%I #19 Mar 01 2022 12:25:24

%S 83,137,191,227,317,353,443,461,587,821,827,839,857,877,977,1031,1091,

%T 1109,1163,1277,1289,1307,1367,1427,1433,1451,1523,1619,1627,1667,

%U 1787,1811,1847,1913,1973,1997,2243,2333,2377,2417,2543,2621,2657,2693

%N Primes of the form pqrs+2 with p,q,r,s odd primes.

%H Charles R Greathouse IV, <a href="/A126711/b126711.txt">Table of n, a(n) for n = 1..10000</a>

%F {A014613(i)+2 such that A014613(i)+2 is in A000040}.

%e a(1) = 83 = 3*3*3*3+2.

%e a(2) = 137 = 3*3*3*5+2.

%e a(3) = 191 = 3*3*3*7+2.

%e a(4) = 227 = 3*3*5*5+2.

%t With[{nn=50},Take[Select[Union[Times@@@Tuples[Prime[Range[2,nn]], 4]+2], PrimeQ], nn]] (* _Harvey P. Dale_, Oct 18 2013 *)

%o (Sage) is_A126711 = lambda n: is_prime(n) and sum(m for p,m in factor(n-2)) == 4 # [D. S. McNeil, Dec 11 2010]

%o (PARI) list(lim)=my(t,tt,v=List()); forprime(p=3,lim\27, forprime(q=p,lim\p\9, forprime(r=q,lim\p\q\3, t=p*q*r; forprime(s=r,lim\t, if(ispseudoprime(tt=t*s+2), listput(v,tt)))))); vecsort(Vec(v)) \\ _Charles R Greathouse IV_, Feb 17 2011

%Y Cf. A000040, A014613, A126608-A126609, A126636, A126660-A126661.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Feb 12 2007

%E Corrected (299 removed) by _D. S. McNeil_, Dec 10 2010