Английская Википедия:257 (number)

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Шаблон:Infobox number 257 (two hundred [and] fifty-seven) is the natural number following 256 and preceding 258.

257 is a prime number of the form <math>2^{2^n}+1,</math> specifically with n = 3, and therefore a Fermat prime. Thus a regular polygon with 257 sides is constructible with compass and unmarked straightedge. It is currently the second largest known Fermat prime.[1]

Analogously, 257 is the third Sierpinski prime of the first kind, of the form <math>n^{n} + 1</math> ➜ <math>4^{4} + 1 = 257</math>.[2]

It is also a balanced prime,[3] an irregular prime,[4] a prime that is one more than a square,[5] and a Jacobsthal–Lucas number.[6]

There are exactly 257 combinatorially distinct convex polyhedra with eight vertices (or polyhedral graphs with eight nodes).[7]

References

Шаблон:Reflist

Шаблон:Integers