31st

← 30 31 32 →
← 30 31 32 33 34 35 36 37 38 39 → List of numbers — Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	thirty-one
Ordinal	31st (thirty-first)
Factorization	prime
Divisors	1, 31
Greek numeral	ΛΑ´
Roman numeral	XXXI
Binary	111112
Ternary	10113
Quaternary	1334
Quinary	1115
Senary	516
Octal	378
Duodecimal	2712
Hexadecimal	1F16
Vigesimal	1B20
Base 36	V36

31 (thirty-one) is the natural number following 30 and preceding 32.

31 is the number of regular polygons with an odd number of sides that are known to be constructible with compass and straightedge.

31 is the third Mersenne prime (2⁵ − 1) and the eighth Mersenne prime exponent, as well as the fourth primorial prime, and together with twenty-nine, another primorial prime, it comprises a twin prime. As a Mersenne prime, 31 is related to the perfect number 496, since 496 = 2^{(5 − 1)}(2⁵ − 1). 31 is also the 4th lucky prime and the 11th supersingular prime.

31 is a centered triangular number, the lowest prime centered pentagonal number and a centered decagonal number.

For the Steiner tree problem, 31 is the number of possible Steiner topologies for Steiner trees with 4 terminals.

At 31, the Mertens function sets a new low of −4, a value which is not subceded until 110.

No integer added up to its base 10 digits results in 31, making 31 a self number.

31 is a repdigit in base 5 (111), and base 2 (11111).

The numbers 31, 331, 3331, 33331, 333331, 3333331, and 33333331 are all prime. For a time it was thought that every number of the form 3_w1 would be prime. However, the next nine numbers of the sequence are composite; their factorisations are:

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