Sixty-one is the smallest proper prime, a prime p which ends in the digit 1in 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/ times).:166
61 is 9th Mersenne prime exponent. (261 − 1 = 2,305,843,009,213,693,951)
It is the sixth Euler zigzag number (or Up/down number).
Since 8! + 1 is divisible by 61 but 61 is not one more than a multiple of 8, 61 is a Pillai prime. In the list of Fortunate numbers, 61 occurs thrice, since adding 61 to either the tenth, twelfth or seventeenth primorial gives a prime number (namely 6,469,693,291; 7,420,738,134,871; and 1,922,760,350,154,212,639,131).
It is also 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...
- The chemical element with the atomic number 61 (promethium), a lanthanide, is the element with the secondary lowest ordinal number that does not possess any stable isotopes. The promethium preceding element with atomic number 60 (neodymium) and the promethium following element 62 (samarium) have all stable isotopes.
- 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 Pisces
- The Saros number of the solar eclipse series which began on -973 May 10 and ended on 289 June 5. The duration of Saros series 61 was 1262.1 years, and it contained 71 solar eclipses.
- The Saros number of the lunar eclipse series which began on -870 October 20 and ended on 609 March 26. The duration of Saros series 61 was 1478.4 years, and it contained 83 lunar eclipses.
- 61 Ursae Majoris is located about 31.1 light-years from Sol.
- 61 Cygni was christened the "Flying Star" in 1792 by Giuseppe Piazzi (1746–1826) for its unusually large proper motion. 
In other fields
- 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 (film) 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 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 Citadel cadets on The Summerall Guards
- The number of points required to win a "standard" game of Cribbage
- The maximum number of tables that can be joined in a single MariaDB or MySQL query
- 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
- R. Crandall and C. Pomerance (2005). Prime Numbers: A Computational Perspective. Springer, NY, 2005, p. 79.
- Dickson, L. E., History of the Theory of Numbers, Volume 1, Chelsea Publishing Co., 1952.
- Hoyle, Edmund Hoyle's Official Rules of Card Games pub. Gary Allen Pty Ltd, (2004) p. 470
- MySQL Reference Manual – Limits of Joins
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