Difference between revisions of "Fermat numbers"
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| − | Any number in the form <math>2^{2^n}+1</math> where <math>n</math> is any natural number is known as a '''Fermat number'''. It was hypothesized by Fermat that every number in this form was prime, but Euler found that the fifth Fermat number can be factored as <math>2^{2^5}+1=641 \cdot 6,700,417</math>. | + | Any number in the form <math>2^{2^n}+1</math> where <math>n</math> is any natural number is known as a '''Fermat number'''. It was hypothesized by Fermat that every number in this form was prime, but Euler found that the fifth Fermat number can be factored as <math>2^{2^5}+1=641 \cdot 6,700,417</math>. There are only five known [[Fermat Primes]], and it is believed that there are only five, but we are still lacking a complete proof. |
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Latest revision as of 21:40, 28 August 2015
Any number in the form 
where 
is any natural number is known as a Fermat number. It was hypothesized by Fermat that every number in this form was prime, but Euler found that the fifth Fermat number can be factored as 
. There are only five known Fermat Primes, and it is believed that there are only five, but we are still lacking a complete proof.
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