Fermat prime: Difference between revisions
(Created page with '{{prime number property}} ==Definition== A '''Fermat prime''' is a Fermat number that is also a prime number. In other words, it is a prime number of the form <math>F_k...') |
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It turns out that if <math>2^n + 1</math> is prime for <math>n</math> a natural number, then <math>n = 2^k</math> for some nonnegative integer <math>k</math>. Thus, a Fermat prime can also be defined as a prime of the form <math>2^n + 1</math> for some natural number <math>n</math>. | It turns out that if <math>2^n + 1</math> is prime for <math>n</math> a natural number, then <math>n = 2^k</math> for some nonnegative integer <math>k</math>. Thus, a Fermat prime can also be defined as a prime of the form <math>2^n + 1</math> for some natural number <math>n</math>. | ||
==Relation with other properties== | |||
===Weaker properties=== | |||
* [[Stronger than::Proth prime]] | |||
==Testing== | |||
{{oeis|A019434}} | |||
Revision as of 16:04, 20 April 2009
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 Fermat prime is a Fermat number that is also a prime number. In other words, it is a prime number of the form , where is a nonnegative integer.
It turns out that if is prime for a natural number, then for some nonnegative integer . Thus, a Fermat prime can also be defined as a prime of the form for some natural number .
Relation with other properties
Weaker properties
Testing
The ID of the sequence in the Online Encyclopedia of Integer Sequences is A019434