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A322842
Primes p such that both p+2 and p-2 are neither prime nor semiprime.
1
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
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
KEYWORD
nonn
AUTHOR
Kyle Buscaglia, Cory Baker, Dec 28 2018
STATUS
approved