##### 1The Sieve of Eratosthenes

One method of computing all of the prime numbers less than a certain fixed positive integer \(N\) is to list all of the numbers \(n\) such that \(1 \lt n \lt N\text{.}\) Begin by eliminating all of the multiples of 2. Next eliminate all of the multiples of 3. Now eliminate all of the multiples of 5. Notice that 4 has already been crossed out. Continue in this manner, noticing that we do not have to go all the way to \(N\text{;}\) it suffices to stop at \(\sqrt{N}\text{.}\) Using this method, compute all of the prime numbers less than \(N = 250\text{.}\) We can also use this method to find all of the integers that are relatively prime to an integer \(N\text{.}\) Simply eliminate the prime factors of \(N\) and all of their multiples. Using this method, find all of the numbers that are relatively prime to \(N= 120\text{.}\) Using the Sieve of Eratosthenes, write a program that will compute all of the primes less than an integer \(N\text{.}\)