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A157358
Triple-safe primes p: p, (p-1)/2, (p-3)/4, and (p-7)/8 are all prime.
6
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
1,1
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
FORMULA
a(n) >> n log^(4) n. - Charles R Greathouse IV, Oct 14 2021
EXAMPLE
(23-1)/2=11, (11-1)/2=5, (5-1)/2=2(prime), ...
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
PROG
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved