Eratosthenes was a Greek scholar from Cyrene (currentday Libya) who was famous for a number of contributions in not just mathematics. He was a geographer, poet, astronomer, and even an athlete! Eratosthenes was appointed as a librarian of the famed librarian of Alexandria and he was a friend to Archimedes. He is the one who gave us the term 'geograph,' which is the descriptive study of the Earth. Many of his contributions are still widely used today (latitude and longitude, for example), yet, most people have never even heard of him. He was the first Greek to calculate the circumference of the Earth (and was only off by mere miles) as well as the tilt of the Earth's axis. He had a nickname—Beta—which is the second letter of the Greek alphabet—because he supposedly proved himself to be the second best in almost any field. Wow, what a guy!
One of Eratosthenes' contributions in mathematics was in number theory; specifically in prime numbers through what is known as his sieve.
A sieve is a strainer of sorts and what Eratosthenes did was come up with a method for straining out the composite numbers in such a way that all that remained was the primes.
 A prime number is a number that has only two distinct positive factors: 1 and itself. For example, 11 is a prime because its factors are 1 and 11.

 A composite number has positive factors in addition to 1 and itself. So, 8 is a composite number because its factors are 1, 2, 4, and 8.

 The number 1 is neither prime nor composite because it has only ONE factor.
Someone made up a short mnemonic rhyme to go with the making of the Sieve of Eratosthenes (although it isn't quite correct!). It goes like this:
Sift the twos and sift the threes
The Sieve of Eratosthenes
When the multiples sublime
The numbers that remain are prime.
