Regular prime

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 $p$ does not divide the class number of the cyclotomic number field $\mathbb {Q} (\zeta _{p})$.

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]

71, 73, 79, 83, 89, 97, 107, 109, 113, 127, 137, 139, 151, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 239, 241, 251, 269, 277, 281, 313, 317, 331, 337, 349, 359, 367, 373, 383, 397, 419, 431

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 $0.6$.