# Prime Numbers : What are Prime Numbers in Mathematics?

### 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 2n-1 where n is prime.Example Merssene’s prime numbers of 3 & 7 are prime numbers. 23-1=7, 27-1=127.
However, all numbers of the form 2n-1 where n is prime, may not be prime.
For eg, 11 is a prime number but 211-1 = 2047, that is not a prime number.

List of prime numbers from 1 to 1000: Prime numbers list from 1 to 1000
What is a prime number

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.