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
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..10000
Programs
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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 *)
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PARI
is(n) = isprime(n) && bigomega(n + 2) > 2 && bigomega(n - 2) > 2 \\ David A. Corneth, Dec 28 2018
Comments