51 (fifty-one) is the natural number following 50 and preceding 52.
In mathematics
thumb|51 as a centered pentagonal number
thumb|51 as a stella octangula number
Fifty-one is
- a pentagonal number as well as a centered pentagonal number and an 18-gonal number
- a stella octangula number
- the 6th Motzkin number, telling the number of ways to draw non-intersecting chords between any six points on a circle's boundary, no matter where the points may be located on the boundary.
- a Perrin number, coming after 22, 29, 39 in the sequence (and the sum of the first two)
- a Størmer number, since the greatest prime factor of 51<sup>2</sup> + 1 = 2602 is 1301, which is substantially more than 51 twice.
- There are 51 different cyclic Gilbreath permutations on 10 elements, and therefore there are 51 different real periodic points of order 10 on the Mandelbrot set.
- Since 51 is the product of the distinct Fermat primes 3 and 17, a regular polygon with 51 sides is constructible with compass and straightedge, the angle is constructible, and the number cos is expressible in terms of square roots.