51 (number)

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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
Hexadecimal 3316
Vigesimal 2B20
Base 36 1F36

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

In mathematics[edit]

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[edit]

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[edit]

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number in the UHF bandplan for American terrestrial television since December 31, 2011, when channels 52—69 were withdrawn

See also[edit]

  • 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[edit]

  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.