Eratosthenes was a Greek mathematician who invented a method for finding prime numbers called Eratosthenes' Sieve. The method involves starting with a list of consecutive integers from 2 to a specified number and systematically removing multiples of primes, leaving the primes. Specifically, beginning with the number 2, all multiples of 2 are crossed out, then all multiples of 3 are crossed out, and so on. The numbers that remain uncovered are the prime numbers within the selected range. This simple and effective method is still used today to identify prime numbers.