The criteria of Kummer and Mirimanoff extended to include 22 consecutive irregular pairs (Q789423)

If the Fermat equation \(x^ p+y^ p+z^ p=0\) (\(p\) an odd prime) has a solution with \(xyz\) prime to \(p\), then \(p\) divides the Bernoulli numbers \(B_{p-3},B_{p-5},\ldots,B_{p-19}\) [see \textit{H. Wada}, Tokyo J. Math. 3, 173--176 (1980; Zbl 0448.10016)]. The authors show by numerical computations that here 19 can be replaced by 45. Their method follows a program proposed by Wada [op. cit.]. The computations involve prime factorizations of certain integers having order of magnitude up to \(10^{60}\).