A322842 Primes p such that both p+2 and p-2 are neither prime nor semiprime.

173, 277, 457, 607, 727, 929, 1087, 1129, 1181, 1223, 1237, 1307, 1423, 1433, 1447, 1493, 1523, 1549, 1597, 1613, 1627, 1811, 1861, 1973, 2011, 2063, 2137, 2297, 2347, 2377, 2399, 2423, 2677, 2693, 2753, 2767, 2797, 2819, 2851, 2917, 3023, 3313, 3323, 3449

Offset: 1

Author

Kyle Buscaglia, Cory Baker, Dec 28 2018

Keywords

• nonn

Comments

Also: Primes p such that both p+2 and p-2 have at least three prime divisors. - David A. Corneth, Dec 28 2018

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001358, A007510, A134797.

Programs

Java

boolean isIsolatedPrime(int num){
    int upper = num + 2;
    int lower = num - 2;
    return isPrime(num) &&
          !isPrime(upper) &&
          !isPrime(lower) &&
          !isSemiPrime(upper) &&
          !isSemiPrime(lower);
   }

Maple

q:= n-> numtheory[bigomega](n)>2:
a:= proc(n) option remember; local p;
      p:= `if`(n=1, 1, a(n-1));
      do p:= nextprime(p);
         if q(p-2) and q(p+2) then break fi
      od; p
    end:
seq(a(n), n=1..50);  # Alois P. Heinz, Dec 28 2018

Mathematica

Select[Prime[Range[1000]], PrimeOmega[#-2] > 2 && PrimeOmega[#+2] > 2&] (* Jean-François Alcover, Nov 26 2020 *)

PARI

is(n) = isprime(n) && bigomega(n + 2) > 2 && bigomega(n - 2) > 2 \\ David A. Corneth, Dec 28 2018