Chapter 4.7, Problem 33ES

The sieve of Eratosthenes, name after its inventor, the Greek scholar Eratosthenes (276-194 B.C.E.), provides a way to find all prime numbers less han or equal to some fixed number n. To construct it, write out all the integers from 2 to n. Cross out all multiples of 2 except 2 itself, then all multiples of 3 except 3 itself, then all multiples of 5 except 5 itself, and so forth. Continue crossing out the multiples of each successive prime number up to $\sqrt{n}.$ The numbers that are not crossed out are all the prime numbers from 2 to n. Here is a sieve of Eratosthenes that includes the numbers from 2 to 27. The multiples of 2 are crossed out with a /, the multiples of 3 with a\. and the multiples of 5 with a —.

Use the sieve of Eratosthenes to find all prime numbers less than 100.