A111668 Primes p such that p-1 has a prime factor > sqrt(p-1).

3, 7, 11, 23, 29, 43, 47, 53, 59, 67, 79, 83, 89, 103, 107, 131, 137, 139, 149, 157, 167, 173, 179, 191, 223, 227, 229, 233, 239, 263, 269, 277, 283, 293, 311, 317, 347, 349, 359, 367, 373, 383, 389, 431, 439, 461, 467, 479, 499, 503, 509, 523, 557, 563, 569

Offset: 1

Author

Rick L. Shepherd, Aug 14 2005

Keywords

• nonn

Comments

Alternatively, primes of the form m*x+1 where x>0 is an integer, m is a prime and m>x. - Frank M Jackson, Nov 27 2015

{a(n)-1, n>=0} is a subsequence of A064052.

Examples

			67 is a term as 67 is prime and 67-1 = 66 = 2*3*11 has prime factor 11 > sqrt(66) = 8.1240....
		

Crossrefs

Cf. A064052.

Programs

Mathematica

Reap[For[p = 3, p < Prime[120], p = NextPrime[p], f = FactorInteger[p-1][[-1, 1]]; If[f > Sqrt[p], Sow[p]]]][[2, 1]] (* Jean-François Alcover, Jan 12 2015 *)

PARI

forprime(p=3,prime(100),f=factor(p-1);sz=matsize(f)[1];if(f[sz,1]>sqrt(p-1),print1(p,",")))