%N Primes p of the form 6k+1 such that 6p+1 is also prime.
%t sp1Q[n_]:=IntegerQ[(n-1)/6]&&PrimeQ[6n+1]; Select[Prime[Range],sp1Q] (* _Harvey P. Dale_, Apr 08 2018 *)
%o (MAGMA) [ p: n in [0..600] | IsPrime(6*p+1) and IsPrime(p) where p is 6*n+1 ];
%Y Subsequence of A007693 which in turn is subsequence of A024899.
%A _Zak Seidov_, Nov 22 2010