OFFSET
1,1
COMMENTS
Dirichlet's theorem on primes in arithmetic progressions tells us, for example, that there are infinitely many primes of the form 4n+1. For primes represented by polynomials of degree greater than 1, the Bateman-Horn paper gives a conjecture on the density.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
P. Bateman and R. A. Horn, A heuristic asymptotic formula concerning the distribution of prime numbers, Mathematics of Computation, 16 (1962), 363-367.
Wikipedia, Bateman-Horn Conjecture
MATHEMATICA
Select[Table[4n^3+1, {n, 1100}], PrimeQ] (* Vincenzo Librandi, Aug 01 2012 *)
PROG
(Magma) [ a: n in [0..200] | IsPrime(a) where a is 4*n^3+1 ]; // Vincenzo Librandi, Nov 08 2011
(PARI) for(n=1, 1e3, if(isprime(t=4*n^3+1), print1(t", "))) \\ Charles R Greathouse IV, Nov 21 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 05 2011
STATUS
approved