31 (number)
From Wikipedia, the free encyclopedia
| 31 | |
|---|---|
| Cardinal | thirty-one |
| Ordinal | 31st (thirty-first) |
| Factorization | prime |
| Divisors | 1, 31 |
| Roman numeral | XXXI |
| Binary | 111112 |
| Octal | 378 |
| Duodecimal | 2712 |
| Hexadecimal | 1F16 |
 |
Look up thirty-one in Wiktionary, the free dictionary. |
31 (thirty-one) is the natural number following 30 and preceding 32.
Contents |
[edit] In mathematics
Thirty-one is the third Mersenne prime ( 25 - 1 ) as well as the fourth primorial prime, and together with twenty-nine, another primorial prime, it comprises a twin prime. As a Mersenne prime, 31 is related to the perfect number 496, since 496 = 25 - 1 ( 25 - 1). 31 is the eighth Mersenne prime exponent. 31 is also the 4th lucky prime and the 11th supersingular prime.
31 is a centered triangular number, a centered pentagonal number and centered decagonal number.
At 31, the Mertens function sets a new low of -4, a value which is not subceded until 110.
No integer added up to its base 10 digits results in 31, making 31 a self number.
31 is a repdigit in base 5 (111), and base 2 (11111).
The numbers 31, 331, 3331, 33331, 333331, 3333331, and 33333331 are all prime. For a time it was thought that every number of the form 3w1 would be prime. However, the next nine numbers of the sequence are composite; their factorisations are:
- 333333331 = 17*19607843
- 3333333331 = 673*4952947
- 33333333331 = 307*108577633
- 333333333331 = 19*83*211371803
- 3333333333331 = 523*3049*2090353
- 33333333333331 = 607*1511*1997*18199
- 333333333333331 = 181*1841620626151
- 3333333333333331 = 199*16750418760469
- 33333333333333331 = 31*1499*717324094199
The recurrence of the factor 31 in the last number above can be used to prove that no sequence of the type RwE or ERw can consist only of primes because every prime in the sequence will periodically divide further numbers. Here, 31 divides every fifteenth number in 3w1 (and 331 every 110th).
[edit] In science
- The atomic number of gallium
[edit] Astronomy
- Messier object M31, a magnitude 4.5 galaxy in the constellation Andromeda. It is also known as the Andromeda Galaxy, and is readily visible to the naked eye in a modestly dark sky.
- The New General Catalogue object NGC 31, a spiral galaxy in the constellation Phoenix
- The Saros number of the solar eclipse series which began on -1805 January 31 and ended on -489 March 31. The duration of Saros series 31 was 1316.2 years, and it contained 74 solar eclipses.
- The Saros number of the lunar eclipse series which began on -1774 May 30 and ended on -476 July 17. The duration of Saros series 31 was 1298.1 years, and it contained 73 lunar eclipses.
[edit] In sports
The jersey number 31 was retired for Baseball Hall of Famer Dave Winfield and by the Indiana Pacers for Shooting guard Reggie Miller.
NASCAR driver Jeff Burton drives #31, a car which was subject to a controversy when one of the sponsors changed its name after merging with another company.
Ice hockey goaltenders (typically backups) use 31 when 30 is taken.
[edit] In other fields
Thirty-one is also:
- The number of days in the months January, March, May, July, August, October and December
- The code for international direct-dial phone calls to the Netherlands
- A type of card game (see Thirty-one (game))[1]
- A type of game played on a backgammon board
- The number of flavors of Baskin-Robbins ice cream and the shops are called 31 Ice Cream in Japan
- ISO 31 is the ISO's standard for quantities and units
- In the title of the anime Ulysses 31
- In the title of Nick Hornby's book 31 Songs
- Turkish slang for masturbation ("otuzbir")
- A women's honorary at The University of Alabama (XXXI)
- The number of the French department Haute-Garonne
- In music, 31-tone equal temperament is a historically significant tuning system (31 equal temperament), first theorized by Christian Huygens and promulgated in the 20th century by Adriaan Fokker
[edit] Historical years
31 A.D., 31 B.C., 1931, 2031, etc.
[edit] References
- ^ Room, Adrian. The Guinness Book of Numbers Middlesex: Guinness Publishing Ltd. (1989): 128
- Prime Curios! 31 from the Prime Pages
