How to identify a large prime number

Prime Numbers: A prime number is a natural number, which can be divided by exactly 2 distinct natural number  1 and itself

Ex: 2 have exactly two factors 2 and 1 so it is prime.

The other positive integers are composite and they have three or more factors.
For example, 9 has factors 1, 3 and 9 (3 factors), so is composite.
2 has factors 1, 2, 3, 4, 6, 12 (6 factors), so is composite.

Ex: 2,3,5,7,11...

Properties of Prime Number

1) 2 and 3 are the lowest even and odd prime numbers respectively.
2) 2 is the only even prime number
3) Prime numbers between 1 and 100 are
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
There are 25 prime numbers between 1 and 100.  Memorize this series(This would be useful for GMAT)
4) There are no negative prime numbers
5) All prime numbers except 2 and 5, end in 1, 3, 7 or 9, since numbers ending in 0, 2, 4, 6 or 8 are multiples of 2 and numbers ending in 0 or 5 are multiples of 5
6) All prime numbers above 3 are of the form 6n ? 1 or 6n + 1, because all other numbers are divisible by 2 or 3 where n>=1

How to check whether a number is prime or not

Let us take a number 2,321

1) Find the square root of the number The Square root of 2,321 is 48.176......
2) Remember that if the square root results in an integer it is automatically composite
3) If your number ends in a 0,2,4,5,6,8 it is NOT PRIME  2,321 ends in a 1, so go to next step
4) Add up the digits of your number, if the sum is divisible by 3, your number is composite -> 2+3+2+1= 8
      8 is not divisible by 3
5) Divide the number by all the prime numbers less than the square root (you can skip 2, 3, and 5)
   Since the square root of 2,321 is 48.176... Divide 2,321 by primes less than 48
  (7,11,13,17,19,23,29,31,37,41,43,47)
   Since 2,321 is divisible by 11, it is NOT prime and therefore composite
6) If a number is not divisible by any of the prime numbers less than the square, it is PRIME otherwise it is COMPOSITE