Regular prime: Difference between revisions
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==Definition== | ==Definition== | ||
A '''regular prime''' is a [[prime number]] such that the corresponding [[cyclotomic ring of integers]] is a [[unique factorization domain]]. | A '''regular prime''' is a [[prime number]] greater than 2 such that the corresponding [[cyclotomic ring of integers]] is a [[unique factorization domain]]. | ||
A prime that is not a regular prime is termed an '''irregular prime'''. | A prime greater than 2 that is not a regular prime is termed an '''irregular prime'''. | ||
==Facts== | ==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 <math>0.6</math>. | * [[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 <math>0.6</math>. | ||
Revision as of 21:53, 2 January 2012
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.
View other properties of prime numbers | View other properties of natural numbers
Definition
A regular prime is a prime number greater than 2 such that the corresponding cyclotomic ring of integers is a unique factorization domain.
A prime greater than 2 that is not a regular prime is termed an irregular prime.
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 .