Regular prime - Revision history

Vipul at 01:21, 3 July 2012

2012-07-03T01:21:25Z

← Older revision		Revision as of 01:21, 3 July 2012
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	==Definition==		==Definition==

	A '''regular prime''' is a [[prime number]] greater than 2 such that {~~{fillin}~~}.		A '''regular prime''' is a [[prime number]] greater than 2 such that <math>p</math> does '''not''' divide the class number of the cyclotomic number field <math>\mathbb{Q}(\zeta_p)</math>.

	A prime greater than 2 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]].

Vipul: /* Definition */

2012-01-15T21:30:27Z

Definition

← Older revision		Revision as of 21:30, 15 January 2012
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	A '''regular prime''' is a [[prime number]] greater than 2 such that {{fillin}}.		A '''regular prime''' is a [[prime number]] greater than 2 such that {{fillin}}.

	A prime greater than 2 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]].

	==Occurrence==		==Occurrence==

Vipul: /* Definition */

2012-01-15T21:30:04Z

Definition

← Older revision		Revision as of 21:30, 15 January 2012
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	A prime greater than 2 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'''.

			==Occurrence==

			===Initial examples===

			<section begin="list"/>[[3]], [[5]], [[7]], [[11]], [[13]], [[17]], [[19]], [[23]], [[29]], [[31]], [[41]], [[43]], [[47]], [[53]], [[61]], <toggledisplay>[[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</toggledisplay>[[Oeis:A007703\|View list on OEIS]]<section end="list"/>

	==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>.

Vipul at 21:58, 2 January 2012

2012-01-02T21:58:23Z

← Older revision		Revision as of 21:58, 2 January 2012
Line 3:		Line 3:
	==Definition==		==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 '''regular prime''' is a [[prime number]] greater than 2 such that {{fillin}}.

	A prime greater than 2 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'''.

Vipul: /* Definition */

2012-01-02T21:53:38Z

Definition

← Older revision		Revision as of 21:53, 2 January 2012
Line 3:		Line 3:
	==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>.

Vipul: Created page with '{{prime number property}} ==Definition== A '''regular prime''' is a prime number such that the corresponding cyclotomic ring of integers is a [[unique factorization dom...'

2009-04-20T19:11:05Z

Created page with '{{prime number property}} ==Definition== A '''regular prime''' is a prime number such that the corresponding cyclotomic ring of integers is a [[unique factorization dom...'

New page

{{prime number property}}

==Definition==

A '''regular prime''' is a [[prime number]] 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'''.

==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>.