# 61 (number)

__: 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, and a twin prime with 59. It is the sum of two consecutive squares, [math]\displaystyle{ 5^2 + 6^2. }[/math] It is also a centered decagonal number,^{[1]} a centered hexagonal number,^{[2]} and a centered square number.^{[3]}

61 is the fourth cuban prime of the form [math]\displaystyle{ p = \frac {x^{3} - y^{3}}{x - y} }[/math] where [math]\displaystyle{ x = y + 1 }[/math],^{[4]} and the forth Pillai prime since [math]\displaystyle{ 8! + 1 }[/math] is divisible by 61, but 61 is not one more than a multiple of 8.^{[5]} It is also a Keith number, as it recurs in a Fibonacci-like sequence started from its base 10 digits: 6, 1, 7, 8, 15, 23, 38, 61, ...^{[6]}

61 is a unique prime in base 14, since no other prime has a 6-digit period in base 14, and palindromic in bases 6 (141_{6}) and 60 (11_{60}). It is the sixth up/down or Euler zigzag number.

61 is the smallest *proper prime*, a prime [math]\displaystyle{ p }[/math] which ends in the digit 1 in decimal and whose reciprocal in base-10 has a repeating sequence of length [math]\displaystyle{ p - 1, }[/math] where each digit (0, 1, ..., 9) appears in the repeating sequence the same number of times as does each other digit (namely, [math]\displaystyle{ \tfrac {p-1}{10} }[/math] times).^{[7]}^{:166}

In the list of Fortunate numbers, 61 occurs thrice, since adding 61 to either the tenth, twelfth or seventeenth primorial gives a prime number^{[8]} (namely 6,469,693,291; 7,420,738,134,871; and 1,922,760,350,154,212,639,131).

There are sixty-one **3**-uniform tilings, where on the other hand, there are one hundred and fifty-one **4**-uniform tilings^{[9]} (with 61 the eighteenth prime number, and 151 the thirty-sixth, twice the index value).^{[10]}^{[lower-alpha 1]}

61 is the exponent of the ninth Mersenne prime, [math]\displaystyle{ M_{61} = 2^{61} - 1 = 2,305,843,009,213,693,951 }[/math]^{[15]} and the next candidate exponent for a potential fifth double Mersenne prime: [math]\displaystyle{ M_{M_{61}} = 2^{2305843009213693951} - 1 \approx 1.695 \times 10^{694127911065419641}. }[/math]^{[16]}

The exotic sphere [math]\displaystyle{ S^{61} }[/math] is the last odd-dimensional sphere to contain a unique smooth structure; [math]\displaystyle{ S^{1} }[/math], [math]\displaystyle{ S^{3} }[/math] and [math]\displaystyle{ S^{5} }[/math] are the only other such spheres.^{[17]}^{[18]}

## 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 one of Philadelphia's tallest buildings at 61 stories
- The number of cadets on The Summerall Guards
- The number of points required to win a "standard" game of cribbage
^{[19]} - The maximum number of tables that can be joined in a single MariaDB or MySQL query
^{[20]}

## 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. The American League record was broken 61 years later in 2022, by Aaron Judge.
- 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.

## Notelist

- ↑ Otherwise, there are eleven total
**1**-uniform tilings (the regular and semiregular tilings), and twenty**2**-uniform tilings (where 20 is the eleventh composite number;^{[11]}together these values add to 31, the eleventh prime).^{[10]}^{[12]}The sum of the first twenty integers is the fourth primorial**210**,^{[13]}^{[14]}equal to the product of the first four prime numbers, and 1, whose collective sum generated is 18.

## References

- ↑ "Sloane's A062786 : Centered 10-gonal numbers". OEIS Foundation. https://oeis.org/A062786.
- ↑ "Sloane's A003215 : Hex (or centered hexagonal) numbers". OEIS Foundation. https://oeis.org/A003215.
- ↑ "Sloane's A001844 : Centered square numbers". OEIS Foundation. https://oeis.org/A001844.
- ↑ "Sloane's A002407 : Cuban primes". OEIS Foundation. https://oeis.org/A002407.
- ↑ "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.
- ↑ Dickson, L. E.,
*History of the Theory of Numbers*, Volume 1, Chelsea Publishing Co., 1952. - ↑ "Sloane's A005235 : Fortunate numbers". OEIS Foundation. https://oeis.org/A005235.
- ↑ Sloane, N. J. A., ed. "Sequence A068599 (Number of n-uniform tilings.)". OEIS Foundation. https://oeis.org/A068599. Retrieved 2024-01-07.
- ↑
^{10.0}^{10.1}Sloane, N. J. A., ed. "Sequence A000040 (The prime numbers.)". OEIS Foundation. https://oeis.org/A000040. Retrieved 2024-01-07. - ↑ Sloane, N. J. A., ed. "Sequence A002808 (The composite numbers: numbers n of the form x*y for x > 1 and y > 1.)". OEIS Foundation. https://oeis.org/A002808. Retrieved 2024-01-07.
- ↑ Sloane, N. J. A., ed. "Sequence A299782 (a(n) is the total number of k-uniform tilings, for k equal to 1..n.)". OEIS Foundation. https://oeis.org/A299782. Retrieved 2024-01-07.
- ↑ Sloane, N. J. A., ed. "Sequence A000217 (Triangular numbers: a(n) is the binomial(n+1,2) equal to n*(n+1)/2 or 0 + 1 + 2 + ... + n.)". OEIS Foundation. https://oeis.org/A000217. Retrieved 2024-01-07.
- ↑ Sloane, N. J. A., ed. "Sequence A002110 (Primorial numbers (first definition): product of first n primes. Sometimes written prime(n)#)". OEIS Foundation. https://oeis.org/A002110. Retrieved 2024-01-07.
- ↑ "Sloane's A000043 : Mersenne exponents". OEIS Foundation. https://oeis.org/A000043.
- ↑ "Mersenne Primes: History, Theorems and Lists". https://t5k.org/mersenne/index.html#unknown.
- ↑ Wang, Guozhen; Xu, Zhouli (2017). "The triviality of the 61-stem in the stable homotopy groups of spheres".
*Annals of Mathematics***186**(2): 501–580. doi:10.4007/annals.2017.186.2.3. - ↑ Sloane, N. J. A., ed. "Sequence A001676 (Number of h-cobordism classes of smooth homotopy n-spheres.)". OEIS Foundation. https://oeis.org/A001676. Retrieved 2023-10-22.
- ↑ Hoyle, Edmund
*Hoyle's Official Rules of Card Games*pub. Gary Allen Pty Ltd, (2004) p. 470 - ↑ MySQL Reference Manual – JOIN clause

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

## External links

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