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Safe primes (A005385) (p and (p-1)/2 are primes) such that 12*p+1 is also prime.
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%I #11 Mar 24 2014 23:55:01

%S 5,23,59,83,383,479,503,719,839,863,1619,2039,2099,2579,2819,2879,

%T 3023,4139,4259,4679,4703,4919,5879,6719,6779,7559,8039,8783,8819,

%U 10799,11279,11423,12203,12659,12899,12983,13523,13799,14159,14303,14699,15683,18119,18443,19259,19379,20183,20663,21059,23663,24083,24239,24659,27239,28163,29123,29339,29483,29759,30803,31139,31583,36923,37463,38603,39119,39503,39839,39983,41879,42299,42443,43403,44519,44939,46679,47339,47819,47963

%N Safe primes (A005385) (p and (p-1)/2 are primes) such that 12*p+1 is also prime.

%e 23 is a prime, so is (23-1)/2=11 and also 12*23+1=277, 59 is a prime, (59-1)/2=29 and 12*59+1=709, ...

%p ts_sgB_var_pras := proc(nmax) local i,tren,atek; tren := 0: for i from 1 to nmax do atek := numtheory[safeprime](i): if (atek > tren) then if (isprime(atek)='true' and isprime(6*atek+1)='true') then tren := atek: fi; fi; od; end: seq(ts_sgB_var_pras(i), i=1..3000);

%t okQ[n_]:=PrimeQ[(n-1)/2]&&PrimeQ[12n+1]

%t Select[Prime[Range[5000]],okQ] (* _Harvey P. Dale_, Nov 21 2010 *)

%Y Cf. A005384, A005385, A059455.

%K nonn

%O 1,1

%A _Jani Melik_, Oct 02 2002

%E More terms from _Harvey P. Dale_, Nov 21 2010