A289250 Primes p such that p + 4 is a semiprime.

2, 5, 11, 17, 29, 31, 47, 53, 61, 73, 83, 89, 107, 137, 139, 151, 157, 173, 179, 181, 197, 199, 211, 233, 263, 283, 317, 331, 337, 367, 373, 389, 409, 433, 443, 449, 467, 523, 541, 547, 569, 577, 587, 593, 607, 619, 631, 677, 683, 691, 709, 719, 727, 733, 751, 787, 809, 811, 827

Offset: 1

Author

Zak Seidov, Jun 29 2017

Keywords

• nonn

Comments

Except for case p=5, p+4 is never a perfect square.

For p = {2, 11, 31, 73, 139, 433, 1759, 2017} p+4 is a product of two consecutive primes.

Examples

			2+4=6=2*3, 5+4=9=3*3, 11+4=15=3*5 (all semiprimes).
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A063637, A082919, A241484,

Programs

Mathematica

Select[Prime@ Range@ 150, PrimeOmega[# + 4] == 2 &] (* Michael De Vlieger, Jun 29 2017 *)

PARI

issemi(n)=bigomega(n)==2
is(n)=isprime(n) && issemi(n+4) \\ Charles R Greathouse IV, Jul 02 2017