Irregular primes to two billion
Number Theory
2016-05-10 v1
Abstract
We compute all irregular primes less than 2^31 = 2 147 483 648. We verify the Kummer-Vandiver conjecture for each of these primes, and we check that the p-part of the class group of Q(zeta_p) has the simplest possible structure consistent with the index of irregularity of p. Our method for computing the irregular indices saves a constant factor in time relative to previous methods, by adapting Rader's algorithm for evaluating discrete Fourier transforms.
Cite
@article{arxiv.1605.02398,
title = {Irregular primes to two billion},
author = {William Hart and David Harvey and Wilson Ong},
journal= {arXiv preprint arXiv:1605.02398},
year = {2016}
}
Comments
19 pages