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Cardinal | fifty-one | |||

Ordinal | 51st (fifty-first) | |||

Factorization | 3 × 17 | |||

Divisors | 1, 3, 17, 51 | |||

Greek numeral | ΝΑ´ | |||

Roman numeral | LI | |||

Binary | 110011_{2} | |||

Ternary | 1220_{3} | |||

Quaternary | 303_{4} | |||

Quinary | 201_{5} | |||

Senary | 123_{6} | |||

Octal | 63_{8} | |||

Duodecimal | 43_{12} | |||

Hexadecimal | 33_{16} | |||

Vigesimal | 2B_{20} | |||

Base 36 | 1F_{36} |

Look up in Wiktionary, the free dictionary.fifty-one |

**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 51^{2} + 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number in the UHF bandplan for American terrestrial television since December 31, 2011, when channels 52—69 were withdrawn
- The number of the laps of the Azerbaijan Grand Prix.
- In the 2006 film
*Cars*, 51 was Doc Hudson's number. - The fire station number in the television series
*Emergency!*.

## See also

- AD 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
- Photo 51, an X-ray image of key importance in elucidating the structure of DNA in the 1950s
*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

**^**"Sloane's A000326 : Pentagonal numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-05-30.**^**"Sloane's A005891 : Centered pentagonal numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-05-30.**^**"Sloane's A051870 : 18-gonal numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-05-30.**^**"Sloane's A001608 : Perrin sequence".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-05-30.**^**"Sloane's A001006 : Motzkin numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-05-30.**^**"Sloane's A005528 : Størmer numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-05-30.**^**Sloane, N. J. A. (ed.). "Sequence A000048".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation.**^**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.