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

1,1

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

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 *)

Prog

(Java)
boolean isIsolatedPrime(int num){
    int upper = num + 2;
    int lower = num - 2;
    return isPrime(num) &&
          !isPrime(upper) &&
          !isPrime(lower) &&
          !isSemiPrime(upper) &&
          !isSemiPrime(lower);
   }
(PARI) is(n) = isprime(n) && bigomega(n + 2) > 2 && bigomega(n - 2) > 2 \\ David A. Corneth, Dec 28 2018

Crossrefs

Cf. A000040, A001358, A007510, A134797.

Sequence in context: A178652 A119567 A142436 * A063645 A142607 A241045

Adjacent sequences: A322839 A322840 A322841 * A322843 A322844 A322845

Keyword

nonn

Author

Kyle Buscaglia, Cory Baker, Dec 28 2018

Status

approved