Thirty-one

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.

Chemistry

• It is the atomic number of the gallon (Ga).

Astronomy

• 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.

Military technology

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