# 51 (number)

 ← 50 51 52 →
Cardinalfifty-one
Ordinal51st
(fifty-first)
Factorization3 × 17
Divisors1, 3, 17, 51
Greek numeralΝΑ´
Roman numeralLI
Binary1100112
Ternary12203
Octal638
Duodecimal4312

51 (fifty-one) is the natural number following 50 and preceding 52.

## In mathematics

Fifty-one is a pentagonal number[1] as well as a centered pentagonal number[2] and an 18-gonal number[3] and a Perrin number.[4] It is also 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.[5]

Since the greatest prime factor of 512 + 1 = 2602 is 1301, which is substantially more than 51 twice, 51 is a Størmer number.[6] There are 51 different cyclic Gilbreath permutations on 10 elements,[7] and therefore there are 51 different real periodic points of order 10 on the Mandelbrot set.[8]

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 π/51 is constructible, and the number cos π/51 is expressible in terms of square roots.

51 is: