31 is the natural number following 30 and preceding 32.

In mathematics

Thirty-one is the third Mersenne prime ( 2⁵ - 1 ) as well as a 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.

In science

• The atomic number of gallium

In 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.
• 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
• Historical years: 31 A.D., 31 B.C., or 1931