A115093 Primes of the form p*q-2, where p and q are distinct primes.

13, 19, 31, 37, 53, 67, 83, 89, 109, 113, 127, 131, 139, 157, 181, 199, 211, 233, 251, 257, 263, 293, 307, 317, 337, 353, 379, 389, 401, 409, 443, 449, 467, 479, 487, 491, 499, 503, 509, 541, 557, 563, 571, 577, 587, 631, 647, 653, 677, 683, 701, 719, 743

Offset: 1

Author

T. D. Noe, Mar 01 2006

Keywords

• nonn

Comments

This sequence is a subset of A063637, which is the union of this sequence and A049002.

Crossrefs

Cf. A049002 (primes of the form p^2-2, where p is prime), A063637 (primes of the form p*q-2 where p and q are primes).

Programs

Mathematica

SemiPrimeQ[n_] := (n>1) && (2==Plus@@(Transpose[FactorInteger[n]][[2]])); Select[Prime[Range[150]], SemiPrimeQ[ #+2] && !IntegerQ[Sqrt[ #+2]]&]