51 (number)

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

In mathematics

Fifty-one is a pentagonal number^[1] as well as a centered pentagonal number^[2] (one of the few numbers to be both) 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.

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number in the UHF bandplan for American terrestrial television since December 31, 2011, when channels 52—69 were withdrawn

See also

• 51, a year in the Julian calendar
• List of highways numbered 51
• The model number of the P-51 Mustang World War II 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.
• Greg Murphy used "#51" for most of the seasons he raced in V8 Supercars

References