Prime numbers have all sorts of remarkable and mysterious properties.
Evenly divisible only by themselves and 1, primes can’t be written as the product of smaller positive integers. There are infinitely many of them, and they appear to be scattered somewhat haphazardly among the whole numbers.
It’s not yet known if there are infinitely many twin primes—pairs of primes that are only 2 apart. Or whether every even integer greater than 2 can be written as the sum of two primes. Or whether there’s always a prime between n2 and (n + 1)2. But it is known that there’s always a prime between n and 2n.