Noun
Fermat number (plural Fermat numbers)
(number theory) An integer which is one more than two raised to a power which is itself a power of two (i.e., is expressible in the form
2
2
n
+
1
{\displaystyle 2^{2^{n}}+1}
for some
n
≥
0
{\displaystyle n\geq 0}
); equivalently, a number that is one more than two raised to some power (is expressible as
2
n
+
1
{\displaystyle 2^{n}+1}
) and is prime.
Hyponym: Fermat prime
However, the very next Fermat number 2 32 + 1 is composite (one of its prime factors is 641), as Euler discovered later, and in fact no further Fermat numbers are known to be prime. Source: Internet