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A204592 Primes p such that (p+1)/2, (p+2)/3, (p+3)/4 and (p+4)/5 are also prime. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 31 18:24 EST 2023. Contains 359980 sequences. (Running on oeis4.)