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A262830 {2,3}-primes (defined in Comments).

%I A262830 #8 Nov 09 2015 16:22:33
%S A262830 2,7,13,67,79,151,181,193,223,283,331,421,631,661,733,877,1201,1321,
%T A262830 1657,1669,1759,1789,1993,2383,2521,3061,3391,3463,3733,3877,3967,
%U A262830 4093,4153,4243,4507,4987,5791,6121,6151,6211,6343,6661,6733,6961,7129,8089,8191
%N A262830 {2,3}-primes (defined in Comments).
%C A262830 Let S = {b(1), b(2), ..., b(k)}, where k > 1 and b(i) are distinct integers > 1 for j = 1..k. Call p an S-prime if the digits of p in base b(i) spell a prime in each of the bases b(j) in S, for i = 1..k. Equivalently, p is an S-prime if p is a strong-V prime (defined at A262729) for every permutation of the vector V = (b(1), b(2), ..., b(k)).
%H A262830 Clark Kimberling, <a href="/A262830/b262830.txt">Table of n, a(n) for n = 1..1000</a>
%t A262830 {b1, b2} = {2, 3};
%t A262830 u = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b1], b2]] &]; (* A235266 *)
%t A262830 v = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b2], b1]] &]; (* A262829 *)
%t A262830 w = Intersection[u, v]; (* A262830 *)
%t A262830 (* _Peter J. C. Moses_, Sep 27 2015 *)
%Y A262830 Cf. A000040, A262729, A235266, A262830.
%K A262830 nonn,easy,base
%O A262830 1,1
%A A262830 _Clark Kimberling_, Oct 31 2015