Sieve of Eratosthenes

# Sieve of Eratosthenes

## Sieve of Eratosthenes

Eratosthenes, a Greek mathematician, gave a simple method of finding prime and composite numbers. This method is known as the Sieve of Eratosthenes.

Using the method of Sieve of Eratosthenes, we can find the prime numbers and the composite numbers between 0 and any number.

In this article, we will learn how to find the prime numbers and the composite numbers between 0 and 100. Using this method, we can also find the prime numbers and composite numbers between 100 and 200, between 200 and 300, between 300 and 400, or between 400 and 500.

## How to Find Prime Numbers between 1 and 100?

1. Write numbers up to 100 except 1 which is neither prime nor composite.

2. Encircle 2 and cross out all other multiples of 2.

3. Encircle 3 and cross out all other multiples of 3.

4. Encircle 5 and cross out all other multiples of 5.

5. Encircle 7 and cross out all other multiples of 7.

6. Continue this process till every number is either encircled or crossed out.

All the encircled numbers so obtained are prime numbers.

Thus, the prime numbers less than 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.

The remaining numbers between 0 and 100 are composite numbers except 1.

1 is neither prime nor composite number.

It may be observed that there is no pattern in the occurrence of prime numbers and as such no formula has been found so far to find prime numbers. Thus, the only way to find whether the given number is prime or not is to find if it has any factor other than 1 and itself.

## Prime Numbers between 0 and 100

There are 25 prime numbers lie between 0 and 100, which are as follows:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97

## Prime Numbers between 100 and 200

There are 21 prime numbers lie between 100 and 200, which are as follows:

101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197 and 199

## Prime Numbers between 200 and 300

There are 16 prime numbers lie between 200 and 300, which are as follows:

211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283 and 293

## Prime Numbers between 300 and 400

There are 16 prime numbers lie between 300 and 400, which are as follows:

307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389 and 397

## Prime Numbers between 400 and 500

There are 17 prime numbers lie between 300 and 400, which are as follows:

401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491 and 499

## Prime Numbers between 0 and 500

There are 95 prime numbers lie between 0 and 500, which are as follows:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491 and 499

Important Topics:

Prime Factorization

Factorization

Natural Numbers

Whole Numbers

Integers

Rational Numbers

Irrational Numbers