Number reference
31 explained.
31: thirty-one, prime, mersenne prime; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- thirty-one
- Classification
- prime
- Factors
- 1, 31
- Prime factorization
- 31
- Square root
- 5.567764
- Cube root
- 3.141381
- Binary
- 11111
- Octal
- 37
- Hexadecimal
- 1F
- Roman numeral
- XXXI
- Digit sum
- 4
- Digital root
- 4
What makes 31 notable
- Prime. 31 is prime: it has exactly two divisors, 1 and itself, so it cannot be split into equal whole-number groups any other way.
- Mersenne prime. 31 = 2^5 − 1 and is prime, making it a Mersenne prime. These are the primes that large prime searches concentrate on.
31 in everyday use
Thirty-one days is the length of seven months of the year — January, March, May, July, August, October, and December. Halloween falls on 31 October. It is the atomic number of gallium, a metal that melts in the hand. Baskin-Robbins built its brand on 31 flavours, one for every day of the month. In the game of cribbage the count in a hand stops at 31, and in some card games the phrase "thirty-one" is the winning call.
Thirty-one is a Mersenne prime, 2⁵ − 1, so in binary it is 11111, five ones in a row. It is the sum of the first five powers of two, 1 + 2 + 4 + 8 + 16, and it pairs with 29 as a twin prime. It is also 1 + 5 + 25, a repunit in base 5 as well as base 2, and the eleventh prime. Because it is a Mersenne prime, 2⁴ × 31 = 496 is a perfect number.
Nearby numbers
How to read this page
Because 31 is prime, the factor list stops at 1 and 31 itself, so it cannot be shared into equal whole-number groups. That is also what makes it useful as a building block: every larger number with 31 in its prime factorisation inherits it from here.
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