31 (number)
Encyclopedia : 3 : 31 : 31N : 31 (number)
31 (thirty-one) is the natural number following 30 and preceding 32.
| Cardinal | 31 thirty-one |
| Ordinal | 31st thirty-first |
| Factorization | prime |
| Roman numeral | XXXI |
| Binary | 11111 |
| Hexadecimal | 1F |
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 fourth lucky 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; the factorisations of the first two are:
- 333333331 = 17*19607843
- 3333333331 = 673*4952947
In science
- The atomic number of gallium
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.
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)
- A type of game played on a backgammon board
- The number of flavors of Baskin Robbins ice cream
- In Star Trek, the name of Section 31, a secret police shadow organization of the Federation
- ISO 31 is the ISO's standard for quantities and units
- In Family Guy, the Griffin house number on Spooner Street
- In the title of the anime Ulysses 31
- In the title of Nick Hornby's book 31 Songs
- The jersey number of famed NHL goaltender Curtis "CuJo" Joseph, who currently plays for the Phoenix Coyotes
- Turkish slang for masturbation ("otuzbir")
Historical years
31 A.D., 31 B.C., 1931, 2031, etc.
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