# Difference between revisions of "Fermat prime"

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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>. | ||

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+ | ==Relation with other properties== | ||

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+ | ===Weaker properties=== | ||

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+ | * [[Stronger than::Proth prime]] | ||

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+ | ==Testing== | ||

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+ | {{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