Prime number

Prime number

The first question of all :

What is a prime number?

Yes!

       A positive integer or a natural number which is greater than 1 and has exactly two factors 1 and itself, is called a Prime number.

     A Prime  number may be defined in another interesting way:

   A prime number is a positive integer greater than 1 which can not be expressed as the product of two smaller positive integers both of which are smaller than that positive integer.

   The family of Prime number starts with 2.

  

These are the prime numbers between 1 and 100.

Here one interesting thing to remember is that, 1 is not a prime number.

Yes, 1 is neither a prime number nor a composite number.

Test of primality:

To check a given number m is prime or not , we have the following steps.

(1) Find the square root of the given number, i.e. √m. Let, n=√m.

(2) now check that , m is divisible by the numbers (2 to n )or not. 

(3) If m is  completely divisible by any one number, then m is a  composite number; otherwise m is a prime number.

As for example,  let , we are to check 17 is prime or not.

Now, √17=4.123(approximately). Let, n=4.

Now, 17 is not divisible by any one of the numbers 2 to 4. So, 17 is a prime number. 

Again, let we are to check the number 16.we see that √16=4, and 16 is divisible by 2,4 .so, it is clear that 16 is a composite number.

There are various prime numbers like Fermat's prime and Mersenne prime.

Fermat's prime: a prime number of the form, 2ᵐ +1, where m= 2ⁿ and 'n' is a positive integer; is called a Fermat's prime. Some known Fermat's prime are: 3, 5, 17,...etc.

Mersenne(Marsenne) prime: It is a specific type of prime number which must be reducible in the form: 2ⁿ -1, where n is a prime number. Some of the known value of n for Mersenne prime are: 2,3,7,..

An interesting fact about prime number is that they are endless. We don't know which is the biggest one member of this family. Till now the biggest prime number :

 the Great Internet Mersenne Prime Search announced that a computer owned by Jonathan Pace in Germantown, Tennessee, discovered a new prime number. At 23,249,425 digits, the number, known as M77232917, is now the largest known prime.

  

 If you find out any incorrect information or know anything more about this , please write it in the comment section!