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 = 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

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.

Integers

Gourt Home::Gourt :: 31 (number)

In mathematics

In science

Astronomy

In other fields

Historical years