# 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.

## In mathematics

Fifty-one is the 14th discrete biprime 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 biprime. 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]

## In sports

As of 2013, the highest number of international test cricket centuries scored by an individual is 51. It is the world record, held by India's Sachin Ramesh Tendulkar.[3]

## 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number in the UHF bandplan for American terrestrial television since December 31, 2011, when channels 52—69 were withdrawn

• 51, a year in the Julian calendar
• List of highways numbered 51
• The model number of the P-51 Mustang WWII fighter aircraft
• Area 51, a parcel of U.S. military-controlled land in southern Nevada, apparently containing a secret aircraft testing facility
• Fifty-One Tales, part of the title of a collection of stories by Lord Dunsany
• "51st State", any future US state, usually referring to Washington D.C. or Puerto Rico. Occasionally used in commentary to refer to non-US entities (such as Alberta) adopting US-like policies or seeking to become part of the US.
• 51 (film), a 2011 American horror film
• "Fifty-One", an episode of Breaking Bad
• Pastis 51, often just called "51", is a brand of pastis owned by Pernod Ricard.

## References

1. ^ "Sloane's A000048 ", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
2. ^ Diaconis, Persi; Graham, Ron (2012), "Chapter 5: From the Gilbreath Principle to the Mandelbrot Set", Magical Mathematics: the mathematical ideas that animate great magic tricks, Princeton University Press, pp. 61–83.
3. ^ "200 facts about Sachin Tendulkar ahead of his 200th Test". Deccan Chronicle. November 12, 2013. Retrieved November 15, 2013.