Irregular primes to two billion

2016/05/09 by William Hart, David Harvey, Hart, William +3
Mathematics · #11R18 #11Y40 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11R18 #msc:11Y40

paper · pdf · doi:10.48550/arxiv.1605.02398

19 pages

arxiv created 2016/05/09 · arxiv updated 2016/05/10

Abstract

We compute all irregular primes less than 2³1 = 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.

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