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| − | {{Types of Primes Infobox|title=Fermat Primes|discov=Pierre de Fermat|amount=Exactly five- Fermat numbers apart from the first five are composite|expression=A prime which is one more than two to the power of a power of two|1st=[[3]], [[5]], [[17]], [[257]], |
+ | {{Types of Primes Infobox|title=Fermat Primes|discov=Pierre de Fermat|amount=Exactly five- Fermat numbers apart from the first five are composite|expression=A prime which is one more than two to the power of a power of two|1st=[[3]], [[5]], [[17]], [[257]], 65,537}} |
'''Fermat primes''' are Fermat numbers that are also prime numbers. A Fermat number has the following properties: F<sub>n</sub> = 2<sup>(2^n)</sup> + 1. |
'''Fermat primes''' are Fermat numbers that are also prime numbers. A Fermat number has the following properties: F<sub>n</sub> = 2<sup>(2^n)</sup> + 1. |
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Revision as of 12:58, 15 July 2016
| Fermat Primes
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Basic Info
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| Discovered by | Pierre de Fermat |
| Number of | Exactly five- Fermat numbers apart from the first five are composite |
| Description | A prime which is one more than two to the power of a power of two |
| First Few | 3, 5, 17, 257, 65,537 |
Fermat primes are Fermat numbers that are also prime numbers. A Fermat number has the following properties: Fn = 2(2^n) + 1.
All the Fermat primes
Note that 65,537 (F5) is the largest known Fermat prime, being 216 + 1. The next Fermat number (F6), 232 + 1 = 4,294,967,297, is divisible by 641 and 6,700,471.
Applications in Mathematics
Fermat primes are related to constructible polygons- regular polygons which one can construct using only a straightedge and circles. Polygons can be constructed if the number of sides' prime factors are either powers of two or powers of Fermat primes