61 (number)

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 (141₆) and 60 (11₆₀). 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

See also: List of highways numbered 61

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

References

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

External links

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