Eratosthenes, a Greek mathematician from the 3rd century BC, developed a simple sieve method for identifying prime numbers. The method works by sieving out multiples of successive numbers, leaving the prime numbers behind. It involves making a list of consecutive numbers up to a certain number, crossing out numbers that are multiples of 2, then crossing out multiples of 3, and so on, leaving the remaining uncrossed numbers as the prime numbers. The document then proceeds to explain Eratosthenes' sieve method in more detail through 5 steps.

1. The Eratosthenes' SieveBack in 200 BC a Greek mathematician named Eratosthenes developed a simple step-by-step method for determining which numbers are prime. This method is called "Eratosthenes' Sieve".

2. A sieveis a strainer that allows small particles to pass through while catching the larger particles.

3. In the case of Eratosthenes' Sieve, the small particles that pass through are all the non-prime numbers and the large particles that remain are the Prime Numbers.

4. Eratosthenes

5. He was born in Cirene (actually Shahhat, Libia, which is in Africa)He studied in AlexandriaArquimedes was his friendHe died at the age of 80.

6. He was a great mathematician, philosopher, poet and astronomer.People knew him as the second Plato or because he was always second in every subject he studied.

7. His method to find out the prime numbers can be divided into 5 simple steps.

8. But wait a minute, folks!

9. What are Prime Numbers?Numbers Divisible Only by Themselves and 1Any number that has only two factors, itself and 1.

10. Is the number 1 a prime number?No, it isn´t. The number 1 is NOT considered Prime Why?Because it only has one factor , itself.

11. What is a sieve?What can we do with Eratosthenes´ sieve?We can find out which of the numbers from 1 to 100 are primeLet´s do it!

12. The Eratosthenes' Sieve - Step 1Make a table of the numbers 1 to 100 organized into 10 rows

13. The Eratosthenes' Sieve - Step 2 Cross out the number 1 because by definition it is NOT Prime number

14. The Eratosthenes' Sieve - Step 3Circle the number 2 and cross out all the multiples of 2 (or all the even numbers)

15. The Eratosthenes' Sieve - Step 4 Look for the following number that is not crossed out. Circle the number and cross out all the multiples of that number.

16. The Eratosthenes' Sieve - Step 5 Repeat step 4 until you get to the number 7.

17. Finished?All of the circled numbers are PRIME NUMBERS!

18. Now you can watch a simulation of the sieve...Pay attention!