A237256 Smallest member of Sophie Germain pair, wherein each member of the prime pair is the smallest of its prime quadruplets (p, p+2, p+8, p+12).

5, 29, 41609, 4287599, 16254449, 87130709, 118916729, 157119089, 173797289, 180210059, 207959879, 309740999, 349066439, 356259989, 401519399, 473953229, 705480749, 912950249, 994719629

Offset: 1

Author

Abhiram R Devesh, Feb 05 2014

Keywords

• nonn

Comments

It is not known if there are infinitely many Sophie Germain pairs with this property.

Examples

			a(1): p = 5; (2*p)+1 = 11; prime quadruplets (5,7,13,17); (11,13,19,23).
a(2): p = 29; (2*p)+1 = 59; prime quadruplets (29,31,37,41); (59,61,67,71).
		

Links

• Abhiram R Devesh and Dana Jacobsen, Table of n, a(n) for n = 1..1155 [first 155 terms from Abhiram R Devesh]
• Eric Weisstein's World of Mathematics, Sophie Germain Prime
• Wikipedia, Sophie Germain Prime

Crossrefs

Cf. A005384, A233540.

Programs

PARI

forprime(p=1, 1e9, my(t=2*p+1); if(isprime(t) && isprime(p+2) && isprime(p+8) && isprime(p+12) && isprime(t+2) && isprime(t+8) && isprime(t+12), print1(p, ", "))) \\ Felix Fröhlich, Jul 26 2014

Perl

use ntheory ":all"; my @p = sieve_prime_cluster(1,2e9,2,8,12); my %h; undef @h{@p}; for (@p) { say if exists $h{2*$+1} } # _Dana Jacobsen, Oct 03 2015

Python

from sympy import isprime, primerange
def is_a237256(p): return all(isprime(q) for q in (p, p+2, p+8, p+12, 2*p+1, 2*p+3, 2*p+9, 2*p+13))
print(*[ p for p in primerange(10**8) if is_a237256(p)], sep=', ')
# David Radcliffe, May 11 2025