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A094319
Prime values of Lehmer's polynomial 263*x^2+3.
2
3, 4211, 51551, 177791, 420803, 4043891, 4444703, 4864451, 9898271, 13196291, 16437503, 16967711, 34846451, 37181891, 44210303, 48628703, 56622851, 64181471, 75558851, 82476803, 95946611, 101097203, 107724803, 113178371, 137858291, 140152703, 165804671
OFFSET
0,1
COMMENTS
For the first 206 primes p assumed by this quadratic form with x>=0, the number 326 is a primitive root modulo p.
REFERENCES
K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory. Springer-Verlag, NY, 1982, p. 47.
D. H. Lehmer, A note on primitive roots, Scripta Math., 26 1963 117-119.
Pieter Moree, Posting to Number Theory List, Jun 03, 2004.
LINKS
Pieter Moree, Primitive root producing quadratics, arXiv:math/0406033 [math.NT], 2004.
MAPLE
P:= x -> 263*x^2+3:
select(isprime, map(P, [$0..1000])); # Robert Israel, Feb 01 2021
MATHEMATICA
Select[Table[263*x^2+3, {x, 0, 800}], PrimeQ] (* Harvey P. Dale, Dec 04 2015 *)
CROSSREFS
Cf. A094320.
Sequence in context: A116213 A136544 A024048 * A362536 A229766 A003166
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 03 2004
STATUS
approved