Difference between revisions of "Mersenne number"

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(Facts)
 
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==Facts==
 
==Facts==
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===Number theory facts===
  
 
* [[Mersenne number for prime or Poulet implies prime or Poulet]]
 
* [[Mersenne number for prime or Poulet implies prime or Poulet]]
 
* [[Mersenne number is prime implies number is prime]]
 
* [[Mersenne number is prime implies number is prime]]
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===Facts in other branches of mathematics===
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* [[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)]]
  
 
==Testing/listing==
 
==Testing/listing==

Latest revision as of 18:59, 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

Number theory facts

Facts in other branches of mathematics

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