31

31 is the natural number that follows 30 and precedes 32. It is an odd prime, the eleventh prime number. In modular arithmetic it is congruent to 3 modulo 4. In various numeral systems, 31 is represented as 11111 in binary, 1011 in base 3, and 37 in base 8; in Roman numerals it is XXXI.

Mathematically, 31 is a Mersenne prime since 31 = 2^5 − 1, placing it among primes of the form 2^p − 1 with p prime. It is not a safe prime, because (31 − 1)/2 = 15 is not prime. The number often serves as a compact example of a small prime with multiple base representations and simple arithmetic properties.

Calendrically, seven months have 31 days: January, March, May, July, August, October, and December.

In science, 31 is the atomic number of gallium (Ga) on the periodic table. Gallium is a soft post-transition metal discovered in 1875 by Paul-Émile Lecoq de Boisbaudran and named after Gaul (France). It has a low melting point for a metal and is widely used in semiconductors and high-temperature applications.

In culture and games, 31 appears in various contexts, such as the traditional card game commonly called 31. The number also appears in media titles and numerological references, reflecting its role as a simple, well-known prime.