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The Irregular Primes to 125000

Samuel S. Wagstaff, Jr.
Mathematics of Computation
Vol. 32, No. 142 (Apr., 1978), pp. 583-591
DOI: 10.2307/2006167
Stable URL: http://www.jstor.org/stable/2006167
Page Count: 9
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The Irregular Primes to 125000
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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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