A237188 Smallest member of Sophie Germain pair, where each member of the prime pair is the smallest of its prime triple (p, p+2, p+8).

5, 29, 2549, 6269, 41609, 259379, 418349, 492059, 514049, 521879, 819029, 1171199, 1659809, 1994339, 2014139, 2325509, 2327399, 2392139, 2420699, 2481179, 2844269, 3142829, 3393359, 3637169, 3990029

Offset

1,1

Comments

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

The sequence is infinite under Dickson's conjecture. Aside from a(1) = 5, all terms are 29 or 179 mod 210. - Charles R Greathouse IV, Feb 05 2014

Links

Abhiram R Devesh and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 135 terms from Devesh)

Eric Weisstein's World of Mathematics, Sophie Germain Prime

Wikipedia, Sophie Germain prime

Example

a(1): p = 5; (2*p)+1 = 11
Prime triples (5,7,13);(11,13,19)
a(2): p = 29; (2*p)+1=59
Prime triples (29,31,37);(59,61,67)

Mathematica

sgpQ[n_]:=Module[{sg=2n+1}, AllTrue[Flatten[{sg+{0, 2, 8}, n+{2, 8}}], PrimeQ]]; Select[Prime[ Range[ 300000]], sgpQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 02 2016 *)

Prog

(Python)
from sympy import isprime
print([5] + [n for m in range(29, 10**8, 210) for n in (m, m+150) if isprime(n) and isprime(n+2) and isprime(n+8) and isprime(2*n+1) and isprime(2*n+3) and isprime(2*n+9)]) # David Radcliffe, Aug 07 2025
(PARI) is(n)=isprime(n) && isprime(n+2) && isprime(n+8) && isprime(2*n+1) && isprime(2*n+3) && isprime(2*n+9) \\ Charles R Greathouse IV, Feb 05 2014

Crossrefs

Cf. A005384.

Sequence in context: A175905 A057706 A057705 * A371347 A086720 A056869

Adjacent sequences: A237185 A237186 A237187 * A237189 A237190 A237191

Keyword

nonn

Author

Abhiram R Devesh, Feb 04 2014

Status

approved