A053341 Euclid-Pocklington primes: primes of the form Product_{i=1..k} prime(i) * prime(k+1)^m + 1 where prime(r) is the r-th prime and Product_{i=1..k} prime(i) < prime(k+1)^m.

3, 5, 7, 17, 19, 151, 163, 257, 487, 751, 1459, 1471, 39367, 65537, 72031, 279511, 33820711, 86093443, 258280327, 372027811, 4092305911, 11149928791, 42638305711, 209481995953231, 411782264189299, 3561193931204911

Offset: 1

Author

N. J. A. Sloane, Jan 05 2000

Keywords

• nonn
• easy
• nice

Comments

Named after the Greek mathematician Euclid (flourished c. 300 B.C.) and the English physicist and mathematician Henry Cabourn Pocklington (1870-1952). - Amiram Eldar, Jun 24 2021

Examples

			5 = 2^2+1 is of this form (with k=0).
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..454

Crossrefs

Cf. A006862.

Programs

Mathematica

eucpock[max_] := Module[{p = 1, prod = 1, m, q, r, s = {}}, While[prod < max, prod *= p; q = NextPrime[p]; m = Max[1, Ceiling @ Log[q, prod]]; r = prod * q^m; While[r + 1 <= max, If[PrimeQ[r + 1], AppendTo[s, r + 1]]; r *= q]; p = NextPrime[p]]; Union[s]]; eucpock[10^16] (* Amiram Eldar, Jun 24 2021 *)

Extensions

More terms from Jud McCranie, Jul 11 2000