Fermat number ... In mathematics, a Fermat number, named after Pierre de Fermat (1601–1665), the first known to have studied them, is a positive integer of the form: where n is a non-negative integer.

Names given without initials in the discoverer column refer to an indirect involvement of programmers whose software was essential for the discovery of the particular prime factor: Durman (Fermat), …

3. Determining primality of Fermat numbers The following necessary and su cient condition for primality of Fermat numbers has been used to prove (with computers) that some Fermat numbers are composite.

There are two definitions of the Fermat number. The less common is a number of the form 2^n+1 obtained by setting x=1 in a Fermat polynomial, the first few of which are 3, 5, 9, 17, 33, ...

A Fermat number is a number of the form where is a nonnegative integer. The first five Fermat numbers (for ) are A prime Fermat number is known as a Fermat prime.

Surprisingly, Fermat primes arise in deciding whether a regular n-gon (a convex polygon with n equal sides) can be constructed with a compass and a straightedge.

Jul 23, 2025 · Fermat numbers are related to the construction of regular polygons. Specifically, a regular polygon with Fn sides can be constructed with a compass and straightedge if Fn is prime.

Nov 20, 2025 · In symbols, he was claiming that if n > 2, there are no whole numbers x, y, z such that xn + yn = zn, a statement that came to be known as Fermat’s last theorem. For three and a half …

Fermat numbers and Fermat primes were first studied by Pierre de Fermat, who conjectured that all Fermat numbers are prime. Indeed, the first five Fermat numbers F0,..., F4 are easily shown to be …

Definition A Fermat number is a natural number of the form $2^ {\paren {2^n} } + 1$, where $n = 0, 1, 2, \ldots$. The number $2^ {\paren {2^n} } + 1$ is, in this context, often denoted $F_n$.