Mersenne prime - Revision history

Vipul: /* Definition */

2012-01-02T19:01:34Z

Definition

← Older revision		Revision as of 19:01, 2 January 2012
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	===Facts in number theory===		===Facts in number theory===

	* [[~~Meresenne~~ number is prime implies number is prime]]		* [[Mersenne number is prime implies number is prime]]
	* [[Mersenne number for prime or Poulet implies prime or Poulet]]		* [[Mersenne number for prime or Poulet implies prime or Poulet]]

Vipul: /* Definition */

2012-01-02T19:00:20Z

Definition

← Older revision		Revision as of 19:00, 2 January 2012
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	It turns out that if <math>M_n</math> is prime, then <math>n</math> itself is also prime, though the converse is not true (the smallest counterexample is <math>n = 11</math>, because <math>M_{11} = 2047 = 23 \cdot 89</math>).		It turns out that if <math>M_n</math> is prime, then <math>n</math> itself is also prime, though the converse is not true (the smallest counterexample is <math>n = 11</math>, because <math>M_{11} = 2047 = 23 \cdot 89</math>).

			==Facts==

			===Facts in number theory===

			* [[Meresenne number is prime implies number is prime]]
			* [[Mersenne number for prime or Poulet implies prime or Poulet]]

			===Facts in other branches of mathematics===

			* [[Groupprops:Order is product of Mersenne prime and one more implies normal Sylow subgroup\|Order is product of Mersenne prime and one more implies normal Sylow subgroup (fact about groups)]]

	==Occurrence==		==Occurrence==

Vipul at 00:03, 22 April 2009

2009-04-22T00:03:59Z

@@ Line 3: / Line 3: @@
 ==Definition==
-A '''Mersenne prime''' is a [[Mersenne number]] that is also a [[prime number]]. In other words, it is a number of the form <math>M_n = 2^n - 1</math> that is prime, where <math>n</math> is a natural number.
+A '''Mersenne prime''' is a [[defining ingredient::Mersenne number]] that is also a [[prime number]]. In other words, it is a number of the form <math>M_n = 2^n - 1</math> that is prime, where <math>n</math> is a natural number.
 It turns out that if <math>M_n</math> is prime, then <math>n</math> itself is also prime, though the converse is not true (the smallest counterexample is <math>n = 11</math>, because <math>M_{11} = 2047 = 23 \cdot 89</math>).

Vipul: Created page with '{{prime number property}} ==Definition== A '''Mersenne prime''' is a Mersenne number that is also a prime number. In other words, it is a number of the form $M_n =...'$

2009-03-21T22:53:25Z

Created page with '{{prime number property}} ==Definition== A '''Mersenne prime''' is a Mersenne number that is also a prime number. In other words, it is a number of the form <math>M_n =...'

New page

{{prime number property}}

==Definition==

A '''Mersenne prime''' is a [[Mersenne number]] that is also a [[prime number]]. In other words, it is a number of the form <math>M_n = 2^n - 1</math> that is prime, where <math>n</math> is a natural number.

It turns out that if <math>M_n</math> is prime, then <math>n</math> itself is also prime, though the converse is not true (the smallest counterexample is <math>n = 11</math>, because <math>M_{11} = 2047 = 23 \cdot 89</math>).

Mersenne prime - Revision history

Vipul: /* Definition */

Vipul: /* Definition */

Vipul at 00:03, 22 April 2009

Vipul: Created page with '{{prime number property}} ==Definition== A '''Mersenne prime''' is a Mersenne number that is also a prime number. In other words, it is a number of the form M_n =...'

Vipul: Created page with '{{prime number property}} ==Definition== A '''Mersenne prime''' is a Mersenne number that is also a prime number. In other words, it is a number of the form $M_n =...'$