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A059452
Safe primes (A005385) that are not Sophie Germain primes.
23
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
1,1
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.
LINKS
Chris K. Caldwell, Cunningham Chain.
Warut Roonguthai, Yves Gallot's Proth.exe and Cunningham Chains. [Wayback Machine link]
FORMULA
A156659(a(n))*(1-A156660(a(n))) = 1. - Reinhard Zumkeller, Feb 18 2009
EXAMPLE
347 is a term because 173 is a prime but 695 is not.
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 *)
PROG
(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
(PARI) is(p) = p > 2 && isprime(p) && isprime((p-1)/2) && !isprime(2*p+1); \\ Amiram Eldar, Jul 15 2024
KEYWORD
nonn
AUTHOR
Labos Elemer, Feb 02 2001
EXTENSIONS
Broken link updated by R. J. Mathar, Apr 12 2010
STATUS
approved