# 51 (number)

 ← 50 51 52 →
Cardinalfifty-one
Ordinal51st
(fifty-first)
Factorization3 × 17
Divisors1, 3, 17, 51
Greek numeralΝにゅーΑあるふぁ´
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 as well as a centered pentagonal number and an 18-gonal 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 512 + 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 πぱい/51 is constructible, and the number cos πぱい/51 is expressible in terms of square roots.

51 is: