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 is an integer then it is not prime

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

Step 3: 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 4: If Steps 1,2 and 3 are not true then find the square root of the number

48.25

Step 5: 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.

Now try a large prime number and let us know whether the method works! We at F1GMAT have been contacted by computer programmers about this method. Trying multiple large numbers is the only test that you can perform before creating a foolproof algorithm.