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Eratosthenes, an ancient Greek Mathematician, developed a simple algorithm for finding prime numbers less than a desired number.

* Draw a table of all numbers less than the desired number n

* Draw a circle around the number 2 and cross out all the multiples of 2.

* Circle the next number not crossed out (this is a prime number) - cross out all the multiples of this number

* Repeat the last step until you have circled a number greater than the square root of n

* Draw a circle around the number 2

** Square 2 giving 4, then starting at 4, cross out every second number

* Circle the next number not crossed out (this is a prime number) and call it "p"

** Square p, giving EQN:p^2 and starting from there, cross out every EQN:p^{th} number

* Repeat the last step until the square is larger than n

All the remaining uncrossed numbers are also prime numbers.