# 61 (number)

From HandWiki

__: Natural number__

**Short description**
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---|---|---|---|---|

Cardinal | sixty-one | |||

Ordinal | 61st (sixty-first) | |||

Factorization | prime | |||

Prime | 18th | |||

Divisors | 1, 61 | |||

Greek numeral | ΞΑ´ | |||

Roman numeral | LXI | |||

Binary | 111101_{2} | |||

Ternary | 2021_{3} | |||

Quaternary | 331_{4} | |||

Quinary | 221_{5} | |||

Senary | 141_{6} | |||

Octal | 75_{8} | |||

Duodecimal | 51_{12} | |||

Hexadecimal | 3D_{16} | |||

Vigesimal | 31_{20} | |||

Base 36 | 1P_{36} |

**61** (**sixty-one**) is the natural number following 60 and preceding 62.

## In mathematics

**61** is:

- the 18th prime number.
- a twin prime with 59.
- a cuban prime of the form
*p*=*x*^{3}−*y*^{3}/*x*−*y*, where*x*=*y*+ 1.^{[1]} - the smallest
*proper prime*, a prime*p*which ends in the digit 1 in base 10 and whose reciprocal in base 10 has a repeating sequence with length*p*− 1. In such primes, each digit 0, 1, ..., 9 appears in the repeating sequence the same number of times as does each other digit (namely,*p*− 1/10 times).^{[2]}^{:166} - the exponent of the 9th Mersenne prime.
^{[3]}(2^{61}− 1 = 2,305,843,009,213,693,951) - the sum of two squares, 5
^{2}+ 6^{2}. - a centered square number.
^{[4]} - a centered hexagonal number.
^{[5]} - a centered decagonal number.
^{[6]} - the sixth Euler zigzag number (or Up/down number).
- a unique prime in base 14, since no other prime has a 6-digit period in base 14.
- a Pillai prime since 8! + 1 is divisible by 61 but 61 is not one more than a multiple of 8.
^{[7]} - a Keith number, because it recurs in a Fibonacci-like sequence started from its base 10 digits: 6, 1, 7, 8, 15, 23, 38, 61...
^{[8]} - palindromic in bases 6 (141
_{6}) and 60 (11_{60})

In the list of Fortunate numbers, 61 occurs thrice, since adding 61 to either the tenth, twelfth or seventeenth primorial gives a prime number^{[9]} (namely 6,469,693,291; 7,420,738,134,871; and 1,922,760,350,154,212,639,131).

## In science

- The chemical element with the atomic number 61 is promethium.

### Astronomy

- Messier object M61, a magnitude 10.5 galaxy in the constellation Virgo
- The New General Catalogue object NGC 61, a double spiral galaxy in the constellation Cetus
- 61 Ursae Majoris is located about 31.1 light-years from the Sun. [1]
- 61 Cygni was christened the "Flying Star" in 1792 by Giuseppe Piazzi (1746–1826) for its unusually large proper motion. [2]

## In other fields

**Sixty-one** is:

- The number of the French department Orne
- The code for international direct dial phone calls to
*Australia* *61**, a 2001 baseball movie directed by Billy Crystal*Highway 61 Revisited*is a Bob Dylan album- The Highway 61 Blues Festival occurs annually in Leland, Mississippi
*Highway 61*is a 1991 film set on U.S. Route 61- U.S. Route 61 is the highway that inspired so much attention on "Highway 61"
- Part 61 is a law created by the FAA regarding medical exams. This law has often come under attack by AOPA.
- The P-61 is the Northrop-designed fighter first designated as the XP-61. It first flew on May 26, 1942. It is also known as the
*Black Widow*as it was the first fighter aircraft designed to be a night fighter - Sixty 1 is a brand tobacco produced by Nationwide Tobacco
- 61A is the London address of Margot Wendice (Grace Kelly) and Tony Wendice (Ray Milland) in the movie
*Dial M for Murder* - 1 Liberty Place is Philadelphia's tallest building at 61 stories
- The number of cadets on The Summerall Guards
- The number of points required to win a "standard" game of cribbage
^{[10]} - The maximum number of tables that can be joined in a single MariaDB or MySQL query
^{[11]}

## In sports

- New York Yankees right fielder Roger Maris hit 61 home runs in 1961, breaking Babe Ruth's single-season record until it was surpassed in 1998 by Mark McGwire and Sammy Sosa.
- Nolan Ryan and Tom Seaver each had 61 career shutouts
- Hockey great Wayne Gretzky holds or shares 61 NHL records (40 for regular season, 15 for Stanley Cup playoff, and 6 for All-Star Games)
- Rotation, a variation of pool, is sometimes called 61
- Richie Evans' NASCAR Whelen Modified Tour car number was 61 until his death in 1985
- The number of the laps of the first Formula One night race, Singapore Grand Prix.

## References

- R. Crandall and C. Pomerance (2005).
*Prime Numbers: A Computational Perspective*. Springer, NY, 2005, p. 79.

- ↑ "Sloane's A002407 : Cuban primes". OEIS Foundation. https://oeis.org/A002407.
- ↑ Dickson, L. E.,
*History of the Theory of Numbers*, Volume 1, Chelsea Publishing Co., 1952. - ↑ "Sloane's A000043 : Mersenne exponents". OEIS Foundation. https://oeis.org/A000043.
- ↑ "Sloane's A001844 : Centered square numbers". OEIS Foundation. https://oeis.org/A001844.
- ↑ "Sloane's A003215 : Hex (or centered hexagonal) numbers". OEIS Foundation. https://oeis.org/A003215.
- ↑ "Sloane's A062786 : Centered 10-gonal numbers". OEIS Foundation. https://oeis.org/A062786.
- ↑ "Sloane's A063980 : Pillai primes". OEIS Foundation. https://oeis.org/A063980.
- ↑ "Sloane's A007629 : Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers)". OEIS Foundation. https://oeis.org/A007629.
- ↑ "Sloane's A005235 : Fortunate numbers". OEIS Foundation. https://oeis.org/A005235.
- ↑ Hoyle, Edmund
*Hoyle's Official Rules of Card Games*pub. Gary Allen Pty Ltd, (2004) p. 470 - ↑ MySQL Reference Manual – JOIN clause

## External links

Original source: https://en.wikipedia.org/wiki/61 (number).
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