Difference between revisions of "Mersenne number"

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(Created page with '{{one-parameter sequence}} ==Definition== Let <math>n</math> be a natural number. The <math>n^{th}</math> '''Mersenne number''', denoted <math>M_n</math>, is defined as: <math...')
 
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* [[Sierpinski number]]
 
* [[Sierpinski number]]
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==Facts==
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* [[Mersenne number for prime or Poulet implies prime or Poulet]]
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* [[Mersenne number is prime implies number is prime]]
  
 
==Testing/listing==
 
==Testing/listing==

Revision as of 18:51, 2 January 2012

This article describes a sequence of natural numbers. The parameter for the sequence is a positive integer (or sometimes, nonnegative integer).
View other one-parameter sequences

Definition

Let be a natural number. The Mersenne number, denoted , is defined as:

.

Sometimes the term Mersenne number is restricted to the case where itself is a prime number.

If itself is prime, it is termed a Mersenne prime. If is prime, so is .

Relation with other properties

Stronger properties

Facts

Testing/listing

The ID of the sequence in the Online Encyclopedia of Integer Sequences is A000225
The ID of the sequence in the Online Encyclopedia of Integer Sequences is A001348