257 (two hundred ndfifty-seven) is the natural number following 256 and preceding 258. 257 is a

prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...

of the form

2^+1,

specifically with ''n'' = 3, and therefore a

Fermat prime 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:F_ = 2^ + 1, where ''n'' is a non-negative integer. The first few Fermat numbers are: 3, 5, ...

. Thus, a regular polygon with 257 sides is constructible with compass and unmarked straightedge. It is currently the second largest known Fermat prime. Analogously, 257 is the third Sierpinski prime of the first kind, of the form

n^ + 1

➜

4^ + 1 = 257

. It is also a balanced prime, an irregular prime, a prime that is one more than a square, and a Jacobsthal–Lucas number. Four-fold 257 is 1028, which is the prime index of the fifth

Mersenne prime In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 1 ...

, 8191. There are exactly 257 combinatorially distinct convex polyhedra with eight vertices (or polyhedral graphs with eight nodes).

References

Integers {{Num-stub