Fermat prime

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This article defines a property that can be evaluated for natural numbers

Definition

Definition with symbols

A natural number N is said to be a Fermat prime if it satisfies the following equivalent conditions:

  • N is prime and there exists a natural number n such that N = 2^{2^n} + 1
  • N is prime and there exists a natural number m such that N = 2^m + 1
  • N is prime and the automorphism group of the cyclic group of order N is a 2-group

Relation with other properties

Stronger properties

Weaker properties

External links

Subject wiki links