# Definify.com

## Definition 2023

## Fermat_prime

# Fermat prime

## English

### Noun

**Fermat prime** (*plural* **Fermat primes**)

- (number theory) A prime number which is one more than a power of two.
- Carl Friedrich Gauss proved the constructibility of the regular 17-gon in 1796. Five years later, he developed the theory of Gaussian periods in his
*Disquisitiones Arithmeticae*. This theory allowed him to formulate a sufficient condition for the constructibility of regular polygons: "A regular*n*-gon can be constructed with compass and straightedge if*n*is the product of a power of 2 and any number of distinct**Fermat primes**." Gauss stated without proof that this condition was also necessary, but never published his proof. A full proof of necessity was given by Pierre Wantzel in 1837. The result is known as the*Gauss–Wantzel theorem*.^{WP}

- Carl Friedrich Gauss proved the constructibility of the regular 17-gon in 1796. Five years later, he developed the theory of Gaussian periods in his