Irregular Pair
If 
divides the Numerator of the Bernoulli Number 
for 
, then 
is called anirregular pair. For 
, the irregular pairs of various forms are 
for 
, 
for 
,none for 
, and 
for 
.
References
Johnson, W. ``Irregular Primes and Cyclotomic Invariants.'' Math. Comput. 29, 113-120, 1975.
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