31 (number)

31 is the natural number following 30 and preceding 32.

List of numbers — Integers << 30 31 32 33 34 35 36 37 38 39 >>
Cardinal	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 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 and a centered pentagonal 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 other fields

Thirty-one is also:

• The atomic number of gallium.
• 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

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