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.
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