
Sieve of Eratosthenes:
This method helps to find out prime numbers up to a given natural number n.
1. The first prime number is 2, leave 2 and round off all the multiples of 2 they are 4,6,8,10,....... the next highest number that is left is 3 and 3 is a prime number.
2. Round off all the multiples of 3. In the remaining numbers which are not being rounded off. They are 9,15,......
The next highest number that is left is 5 and this is also a prime number. Round off all the multiples of 5. By proceeding like this process will end at a stage. Observe all the numbers that are not being rounded off are prime numbers.
Example:
Solution:
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Note: 1 is neither prime nor a composite number.
Directions: Using above method find the prime numbers for the following problems.
1. Find out the prime numbers 100 to 200 natural numbers using the sieve of Eratosthenes.
2. Find out the prime numbers 200 to 300 natural numbers using the sieve of Eratosthenes.
3. Find out the prime numbers 300 to 400 natural numbers using the sieve of Eratosthenes. 