31 (number)

31 is a natural number that lies between 30 and 32 in the sequence of integers. It is used in counting and measurement, and is written with the symbol '31' in the Hindu-Arabic numeral system with base ten (decimal).

The most notable property of 31 is that it is a prime number, meaning it cannot be divided by anything other than 1 and itself. It is the 11th prime number, coming after 29 and before 37.

Mathematical properties

31 and 29 form a pair of twin primes, since their difference is two. Similarly, 31 equals 2 to the power of 5 minus one (2⁵ − 1), making it a Mersenne number. Prime Mersenne numbers are related to perfect numbers.

When written in binary (base two), 31 becomes 11111—five consecutive ones. For this reason it is significant in computer science, particularly in places where five bits are measured.

Calendar use

In the Gregorian calendar, seven months have 31 days: January, March, May, July, August, October, and December. This makes 31 the maximum number of days a month can have in that calendar system.

Other uses

31 is used as a numerical symbol in many systems of notation and coding, such as international telephone numbers, counting units, and game numbers. The meaning assigned to it depends on the convention of the system in which it is used, and is not a property of the number itself.