# What is the Sieve of Eratosthenes?

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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The Sieve of Eratosthenes decants composite numbers, leaving behind the prime numbers.

A  prime number is a positive integer, whose factors are 1 and the number itself. A prime number will always allow only 2 factors.

Let's see how Eratosthenes's sieve works:

We'll write rows with numbers from 1 to 10, 10 to 20,...90 to 100.

1   2   3   4   5   6   7   8   9   10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

.................................................

91 92 93 94 95 96 97 98 99 100

Since 1 is not a prime, we'll take 2 as the first even prime number and then we'll cross out each multiple of 2.

We'll take 3 as the next positive integer prime and we'll cross out it's multiples. Some of the number are already crossed out, since they were the multiples of the prime 2, also.

We'll take the next number, namely 5 and we'll cross out the multiples of 5.

We'll continue to do that until we'll finish all the numbers up to 100. The crossed out numbers are the multiples, the open numbers being the primes.