Sieve of Eratosthenes: the algorithm for finding the prime numbers in a list; remove the multiples of the smaller prime numbers

The Greek mathematician ERATOSTENE (275 - 194 BC) has applied an easy method to determine whether the numbers in a list are prime or not. Starting from the known small prime numbers, 2, 3, 5, 7, 11, 13, 17, 21, etc. it is clear that all their multiples are not prime but composed. He has ordered a list of natural numbers in ascending order and then he removed all the multiples of the first prime numbers to identify the rest of the larger prime numbers in that list. We will exemplify this method below on a list of numbers ranging from 2 to 100:

What is a prime number?

What is a composite number?

Prime numbers up to 1,000

Prime numbers up to 10,000

Sieve of Eratosthenes

Euclid's algorithm

Simplifying ordinary (common) math fractions (reducing to lower terms): steps to follow and examples