31 (number)

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← 30 32 → 31
← 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	thirty-one
Ordinal	31st (thirty-first)
Factorization	prime
Divisors	1, 31
Roman numeral	XXXI
Binary	11111
Hexadecimal	1F

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

Look up thirty-one in
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1 In mathematics
2 In science
- 2.1 Astronomy
3 In sports
4 In other fields
5 Historical years
6 References

[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 4th lucky prime and the 11th supersingular 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; their factorisations are:

333333331 = 17*19607843
3333333331 = 673*4952947
33333333331 = 307*108577633
333333333331 = 19*83*211371803
3333333333331 = 523*3049*2090353
33333333333331 = 607*1511*1997*18199
333333333333331 = 181*1841620626151
3333333333333331 = 199*16750418760469
33333333333333331 = 31*1499*717324094199

The recurrence of the factor 31 in the last number above can be used to prove that no sequence of the type R_wE or ER_w can consist only of primes because every prime in the sequence will periodically divide further numbers. Here, 31 divides every fifteenth number in 3_w1 (and 331 every 110th).

[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 shirt number of Bayern Munich midfielder Bastian Schweinsteiger
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 Baseball 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
the jersey number of Phoenix Suns forward Shawn Marion
The jersey number for Cleveland Browns Running Back Jamal Lewis
The car number of NASCAR driver Jeff Burton
The jersey number of San Diego Chargers' defensive back Antonio Cromartie.
The old jersey number of Dallas Cowboys safety Roy Williams, before switching to 38.
The jersey number of retired Melbourne and Cartlon great Ron Barassi.
The jersey number of Retired Green Bay Packers Fullback Jim Taylor

[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))^[1]
A type of game played on a backgammon board
The number of flavors of Baskin Robbins ice cream and the shops are called 31 Ice Cream in Japan
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 the title of the anime Ulysses 31
In the title of Nick Hornby's book 31 Songs
Turkish slang for masturbation ("otuzbir")
A women's honorary at The University of Alabama (XXXI)