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

References

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