### What are prime numbers ?

A natural number which has only 2 distinct factors, which are, 1 and the number itself is called a prime number. The property of being prime is called primality.2 is the smallest and the only even prime number.

One is not a prime number. Earlier it was counted as a prime number but since it has only one factor that is 1, it is now excluded from prime numbers.

### Twin prime numbers :

Successive prime numbers(except 2 and 3), which have difference two.

Eg. (3 & 5), (5 & 7), (11 & 13), (59 & 61) etc.

### Mersenne’s prime numbers :

Prime numbers of the form 2

^{n}-1 where n is prime.Example Merssene’s prime numbers of 3 & 7 are prime numbers. 2

^{3}-1=7, 2

^{7}-1=127.

However, all numbers of the form 2

^{n}-1 where n is prime, may not be prime.

For eg, 11 is a prime number but 2

^{11}-1 = 2047, that is not a prime number.

*List of prime numbers from 1 to 1000:*Prime numbers list from 1 to 1000 |

**Test of primality**(whether the given number is prime or not)

**:**

To check if a number is a prime number trial division can be done. the most common and easy way of trial method is to check whether the prime number is a multiple of a number which lies between 2 and √n, where n is the prime number to be checked.

If n is a multiple of any of these integers then it is a composite number, and so not prime; if it is not a multiple of any of these integers then it is prime. Since this method requires trial division till √n, it becomes very lengthy and is not suitable for large numbers.

**Example**To check if 3 is a prime number :

Step I- find numbers between 2 and √3(=1.732)

There are no integers between 2 and √3. Thus 3 is a prime number as it is not a multiple of the numbers between 2 and √3.

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