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- the 18th prime number.
- a twin prime with 59.
- a cuban prime of the form p = x3 − y3/, where x = y + 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/ times).:166
- the exponent of the 9th Mersenne prime. (261 − 1 = 2,305,843,009,213,693,951)
- the sum of two squares, 52 + 62.
- a centered square number.
- a centered hexagonal number.
- a centered decagonal number.
- 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.
- 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...
- palindromic in bases 6 (1416) and 60 (1160)
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).
- 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
- 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
- The number of the laps of the first Formula One night race, Singapore Grand Prix.
- R. Crandall and C. Pomerance (2005). Prime Numbers: A Computational Perspective. Springer, NY, 2005, p. 79.
- "Sloane's A002407 : Cuban primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- Dickson, L. E., History of the Theory of Numbers, Volume 1, Chelsea Publishing Co., 1952.
- "Sloane's A000043 : Mersenne exponents". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- "Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- "Sloane's A003215 : Hex (or centered hexagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- "Sloane's A062786 : Centered 10-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- "Sloane's A063980 : Pillai primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- "Sloane's A007629 : Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- "Sloane's A005235 : Fortunate numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- 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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