A117244 Single (or isolated or non-twin) primes (A007510) that are not Chen primes (A109611).

79, 97, 163, 173, 223, 277, 331, 367, 373, 383, 397, 439, 457, 547, 593, 607, 613, 673, 691, 709, 727, 733, 739, 757, 773, 853, 907, 929, 967, 997, 1013, 1069, 1087, 1103, 1123, 1129, 1171, 1181, 1213, 1223, 1237, 1249, 1307, 1373, 1423, 1433, 1447, 1493

Offset: 1

Author

Jani Melik, Apr 22 2006

Keywords

• nonn

Examples

			79 is single prime, but not Chen prime, since 79 -2 = 77 = 7*11 is composite, and 79 + 2 = 81 = 3^4 is neither prime nor semiprime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007510, A109611.

Programs

Maple

isA001358 := proc(n) numtheory[bigomega](n) = 2 ; end proc: isA109611 := proc(n) if isprime(n) then isprime(n+2) or isA001358(n+2) ; else false; end if; end proc: isA007510 := proc(n) if isprime(n) then not isprime(n-2) and not isprime(n+2) ; else false; end if ; end proc: isA117244 := proc(n) isA007510(n) and not isA109611(n) ; end proc: for n from 1 to 4000 do if isA117244(n) then printf("%d,",n) ; fi; end do ; # R. J. Mathar, Dec 09 2009

Mathematica

Select[Range[1500], PrimeQ[#] && !PrimeQ[#-2] && PrimeOmega[#+2] > 2 &] (* Amiram Eldar, Oct 19 2021 *)

PARI

isok(p) = isprime(p) && !isprime(p-2) && !isprime(p+2) && (bigomega(p+2) > 2); \\ Michel Marcus, Oct 19 2021

Extensions

Terms beyond 397 from R. J. Mathar, Dec 09 2009

Offset corrected by Amiram Eldar, Oct 19 2021