Thirty-one

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Thirty-one is the natural number that follows after 30 and comes before 32.

Math

It's the 11th prime number, after 29th and before 37.
It is a permutable cousin with 13 (since by changing the position of numbers you get another prime number).
Form a pair of twin prime numbers along with 29.
31 is the third prime number of Mersenne (2 ⁵ - 1).
It is the exponent of the 8th cousin of Mersenne M8 = M 31 = 2 31 - 1.
31 is related to the perfect number 496 as 496 = 2 ^{(5 - 1)} (22) ⁵ - 1).
It's a lucky number.
It's the 5th happy cousin number.
Numbers 31, 331, 3331, 33331, 333331, 33331 and 33333331 are all cousins. For a while it was thought that each number of the 3w1 form would be a cousin. However, the following nine numbers of the sequence are compounded; their factors are:
1. 333333331 = 17 × 19607843
2. 3333333331 = 673 × 4952947
3. 33333333331 = 307 × 108577633
4. 333333333331 = 19 × 83 × 211371803
5. 333333333333331 = 523 × 3049 × 2090353
6. 33333333333331 = 607 × 1511 × 1997 × 18199
7. 33333333333333331 = 181 × 1841620626151
8. 3333333333333331 = 199 × 16750418760469 and
9. 33333333333333331 = 31 × 1499 × 717324094199.
Belfegor's number is a 31-digit prime number.
It forms a triplet of sexy prime numbers (31, 37, 43).
It can be expressed as the sum of four squares of integers: 5 ² + 2 ² + 1 ² + 1² (theorem of the four squares). This is a property of any positive integer.
Tenth regular cousin.
It's a self-number.

It's a centered pentagonal number.

The months January, March, May, July, August, October and December have 31 days each.
Object of Messier M31, is also known as the Andromeda galaxy which is the closest galaxy to the Milky Way.
Object of the New General Catalogue NGC 31 is a spiral galaxy in the constellation of the Phoenix.
(31) Euphrosyne is an asteroid belonging to the asteroid belt.

Mikoyán MiG-31 is a hunter designed for the air intercept mission and tactical escort of bomber planes.

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