##  [Irregular Prime](/irregular-prime) 

  ##  [Irregular Prime](https://puremath.quantumdictionary.io/irregular-prime-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A prime p that divides the numerator of some Bernoulli number B_k (typically for even k with 2 ≤ k ≤ p−3), so p fails Kummer's regularity condition and introduces complications in class groups of cyclotomic fields and related cyclotomic arithmetic.