New congruences for the Bernoulli numbers

Tanner, Jonathan W.; Wagstaff, Samuel S.

doi:10.1090/S0025-5718-1987-0866120-4

New congruences for the Bernoulli numbers
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by Jonathan W. Tanner and Samuel S. Wagstaff PDF

Math. Comp. 48 (1987), 341-350 Request permission

Abstract:

We prove a new congruence for computing Bernoulli numbers modulo a prime. Since it is similar to Vandiver’s congruences but has fewer terms, it may be used to test primes for regularity efficiently. We have programmed this test on a CYBER 205 computer. Fermat’s "Last Theorem" has been proved for all exponents up to 150000.

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