On the distribution of irregular primes

Johnsen, John

doi:10.1016/0022-314x(76)90091-3

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1978

2015

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“…In the table below we give tts(x) and us(x) for x = 125000, and 0 < s < 5. The data support the hypothesis very well, especially since a change of 1 in it(x) (to include 2 or discard 3, say) would alter the fourth significant figure of us(x), [23] and [7].) In particular, there are infinitely many irregular primes.…”

supporting

confidence: 55%

The irregular primes to 125000

Wagstaff¹

1978

Math. Comp.

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Abstract.We have determined the irregular primes below 12 5000 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 u \ v , and found that u" = 0 for all p < 12 5000. The complete factorizations of the numerators of the Bernoulli numbers B2k for 2k « 60 and of the Euler numbers E2k for 2k < 42 are given.

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supporting

confidence: 55%