A prime number is only divisible by 1 and itself. The first primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...
There are infinitely many primes (proven by Euclid). The largest known prime has over 41 million digits.
Test divisibility by all integers from 2 to √n. If none divide evenly, it's prime.