A027755 Primes of the form k^2 + k + 5.

5, 7, 11, 17, 47, 61, 137, 277, 311, 347, 467, 557, 761, 997, 1061, 1487, 1811, 2357, 2657, 3911, 4561, 5261, 5407, 5857, 6011, 6977, 7487, 8377, 8747, 9511, 11777, 12437, 13577, 14767, 16007, 17827, 18637, 18911, 21467, 23567, 25127

Offset: 1

Author

Patrick De Geest

Keywords

• nonn

Comments

a(5) through a(14) are identical to the first 10 values of q, the left-hand column of "Example 2.3. We give examples of maximal and minimal elliptic curves over finite fields over F_q with discriminant -19 for all q < 1000", p. 4, and "Example 5.2. We produce examples of optimal curves over finite fields with discriminant -19" pp. 10-11 of E. Alekseenko, et al. - Jonathan Vos Post, Feb 12 2009

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000
• E. Alekseenko, S. Aleshnikov, N. Markin and A. Zaytsev, Optimal Curves of Genus 3 over Finite Fields with Discriminant -19, arXiv:0902.1901 [math.AG], 2009-2011.
• P. De Geest, World!Of Numbers

Crossrefs

Cf. A014556, A027754.

Programs

Magma

[a: n in [0..250]|IsPrime(a) where a is n^2+n+5]; // Vincenzo Librandi, Dec 20 2010

Mathematica

nn = Range[0, 200]; Select[nn^2 + nn + 5, PrimeQ] (* Jean-François Alcover, Nov 17 2018 *)

Formula

a(n) = A027754(n)^2 + A027754(n) + 5. - Seiichi Manyama, Mar 19 2017

a(n) >> n^2 log n (Brun sieve). - Charles R Greathouse IV, Nov 01 2022