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

Author

M. F. Hasler, Feb 26 2012

Keywords

• nonn

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

Programs

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 *)

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

Formula

A204592 = A163573 intersect A136061.