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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

The irregular primes to $ 125000$


Author: Samuel S. Wagstaff
Journal: Math. Comp. 32 (1978), 583-591
MSC: Primary 10A40; Secondary 10B15, 12A35
MathSciNet review: 0491465
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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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DOI: http://dx.doi.org/10.1090/S0025-5718-1978-0491465-4
PII: S 0025-5718(1978)0491465-4
Keywords: Bernoulli numbers, Euler numbers, irregular primes, Fermat's Last Theorem, cyclotomic invariants
Article copyright: © Copyright 1978 American Mathematical Society