A059322 First differences of sequence of consecutive safe primes.

2, 4, 12, 24, 12, 24, 24, 60, 12, 48, 36, 84, 12, 24, 84, 12, 24, 60, 24, 132, 120, 24, 24, 96, 36, 168, 96, 24, 12, 48, 72, 48, 36, 96, 204, 84, 120, 12, 24, 36, 108, 240, 12, 120, 240, 60, 24, 60, 36, 24, 96, 48, 36, 264, 156, 156, 24, 60, 84, 60, 72, 48, 12, 120, 24

Offset: 1

Author

Labos Elemer, Jan 26 2001

Keywords

• nonn

Comments

Except for (5,7) and (7,11), all terms are divisible by 12, since safe primes are congruent to 5 modulo 6 except 7 and safe_prime + 6 is not a safe prime. Closest safe primes differ by 12 like (11,23) or (83207,83219).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..5001 from G. C. Greubel)

Crossrefs

Cf. A005385, A033299.

Programs

Mathematica

Differences[Select[Prime[Range[500]],PrimeQ[(#-1)/2]&]]  (* Harvey P. Dale, Jan 12 2011 *)

PARI

list(lim) = {my(p1 = 5); forprime(p2 = 7, lim, if(isprime((p2-1)/2), print1(p2-p1, ", "); p1 = p2));} \\ Amiram Eldar, Mar 02 2025

Formula

a(n) = A005385(n+1) - A005385(n). [corrected by Harvey P. Dale, Jan 12 2011 and Zak Seidov, Sep 19 2016]

Extensions

Offset corrected by Amiram Eldar, Mar 02 2025