Irregular Pair

If p divides the numerator of the Bernoulli number B_(2k) for 0<2k<p-1, then (p,2k) is called an irregular pair. For p<30000, the irregular pairs of various forms are p=16843 for (p,p-3), p=37 for (p,p-5), none for (p,p-7), and p=67,877 for (p,p-9).

See also

Bernoulli Number, Irregular Prime

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Johnson, W. "Irregular Primes and Cyclotomic Invariants." Math. Comput. 29, 113-120, 1975.

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Irregular Pair

Cite this as:

Weisstein, Eric W. "Irregular Pair." From MathWorld--A Wolfram Web Resource.

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