A059452 Safe primes (A005385) that are not Sophie Germain primes.

7, 47, 59, 107, 167, 227, 263, 347, 383, 467, 479, 503, 563, 587, 839, 863, 887, 983, 1187, 1283, 1307, 1319, 1367, 1487, 1523, 1619, 1823, 1907, 2027, 2099, 2207, 2447, 2579, 2879, 2999, 3119, 3167, 3203, 3467, 3947, 4007, 4079, 4127, 4139, 4259, 4283

Offset: 1

Author

Labos Elemer, Feb 02 2001

Keywords

• nonn

Comments

Except for 7, these primes are congruent to 11 modulo 12.

Terminal primes in complete Cunningham chains of first kind, i.e., the chains cannot be continued from these primes.

Examples

			347 is a term because 173 is a prime but 695 is not.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Chris K. Caldwell, Cunningham Chain.
• Warut Roonguthai, Yves Gallot's Proth.exe and Cunningham Chains. [Wayback Machine link]

Crossrefs

Intersection of A005385 and A053176.

Cf. A005384, A059452, A059453, A059454, A059455, A059456, A007700, A005602, A023272, A023302, A023330, A156659, A156660.

Programs

Mathematica

lst={};Do[p=Prime[n];If[PrimeQ[(p-1)/2],If[ !PrimeQ[2*p+1],AppendTo[lst,p]]],{n,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Jun 24 2009 *)

PARI

is(p) = p > 2 && isprime(p) && isprime((p-1)/2) && !isprime(2*p+1); \\ Amiram Eldar, Jul 15 2024

Python

from itertools import count, islice
from sympy import isprime, prime
def A059452_gen(): # generator of terms
    return filter(lambda p:isprime(p>>1) and not isprime(p<<1|1),(prime(i) for i in count(1)))
A059452_list = list(islice(A059452_gen(),10)) # Chai Wah Wu, Jul 12 2022

Formula

A156659(a(n))*(1-A156660(a(n))) = 1. - Reinhard Zumkeller, Feb 18 2009

Extensions

Broken link updated by R. J. Mathar, Apr 12 2010