3 is the second prime number, and the second single digit prime number. 3's prime factors are 1 and 3. It is said to be the first odd prime, because the previous prime number is 2, which is even.
3 and 7 are four numbers apart, therefore, they are cousin primes.
9, the odd number following 7, is not a prime number. It is a square number, and the first odd composite number.
Usage
General
Trilogy refers to a set of three works of art that are connected, either as a single work or three individual works.
Science
Lithium's atomic number and number of electrons are 3.
Group three elements also have the valence of +3. Similarly, group five elements have the valence of -3.
Tritium / hydrogen-3, has a nucleon number of 3.
Sports
In basketball, a shot behind the three-point arc is worth three points, unless in the 3x3 variant.
In baseball, 3 strikes are required for the player to be considered "out", and 3 outs are required for the attacking team to exchange with the opposing team.
Video Games
In The Legend of Zelda series, there is a sacred relic called Triforce, which consists of three separate golden triangles.