A204592 Primes p such that (p+1)/2, (p+2)/3, (p+3)/4 and (p+4)/5 are also prime.

19441, 266401, 423481, 539401, 600601, 663601, 908041, 1113961, 1338241, 1483561, 1657441, 1673401, 2578801, 3109681, 3150841, 3336601, 3613681, 4112761, 4160641, 4798081, 5114881, 5412961, 5516281, 5590201, 5839681, 6078361, 7660801, 8628481, 9362641, 9388801, 9584401, 9733081

Offset

1,1

Comments

Equivalently, primes p in A163573 such that p+4 is a semiprime. (Since all p in A163573 are of the form p=120k+1, p+4 is necessarily a multiple of 5. The other prime factor is then (p+4)/5 = 24k+1.)

Links

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

Formula

A204592 = A163573 intersect A136061.

Mathematica

Select[Prime[Range[700000]], AllTrue[{(#+1)/2, (#+2)/3, (#+3)/4, (#+4)/5}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 05 2017 *)

Prog

(PARI) {my(p=1); until(, isprime(p+=120) || next; for( j=2, 5, isprime(p\j+1) || next(2)); print1(p", "))}
(PARI) forprime(p=2, 1e7, if(p%120==1&&isprime((p+1)/2)&&isprime((p+2)/3)&& isprime((p+3)/4)&&isprime((p+4)/5), print1(p", "))) \\ Charles R Greathouse IV, Feb 26 2012

Crossrefs

Sequence in context: A126721 A323558 A321642 * A140930 A254486 A254493

Adjacent sequences: A204589 A204590 A204591 * A204593 A204594 A204595

Keyword

nonn

Author

M. F. Hasler, Feb 26 2012

Status

approved