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

1,1

Comments

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

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

Links

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

Example

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.

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]&]

Prog

(PARI) s=[]; forprime(p=2, 1000, if(isprime(p^2+p+41), s=concat(s, p))); s \\ Colin Barker, Feb 20 2014
(Magma) [p: p in PrimesUpTo(400)| IsPrime(p^2+p+41)]; // Vincenzo Librandi, Feb 22 2014

Crossrefs

Cf. A000040, A005846, A202018, A097823.

Sequence in context: A341661 A268513 A256484 * A197298 A211654 A363998

Adjacent sequences: A238239 A238240 A238241 * A238243 A238244 A238245

Keyword

nonn

Author

K. D. Bajpai, Feb 20 2014

Status

approved