A364778 Products of two distinct strong primes.

121, 187, 289, 319, 407, 451, 493, 629, 649, 697, 737, 781, 841, 869, 1003, 1067, 1073, 1111, 1139, 1177, 1189, 1207, 1343, 1369, 1397, 1507, 1517, 1639, 1649, 1681, 1711, 1717, 1793, 1819, 1943, 1969, 2059, 2101, 2159, 2167, 2183, 2291, 2329, 2419, 2453, 2479, 2497, 2533, 2627, 2629, 2747

Offset: 1

Author

Massimo Kofler, Aug 07 2023

Keywords

• nonn

Comments

Strong primes: prime(n) > (prime(n-1) + prime(n+1))/2.

Examples

			121 = 11^2 and 11 > (7+13)/2.
187 = 11*17 and 11 > (7+13)/2, 17 > (13+19)/2.
493 = 17*29 and 17 > (13+19)/2, 29 > (23+31)/2.
		

Crossrefs

Cf. A001358, A051634, A363167, A363782.

Programs

Mathematica

strongQ[p_] := p > 2 && 2*p > Total[NextPrime[p, {-1, 1}]]; Select[Range[1, 3000, 2], MemberQ[{{1, 1}, {2}}, (f = FactorInteger[#])[[;; , 2]]] && AllTrue[f[[;; , 1]], strongQ] &] (* Amiram Eldar, Aug 07 2023 *)

Extensions

Definition clarified by N. J. A. Sloane, Oct 08 2023