Since 6, 8, 9, and 10 are multiples of other numbers, you no longer need to worry about those multiples. For example, with a grid of 1 to 100, you would cross out the multiples of 2, 3, 4, 5, 6, 7, 8, 9, and 10, since 10 is the square root of 100.
Eratosthenes put numbers in a grid and then crossed out all multiples of numbers until the square root of the largest number in the grid is crossed out. This algorithm is one of the earliest algorithms ever written. In 200 B.C., Eratosthenes created an algorithm that calculated prime numbers, known as the Sieve of Eratosthenes.
A Mersenne prime is a prime number that can be calculated with the equation 2 n-1. In “Elements,” Euclid solves the problem of how to create a perfect number, which is a positive integer equal to the sum of its positive divisors, using Mersenne primes. Euclid also provides proof of the Fundamental Theorem of Arithmetic - every integer can be written as a product of primes in a unique way. In Book 9 of the “Elements,” Euclid writes that there are infinitely many prime numbers. Euclid’s “Elements,” published about 300 B.C., proved several results about prime numbers. Prime numbers have been studied for thousands of years.
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