Infinitude conjecture for regular primes

This article states a conjecture about there existing infinitely many of the following numbers/structures: regular prime
View other infinitude conjectures | View infinitude facts

Statement

The conjecture is that there exist infinitely many regular primes. A regular prime is a prime for which the corresponding cyclotomic ring is a unique factorization domain, or equivalently, a ring whose class number is one.

Relation with other conjectures

Stronger conjectures

• Distribution conjecture for regular primes: This conjecture states that the limit, as $n$ tends to $\infty$, of the fraction of primes less than $n$ that are regular, is $e^{-1/2}\simeq 0.6065$.