The irregular primes to $125000$

Author:
Samuel S. Wagstaff

Journal:
Math. Comp. **32** (1978), 583-591

MSC:
Primary 10A40; Secondary 10B15, 12A35

DOI:
https://doi.org/10.1090/S0025-5718-1978-0491465-4

MathSciNet review:
0491465

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Abstract | References | Similar Articles | Additional Information

Abstract: We have determined the irregular primes below 125000 and tabulated their distribution. Two primes of index five of irregularity were found, namely 78233 and 94693. Fermat’s Last Theorem has been verified for all exponents up to 125000. We computed the cyclotomic invariants ${\mu _p}$, ${\lambda _p}$, ${\nu _p}$, and found that ${\mu _p} = 0$ for all $p < 125000$. The complete factorizations of the numerators of the Bernoulli numbers ${B_{2k}}$ for $2k \leqslant 60$ and of the Euler numbers ${E_{2k}}$ for $2k \leqslant 42$ are given.

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Additional Information

Keywords:
Bernoulli numbers,
Euler numbers,
irregular primes,
Fermat’s Last Theorem,
cyclotomic invariants

Article copyright:
© Copyright 1978
American Mathematical Society