3

The number 3 is a natural number, the third positive integer, coming after 2 and before 4. In the decimal system it is written as the digit 3, and it appears in many other numeral systems with distinct symbols. In mathematics, 3 is notable for being the smallest odd prime and the second prime overall, and it can be expressed as 2^2 − 1, making it a Mersenne prime.

In number theory, 3 is also a triangular number, equal to T2 in the sequence Tn = n(n+1)/2. It is a Fibonacci number, appearing in the sequence 1, 1, 2, 3, 5, …, where 3 is F4. Additionally, 3 is a Fermat prime, since 3 = 2^(2^0) + 1.

In geometry and science, three is associated with the triangle, the simplest polygon with three sides and three interior angles. The concept of three dimensions is a common model of space in classical physics and everyday perception, and ternary systems use base 3 in contrast to the more widespread base-2 binary systems.

Culturally and linguistically, the number 3 appears in many traditions and motifs, such as triplets and triads, and in religious symbolism like the Holy Trinity. In music, a triad is a three-note chord; in literature and folklore, thirds and triads often structure motifs and groupings.

Numeral representations include Roman numerals III, and in positional numeral systems: binary 11, decimal 3, and ternary 10.