How to Find Prime Numbers?

A prime number is a number that can be divided only by one and the number itself. There are different ways to identify prime numbers and factorization is the easiest way to find out whether a number is prime or not. We can also use properties of certain numbers to find if a given number is prime or not.

We can identify whether a number is prime or not by finding the factors of the given number. For this, we use the factorization method which is the easiest way to find prime numbers. Observe the following steps which show the way to find prime numbers.

• Step 1: Find the factors of the given number and list them.
• Step 2: Check the total number of factors of that number.
• Step 3: If the number has just two factors- one and the number itself, then the given number is a prime number. However, if it has more than two factors, then it is a composite number.

Example 1: Check whether 23 is a prime number or not.
The factors of 23 are 1 and 23; Since it has only two factors, 1 and the number itself, 23 is a prime number.

Example 2: Is 63 a prime number?
The factors of 63 are: 1, 3, 7, 9, 21, 63
Since 63 has more than two factors, therefore, it is not a prime number.

Prime numbers can be identified through many ways. To identify whether a large number is a prime number or not, there are a few methods which can be used:

• If a large number ends with the digits 0, 2, 4, 6 and 8, then it is not a prime number. It is an even number which is easily divided by 2.
• Add the digits of the large number and then divide it by 3. If it is exactly divisible by 3 then the large number is not a prime number.
• If the result of the first two methods is false, take out the square root of the number.
• List all the prime numbers below this square root value and divide the given number by all these listed prime numbers.
• If the number is divided by any of the prime numbers less than its square root value, then it is not a prime number; otherwise, it is prime.
• A large number ending with digit 5 or 0 is not a prime number because it can easily be divided by 5.

The following chart shows the prime numbers upto 200.

Important points

• 2 is the only even number which is prime, all the remaining prime numbers are odd numbers.
• Numbers ending with an even digit are not prime numbers like 252, 324, etc.
• The numbers 1 and 0 are neither prime nor composite.

Related Articles

Check out these interesting articles to know more about how to find prime numbers and its related topics.

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What is the Easiest Way to Find a Prime Number?

The easiest way to identify a prime number is by finding the factors of the given number. If the number has more than two factors, then it is not a prime number. However, if the given number has only two factors - 1 and the number itself, then it is a prime number.

Why is 2 a Prime Number?

2 is a prime number because it has only two factors, that is, 1 and the number 2 itself. It is interesting to note that 2 is the only even prime number.

What are Co-Prime Numbers?

Any two numbers are co-prime if they have only 1 as their common factor. For example, 3 and 5 are said to be co-prime because their only common factor is 1. Co-prime numbers need not be prime numbers. For example, 4 and 9 are also co-prime numbers.

How to Check if a Large Number is Prime or Not?

Prime numbers can be identified through many ways. To identify whether a large number is a prime number or not, there are a few methods which can be used:

• If a large number ends with the digits 0, 2, 4, 6 and 8, then it is not a prime number. It is an even number which can easily be divided by 2.
• Add the digits of the large number and then divide it by 3. If it is exactly divisible by 3 then the large number is not a prime number.
• If the result of the first two methods is false, take out the square root of the number.
• After taking out the square root, list all the prime numbers below this square root value and divide the given number by all these listed prime numbers.
• If the number is divided by any of the prime numbers less than its square root value, then it is not a prime number; otherwise, it is prime.

Can Prime Numbers be Negative?

Since prime numbers are positive integers that are greater than one, they cannot be negative.

What is the Sieve of Eratosthenes?

The sieve of Eratosthenes is an ancient technique to identify the prime numbers up to a given limit. In this technique, we select the smallest prime number from the list of numbers. For example, we have a list of numbers from 2 to 100. Starting with 2, we cross out all the multiples of 2 because all these will not be prime numbers since they are divisible by 2. Then, we proceed to the next number which is not crossed out and find our next prime number. Similarly, we cross off every number which is a multiple of a prime number. Finally, we have a number set in which there are only prime numbers.