31 (number)

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31 (thirty-one) is the natural number following 30 and preceding 32.

← 30 31 32 33 34 35 36 37 38 39 → List of numbers — Integers 0 10 20 30 40 50 60 70 80 90 →
Cardinal	31 thirty-one
Ordinal	31st thirty-first
Factorization	prime
Divisors	1, 31
Roman numeral	XXXI
Binary	11111
Hexadecimal	1F

Contents 1 In mathematics 2 In science 2.1 Astronomy 3 In sports 4 In other fields 5 Historical years

[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 = 2^{5 - 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 3_w1 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

[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 of basketball great and retired Indiana Pacer Reggie Miller

• The jersey number of famed NHL goaltender Curtis "CuJo" Joseph, who currently plays for the Phoenix Coyotes

• Is the jersey number of Hall of Famer Ferguson Jenkins and Greg Maddux

• Is the retired jersey number of Baseball Hall of Famer Dave Winfield

• The jersey number of Hall of Fame NHL Goaltender Grant Fuhr

[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))
• 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
• Turkish slang for masturbation ("otuzbir")
• Jeff Burton's racing #
• 31 Records, a record label

[edit] Historical years

31 A.D., 31 B.C., 1931, 2031, etc.