If 
divides the numerator
of the Bernoulli number 
for 
, then 
is called an irregular pair. For 
, the irregular pairs of various forms are 
for 
, 
for 
, none for 
, and 
for 
.
Irregular Pair
See also
Bernoulli Number, Irregular PrimeExplore with Wolfram|Alpha
References
Johnson, W. "Irregular Primes and Cyclotomic Invariants." Math. Comput. 29, 113-120, 1975.Referenced on Wolfram|Alpha
Irregular PairCite this as:
Weisstein, Eric W. "Irregular Pair." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/IrregularPair.html