61 (number)
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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 | 1111012 | |||
| Ternary | 20213 | |||
| Quaternary | 3314 | |||
| Quinary | 2215 | |||
| Senary | 1416 | |||
| Octal | 758 | |||
| Duodecimal | 5112 | |||
| Hexadecimal | 3D16 | |||
| Vigesimal | 3120 | |||
| Base 36 | 1P36 | |||
61 (sixty-one) is the natural number following 60 and preceding 62.
In mathematics
61 is:
- the 18th prime number.
- a twin prime with 59.
- a cuban prime of the form p = x3 − y3/x − y, where x = y + 1.[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 − 1/10 times).[2]:166
- the exponent of the 9th Mersenne prime.[3] (261 − 1 = 2,305,843,009,213,693,951)
- the sum of two squares, 52 + 62.
- a centered square number.[4]
- a centered hexagonal number.[5]
- a centered decagonal number.[6]
- 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.[7]
- 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...[8]
- 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[9] (namely 6,469,693,291; 7,420,738,134,871; and 1,922,760,350,154,212,639,131).
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 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
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 (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[10]
- The maximum number of tables that can be joined in a single MariaDB or MySQL query[11]
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.
- ↑ "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
External links
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