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# 51 (number)

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 Title: 51 (number) Author: World Heritage Encyclopedia Language: English Subject: Collection: Integers Publisher: World Heritage Encyclopedia Publication Date:

### 51 (number)

 ← 50 51 52 →
Cardinal fifty-one
Ordinal 51st
(fifty-first)
Factorization 3 × 17
Divisors 1, 3, 17, 51
Roman numeral LI
Binary 1100112
Ternary 12203
Quaternary 3034
Quinary 2015
Senary 1236
Octal 638
Duodecimal 4312
Vigesimal 2B20
Base 36 1F36

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

## Contents

• In mathematics 1
• In other fields 2
• References 4

## In mathematics

Fifty-one is the 14th discrete semiprime and the 5th in the {3.q} semiprime family having the prime factors (3.17). The aliquot sum of 51 is 21, itself a discrete semiprime. 51 is the 4th member of the 11-aliquot tree with the sequence (51, 21, 11, 1, 0).

51 is a pentagonal number as well as a centered pentagonal number (one of the few numbers to be both) and an 18-gonal number and a Perrin number. 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.

Since the greatest prime factor of 512 + 1 = 2602 is 1301, which is clearly more than 51 twice, 51 is a Størmer number.

There are 51 different cyclic Gilbreath permutations on 10 elements,[1] and therefore there are 51 different real periodic points of order 10 on the Mandelbrot set.[2]

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 \pi/51 is constructible, and the number \cos(\pi/51) is expressible in terms of square roots.

## In other fields

51 is:

• The atomic number of antimony
• The code for international direct dial phone calls to Peru
• The last possible television channel number in the UHF bandplan for American terrestrial television since December 31, 2011, when channels 52—69 were withdrawn

## References

1. ^ "Sloane's A000048 ", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
2. ^ .
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