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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

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The irregular primes to $125000$
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by Samuel S. Wagstaff PDF
Math. Comp. 32 (1978), 583-591 Request permission

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
  • © Copyright 1978 American Mathematical Society
  • 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