Primitive root producing quadratics

Pieter Moree

Primitive root producing quadratics

Number Theory 2008-02-01 v2

Authors: Pieter Moree

Abstract

D.H. Lehmer found a quadratic polynomial such that 326 is a primitive root for the first 206 primes represented by this polynomial. It is shown that this is related to the class number one problem and prime producing quadratics. An algorithm is described to find more impressive examples in the same spirit. Y. Gallot used it to establish the current record in which 206 is being replaced by 31082.

Keywords

prime numbers polynomial roots prime number theory

Cite

@article{arxiv.math/0406033,
  title  = {Primitive root producing quadratics},
  author = {Pieter Moree},
  journal= {arXiv preprint arXiv:math/0406033},
  year   = {2008}
}

Comments

17 pages, includes some examples due to Yves Gallot and a (conditional) result essentially due to Andrew Granville. Record has been improved to 31082 and a record for small base number g has been included (Y. Gallot)

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