To find prime number from 1 to 100 by Eratosthener sieve method
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Prime Numbers: How to Find Them with the Sieve of Eratosthenes
A prime number is one which is only divisible by 1 and itself. It’s as simple as that; the downside is that there’s no mathematical formula to make sure whether a number is prime or not.
Think of a high number like 191,587. We don’t have the formula to determine whether or not it’s prime!
We have to find out if it has any divisors, and is therefore composite. In this case, we would discard it as a prime number.
It’s easy to check if the first few prime numbers (2, 3, 5, 7, 11) have divisors using the help of divisibility criteria. But it’s not so easy for larger numbers.
Imagine having to check all the divisors of such a large number! It would be crazy!
The Sieve of Eratosthenes
The Greek mathematician Eratosthenes (3rd-century B.C.E) designed a quick way to find all the prime numbers. It’s a process called the Sieve of Eratosthenes. We’re going to see how it works by finding all the prime numbers between 1 and 100.
The idea is to find numbers in the table that are multiples of a number and therefore composite, to discard them as prime. The numbers that are left will be prime numbers.
The Sieve of Eratosthenes stops when the square of the number we are testing is greater than the last number on the grid (in our case 100).
Since 112 = 121 and 121>100, when we get to the number 11, we can stop looking.
Prime numbers between 1 and 100 with the Sieve of Eratosthenes
We start by placing the numbers from 1 to 100 in a table like this. This way it’s very easy to see the patterns that the multiples of each number make. We highlight the 1, which is not a prime number.
prime numbers
First, we look for the multiples of 2 and highlight them (leaving the 2, since we know it only has divisors of 1 and 2 and is therefore prime). All the highlighted numbers will be composite. Have you seen the lovely pattern that the even numbers make?
Now, from the numbers that are left, we look for the multiples of 3 and highlight them (except for 3, since it’s prime). An easy way to do it is by counting in threes. We get another interesting pattern when we’re done.
prime numbers
Now it’s time to look for the multiples of 5. We don’t need to look for the multiples of 4, because all the multiples of 4 are also multiples of 2, so we’ve already highlighted them. It’s easy to find the multiples of 5, they all end in either 0 or 5. We don’t highlight the 5, because it’s prime.
prime numbers
Let’s move on to the multiples of 7 (6 = 2 x 3 and we’ve already found the multiples of 2 and 3). We don’t highlight the 7 since it’s prime.
prime numbers
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