Theorem fmtno3prm

Description: The 3 rd Fermat number is a prime (_fourth Fermat prime_). (Contributed by AV, 15-Jun-2021)

	Ref	Expression
Assertion	fmtno3prm	$$⊢\mathrm{FermatNo}\left(3\right)\in \mathbb{P}$$

Proof

Step	Hyp	Ref	Expression
1		fmtno3	$$⊢\mathrm{FermatNo}\left(3\right)=257$$
2		257prm	$$⊢257\in \mathbb{P}$$
3	1 2	eqeltri	$$⊢\mathrm{FermatNo}\left(3\right)\in \mathbb{P}$$