(with William Hart and Wilson Ong)
To appear in Mathematics of Computation.
arXiv preprint (May 2016).
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(ζp) 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.
This file contains one line for each odd prime p < 2147483648. Each line contains p followed by the irregular indices k for p. For example, the line
1767218027 63562190 274233542 290632386 619227758 902737892 1279901568 1337429618 1603159110 1692877044means that p = 1767218027 has index of irregularity 9, and that Bk = 0 mod p for k = 63562190, ..., 1692877044. If a prime is regular, it appears on the line by itself.