A238242 Primes p such that p^2+p+41 is also prime.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 97, 101, 103, 107, 113, 131, 137, 139, 149, 151, 157, 167, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 241, 257, 263, 269, 277, 281, 293, 307, 311, 313, 317, 337, 353

Offset: 1

Author

K. D. Bajpai, Feb 20 2014

Keywords

• nonn

Comments

n^2 + n + 41 is Euler’s prime generating polynomial.

The first 12 terms in the sequence are the first 12 consecutive primes.

Examples

			13 is in the sequence because 13 is prime and 13^2+13+41 = 223 is also prime.
113 is in the sequence because 113 is prime and 113^2+113+41 =  12923 is also prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..3372

Crossrefs

Cf. A000040, A005846, A202018, A097823.

Programs

Magma

[p: p in PrimesUpTo(400)| IsPrime(p^2+p+41)]; // Vincenzo Librandi, Feb 22 2014

Maple

with(numtheory):KD := proc() local a,b; a:=ithprime(n); b:=a^2+a+41;  if isprime(b) then RETURN (a);  fi; end: seq(KD(), n=1..500);

Mathematica

Select[Prime[Range[200]],PrimeQ[#^2+#+41]&]

PARI

s=[]; forprime(p=2, 1000, if(isprime(p^2+p+41), s=concat(s, p))); s \\ Colin Barker, Feb 20 2014