How can identify prime numbers ?

Find the square root of the number (N)

Divide the number by every prime number from 1 to sqrt(N). We'll call those number p

If Nmodp = 0, then N is not a prime number. That is, if N is evenly divisible by p, then N is not a prime number.

There are other methods that are much faster, but that's the most basic one

Prime numbers are whole numbers that have only two factors which are themselves and one such as 2 3 5 7 11 13 ... etc

Prime numbers are numbers that have only 2 factors: 1 and themselves.

For example, the first 5 prime numbers are 2, 3, 5, 7, and 11.

By contrast, numbers with more than 2 factors are called composite numbers.

A prime number is an integer above 1 whose only factors are 1 and itself.

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A prime number is a number that can be divided by itself and one only.

The first few prime numbers are :-

2 , 3 , 5 , 7 ,11 , 13 , 17 , 19

6 years ago you asked:

"If 2^(n) -1 is prime then n is prime where n is element of integer?"

You seem to have gone backwards quite a lot in 6 years! Well done!

A prime number is an integer that is evenly divisible only by 1 and itself. For smaller numbers, you can just try, "Is it divisible by 2? Is it divisible by 3? Is it divisible by 4? ... Is it divisible by n?" up until n^2 is bigger than the number. There are optimizations, like, you only need to check divisors that are, themselves, prime.

For bigger numbers, you can find factoring servers on the internet, or just run the "factor" program in linux.

For really big numbers, it takes a lot of computer power to assure that an arbitrary number is prime, but you can get a pretty good idea that something is probably prime with things like the Lehman-Lehrer Test (beyond the scope of this answer).

They are only divisible by themselves and 1