A126711 Primes of the form pqrs+2 with p,q,r,s odd primes.

83, 137, 191, 227, 317, 353, 443, 461, 587, 821, 827, 839, 857, 877, 977, 1031, 1091, 1109, 1163, 1277, 1289, 1307, 1367, 1427, 1433, 1451, 1523, 1619, 1627, 1667, 1787, 1811, 1847, 1913, 1973, 1997, 2243, 2333, 2377, 2417, 2543, 2621, 2657, 2693

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

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

Example

a(1) = 83 = 3*3*3*3+2.
a(2) = 137 = 3*3*3*5+2.
a(3) = 191 = 3*3*3*7+2.
a(4) = 227 = 3*3*5*5+2.

Mathematica

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

Prog

(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]
(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

Crossrefs

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

Sequence in context: A140038 A260495 A165502 * A039548 A141976 A142652

Adjacent sequences: A126708 A126709 A126710 * A126712 A126713 A126714

Keyword

easy,nonn

Author

Jonathan Vos Post, Feb 12 2007

Extensions

Corrected (299 removed) by D. S. McNeil, Dec 10 2010

Status

approved