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

%I A059452 #28 Jul 15 2024 10:23:52
%S A059452 7,47,59,107,167,227,263,347,383,467,479,503,563,587,839,863,887,983,
%T A059452 1187,1283,1307,1319,1367,1487,1523,1619,1823,1907,2027,2099,2207,
%U A059452 2447,2579,2879,2999,3119,3167,3203,3467,3947,4007,4079,4127,4139,4259,4283
%N A059452 Safe primes (A005385) that are not Sophie Germain primes.
%C A059452 Except for 7, these primes are congruent to 11 modulo 12.
%C A059452 Terminal primes in complete Cunningham chains of first kind, i.e., the chains cannot be continued from these primes.
%H A059452 Amiram Eldar, <a href="/A059452/b059452.txt">Table of n, a(n) for n = 1..10000</a>
%H A059452 Chris K. Caldwell, <a href="https://t5k.org/glossary/page.php?sort=cunninghamchain">Cunningham Chain</a>.
%H A059452 Warut Roonguthai, <a href="http://web.archive.org/web/20010405230842/http://ksc9.th.com/warut/cunningham.html">Yves Gallot's Proth.exe and Cunningham Chains</a>. [Wayback Machine link]
%F A059452 A156659(a(n))*(1-A156660(a(n))) = 1. - _Reinhard Zumkeller_, Feb 18 2009
%e A059452 347 is a term because 173 is a prime but 695 is not.
%t A059452 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 *)
%o A059452 (Python)
%o A059452 from itertools import count, islice
%o A059452 from sympy import isprime, prime
%o A059452 def A059452_gen(): # generator of terms
%o A059452     return filter(lambda p:isprime(p>>1) and not isprime(p<<1|1),(prime(i) for i in count(1)))
%o A059452 A059452_list = list(islice(A059452_gen(),10)) # _Chai Wah Wu_, Jul 12 2022
%o A059452 (PARI) is(p) = p > 2 && isprime(p) && isprime((p-1)/2) && !isprime(2*p+1); \\ _Amiram Eldar_, Jul 15 2024
%Y A059452 Intersection of A005385 and A053176.
%Y A059452 Cf. A005384, A059452, A059453, A059454, A059455, A059456, A007700, A005602, A023272, A023302, A023330, A156659, A156660.
%K A059452 nonn
%O A059452 1,1
%A A059452 _Labos Elemer_, Feb 02 2001
%E A059452 Broken link updated by _R. J. Mathar_, Apr 12 2010