How to identify a large prime number

Let us start with the definition of a Prime Number.

Do you remember?

A natural number that can be divided by only 2 numbers – 1 and the number itself is called a prime number.

The first prime number that comes to our mind is “1” but if you had paid attention to your Math teacher, then you will know that: 1 is neither primer nor composite. The reason behind this conclusion is a topic for another post. Let us look at identifying prime numbers.

6 – Prime or Composite?

Steps to identify prime numbers

1) Divide the number into factors

2) If the number of factors is more than two then it is composite.

Ex: 6 has three factors 2, 3, 1. So 6 is not prime
6 = 2 x 3 x 1

Before going into shortcuts to find large prime number, here are a few properties of Prime Numbers

1) The lowest even prime number is 2

2) The lowest odd prime number is 3

3) All prime numbers above 3 can be represented by the formula 6n + 1 and 6n -1 for n>=1

Prove It!

Take 5 = 6 x 1 -1
Take 7 = 6 x 1 + 1
Take 47 = 6 x 8 – 1

4) There are 25 prime number between 1 and 100

List Them: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.

P.S: Learn the series for GMAT.

5) All prime numbers except 2 and 5 ends in 1, 3, 7 or 9 (noticed it?)

How to find whether a large number is prime or not

Let us take a number 2,329

Step 1: If the number ends in 0,2,4,6,8 then it is not prime

Step 2: Add the digits of your number; if the sum is divisible by 3 then it is not a prime number

2329 = 2 + 3 + 2 + 9 = 16

Still would be a prime number!

Step 3: If Steps 1 and 2 are not true then find the square root of the number

48.25

Step 4: Divide the number by all prime numbers less than 48.25 (exclude 2, 3, 5)

Prime Numbers less than 48: 7,11,13,17,19,23,29,31,37,41,43,47

Still would be a prime number!!!!!

Dammit!!!

2329 = 17 x 137 (Divisible by 17)

2329 is not a prime number.