A153645 Primes p such that p^2 + 4 and p^2 + 4p + 2 are also prime.
3, 5, 7, 13, 17, 47, 67, 73, 137, 167, 277, 307, 313, 487, 503, 593, 607, 613, 787, 823, 1117, 1123, 1237, 1523, 1543, 1637, 1987, 2777, 2887, 3037, 3163, 3433, 3457, 3463, 3797, 3853, 4093, 4283, 4583, 5113, 5297, 5323, 5683, 5953, 6047, 6577, 6803, 6823
Offset: 1
Examples
For prime p = 3, p^2+4 = 13 and p^2+4p+2 = 23 are prime; for p = 67, p^2+4 = 4493 and p^2+4p+2 = 4759 are prime.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Crossrefs
Cf. A062324 (p and p^2+4 are both prime).
Programs
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Magma
[ p: p in PrimesUpTo(7000) | IsPrime(p^2+4) and IsPrime(p^2+4*p+2) ];
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Maple
a := proc (n) if isprime(n) = true and isprime(n^2+4) = true and isprime(n^2+4*n+2) = true then n else end if end proc: seq(a(n), n = 1 .. 7000); # Emeric Deutsch, Jan 02 2009
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Mathematica
Select[Prime[Range[10000]],PrimeQ[#^2+4]&&PrimeQ[#^2 +4#+2]&] (* Vincenzo Librandi, Jul 27 2012 *)
Extensions
Edited, corrected (three terms deleted) and extended beyond a(10) by Klaus Brockhaus, Jan 02 2009
Corrected and extended by Emeric Deutsch, Jan 02 2009
Comments