A360827 Primes p, not safe primes, such that the smallest factor of (2^(p-1)-1) / 3 is equal to p.

443, 647, 1847, 2243, 2687, 2699, 6263, 6563, 7487, 7583, 8627, 8663, 9419, 9767, 10223, 11867, 12323, 13187, 13907, 14627, 14723, 14783, 17747, 17783, 19739, 20639, 20807, 21863, 22307, 23747, 24107, 24923, 25127, 26759, 27983, 29207, 29819, 30839, 31247, 32303, 34403, 34439

Offset: 1

Author

Alain Rocchelli, Feb 22 2023

Keywords

• nonn

Examples

			443 is the first term since p = 443 is the first term of A359387 that is not in A005385 (i.e., (443-1)/2 = 13*17 is not prime).
647 is the second term since p = 647 is the first term (> 443) of A359387 that is not in A005385 (i.e., (647-1)/2 = 17*19 is not prime).
		

Crossrefs

Equals A359387 \ A005385.

Programs

Mathematica

q[p_] := ! PrimeQ[(p - 1)/2] && AllTrue[Range[p], ! PrimeQ[#] || PowerMod[2, p - 1, 3*p*#] > 1 &]; Select[Prime[Range[4, 4000]], q] (* Amiram Eldar, Mar 01 2023 *)

PARI

forprime(p=11, 40000, if(!isprime((p-1)/2), forprime(div=5, p-1, if(Mod(2, div)^(p-1)==1, next(2))); print1(p, ", ")))