71,73,79,97,101,109,113,127,137,151,157,
%T A262839 181,191,193,197,199,233,239,251,263,277,281,311,317,337,349,359,379,
%U A262839 401,409,431,433,449,461,463,503,521,541,557,613,617,631,643,647
%N A262839 (5,7)-primes (defined in Comments).
%C A262839 Let V = (b(1), b(2), ..., b(k)), where k > 1 and b(i) are distinct integers > 1 for j = 1..k. Call p a V-prime if the digits of p in base b(1) spell a prime in each of the bases b(2), ..., b(k).
%H A262839 Clark Kimberling, <a href="/A262839/b262839.txt">Table of n, a(n) for n = 1..10000</a>
%t A262839 {b1, b2} = {5, 7};
%t A262839 u = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b1], b2]] &];  (* A235635 *)
%t A262839 v = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b2], b1]] &];  (* A262839 *)
%t A262839 w = Intersection[u, v]; (* A262840 *)
%t A262839 (* _Peter J. C. Moses_, Sep 27 2015 *)
%Y A262839 Cf. A000040, A235635, A262840, A262829.
%K A262839 nonn,easy,base
%O A262839 1,1
%A A262839 _Clark Kimberling_, Nov 09 2015