A157358 Triple-safe primes p: p, (p-1)/2, (p-3)/4, and (p-7)/8 are all prime.

23, 47, 719, 1439, 2879, 4079, 9839, 11279, 21599, 28319, 51599, 84719, 92399, 95279, 96959, 137279, 157679, 159119, 178799, 209519, 219839, 243119, 349199, 429119, 430799, 441839, 462719, 481199, 491279, 507359, 533999, 571199, 597599

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Feb 27 2009

Keywords

• nonn
• easy

Comments

These occur in a proof of nonexistence of a certain type of permutation group for p (Theorem 8 by Ito). - R. J. Mathar, May 29 2011

Examples

			(23-1)/2=11, (11-1)/2=5, (5-1)/2=2(prime), ...
		

Links

• Noboru Ito, Transitive permutation groups of degree p=2q+1, p and q being prime numbers, Bull. AMS 69 (2) (1963), 165-192.

Crossrefs

Cf. A005385, A066179, A157357.

Programs

Mathematica

lst={};Do[p=Prime[n];If[PrimeQ[a=(p-1)/2]&&PrimeQ[b=(a-1)/2]&&PrimeQ[(b-1)/2],AppendTo[lst,p]],{n,9!}];lst

PARI

is(n)=n%8==7 && isprime(n) && isprime(n\2) && isprime(n\4) && isprime(n\8) \\ Charles R Greathouse IV, Oct 14 2021

PARI

list(lim)=my(v=List()); forprimestep(p=23,lim\1,8, if(isprime(p\8) && isprime(p\4) && isprime(p\2), listput(v,p))); Vec(v); \\ Charles R Greathouse IV, Oct 14 2021

Formula

a(n) >> n log^(4) n. - Charles R Greathouse IV, Oct 14 2021