Английская Википедия:61 (number)
Шаблон:For Шаблон:Infobox 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>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>p = \frac {x^{3} - y^{3}}{x - y}</math> where <math>x = y + 1</math>,[4] and the forth Pillai prime since <math>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>p</math> which ends in the digit 1 in decimal and whose reciprocal in base-10 has a repeating sequence of length <math>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>\tfrac {p-1}{10}</math> times).[7]Шаблон:Rp
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).
61 is the exponent of the ninth Mersenne prime, <math>M_{61} = 2^{61} - 1 = 2,305,843,009,213,693,951</math>[9] and the next candidate exponent for a potential fifth double Mersenne prime: <math>M_{M_{61}} = 2^{2305843009213693951} - 1 \approx 1.695 \times 10^{694127911065419641}.</math>[10]
The exotic sphere <math>S^{61}</math> is the last odd-dimensional sphere to contain a unique smooth structure; <math>S^{1}</math>, <math>S^{3}</math> and <math>S^{5}</math> are the only other such spheres.[11][12]
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
Шаблон:Seealso 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[13]
- The maximum number of tables that can be joined in a single MariaDB or MySQL query[14]
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.
External links
Шаблон:Wiktionary Шаблон:Commons category
- ↑ Шаблон:Cite web
- ↑ Шаблон:Cite web
- ↑ Шаблон:Cite web
- ↑ Шаблон:Cite web
- ↑ Шаблон:Cite web
- ↑ Шаблон:Cite web
- ↑ Dickson, L. E., History of the Theory of Numbers, Volume 1, Chelsea Publishing Co., 1952.
- ↑ Шаблон:Cite web
- ↑ Шаблон:Cite web
- ↑ Шаблон:Cite web
- ↑ Шаблон:Cite journal
- ↑ Шаблон:Cite OEIS
- ↑ Hoyle, Edmund Hoyle's Official Rules of Card Games pub. Gary Allen Pty Ltd, (2004) p. 470
- ↑ MySQL Reference Manual – JOIN clause