# Definition:Regular Prime

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## Definition

A **regualr prime** is a prime number $p$ that is not a divisor of the class number of the field obtained by adjoining to the rational numbers a primitive $p$th root of unity.

## Also see

- Results about
**regular primes**can be found**here**.

## Historical Note

The concept of a **regular prime** was conceived by Ernst Eduard Kummer in $1850$ in his work on Fermat's Last Theorem.

He proved that Fermat's Last Theorem holds for all exponents $p$ such that $p$ is a **regular prime**.

## Sources

- 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**regular prime** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**regular prime**