# Regular prime

From Number

This article defines a property that can be evaluated for a prime number. In other words, every prime number either satisfies this property or does not satisfy this property.

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## Definition

A **regular prime** is a prime number greater than 2 such that does **not** divide the class number of the cyclotomic number field .

A prime greater than 2 that is not a regular prime is termed an irregular prime.

## Occurrence

### Initial examples

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 43, 47, 53, 61, [SHOW MORE]View list on OEIS## Facts

- Infinitude conjecture for regular primes: It is conjectured that there are infinitely many regular primes, and in fact, the asymptotic density of regular primes is conjectured to be around .