31 (number)

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

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 4th lucky prime and the 11th supersingular prime.

31 is a centered triangular number, the lowest prime centered pentagonal number and a centered decagonal number.

For the Steiner tree problem, 31 is the number of possible Steiner topologies for Steiner trees with 4 terminals.

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; their factorisations are:

Thirty-one (card game)

Thirty-one (French Trente et un) is a gambling card game played by two to seven people, where players attempt to assemble a hand which totals 31. Such a goal has formed the whole or part of various games like Commerce, Cribbage, Trentuno, and Wit and Reason since the 15th century.

The game is also known as Big Tonka, Nickel Nock, Blitz, Clinker, Klinker, Skat, Cadillac in south Louisiana and Mississippi, Cad in Pennsylvania, Whammy! in central Indiana, and as Skedaddle, Snip Snap Snoop, Schnautz and Schnitzel in other countries.

Object

The object is to obtain a hand with a value total as close as possible to 31, from which the name of the game is taken. The game is usually best played with at least four players.

Details of play

Thirty-one uses a standard deck of 52 playing cards. Aces are high, counting 11, face cards count 10, and all other cards count face value. Each player gets a hand of three cards. The rest of the deck sits in the middle of the table as stock for the game, and the top card of the stock is turned over to begin the discard. Players keep track of how many games they have lost by folding the corners of a five-dollar note. The five-dollar note is also their stake in the game. This can be substituted with other denominations or currency.

31 (disambiguation)

Thirty-one or 31 may refer to: