*how to find prime numbers*easily. Because we have covered everything you need to know about Prime numbers.

**Contents**

## What does prime number mean?

**Examples :**

## What is Prime Factorization – Calculating Prime Factors

*prime factors*.

#### Factor Tree :

**prime factorization**.

## Finding all prime numbers between 1 to 100 in a simple way

- First arrange numbers in a table like shown in figure.
- Enter 6 numbers in each row until the last number (in this it is 100) reaches.
- First we select a number and we strike off all the numbers divisible by that number.
- Start with 2 which is greater than 1.
- Round off number 2 and strike off entire column until the end.
- Similarly strike off 4th column and 6th column as they are divisible by 2.
- Now round off next number 3 and strike off entire column until end.
- 4 is gone.
- Now round off next number 5 and strike off numbers in inclined fashion as shown in figure (they are divisible by 5). When striking off ends in some row, start again striking off with number in another end which is divisible by 5. new striking off line should be parallel to previous strike off line as shown in figure.
- 6 is gone.
- Now round off number 7 and strike off numbers as we did in case of number 5.
- 8,9,10 are gone.
- Stop at this point. Wonder why do we need to stop??
- We have to do this procedure until we reach square root of bigger number in our numbers. (in this case square root of 100 is 10)
- This technique was developed in 3rd century B.C.

## How to find a prime number

Check whether the given number is divisible by any of the numbers below it except 1.

If it is not divisible by any number then it is prime number.

“Divisible by” means when you divide the whole number with another whole number result should be whole number with remainder zero.

Next check with 3, 5, 7, 11,13…..

Find prime numbers below n and divide p with only those prime numbers below n.Actually, we used the same procedure in the above figure of finding all prime numbers upto 100.

**Ex : 1 – Number is 149**

[square root of 149= 12.20 < 13] prime numbers below 13 are 2,3,5,7,11….

149 is not exactly divisible by 3, because the sum of numbers 1+4+9= 14 is not divisible by 3.

149 is not exactly divisible by 5, because it don’t has 0 or 5 at end.

149 is not exactly divisible by 7,11.

So, 149 is prime number…

**Ex: 2 – number is 631**

[square root of 631= 25.11 < 26] prime numbers below 26 are 2,3,5,7,11,13,17,19,23….

So, 631 is prime number…For easy divisibility checking, you should know the divisibility rules.

### Some Facts on Prime Numbers

**Co Primes: **

If a number N is divisible by two numbers a and b, where a,

b are co primes, then N is divisible by ab.

**Twin Primes:**

If a Number M is a prime number and N is a next prime

number, the average difference between M and N is “ ln(M) ” [natural logarithm

of M]

*2 is the only one prime even number.*

Numbers greater than 1 and which are *non prime numbers* are composite numbers.

Some probabilistic methods are available for checking big prime numbers.

## List of all prime numbers upto 1000

Here is the list of prime numbers upto 1000 for your reference.

Thats all about Prime Numbers.

Generalized divisibility rules