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I have posted a video on YouTube to discuss about Prime Numbers
Attached pdf of this Article as SPOILER at the top! Happy learning!
Following is Covered in the Video
Theory
¤ What is a Prime Number? ¤ Generic form of a Prime Number ¤ How to check if a number is prime? ¤ Sample Problems
What is a Prime Number?
Prime numbers are the numbers which have only two factors ¤ The number itself ¤ And 1
Example of Prime numbers are : 2, 3, 5, 7, 11, 13
2 is the only even prime number
Only positive numbers can be prime numbers
Generic Form of Prime Numbers
All Prime Numbers (apart from 2 and 3) can be written as ¤ 6n + 1 or ¤ 6n - 1
Example
7 = 6 +1 (of the form 6n+1) 11 = 12 – 1 (of the form 6n-1) 13 = 12 + 1 (of the form 6n+1) 17 = 18 -1 (of the form 6n-1)
How to check if a number (n) is prime?
¤ Divide the number by 6 and check if the remainder is 1 or 5 ¤ If the remainder is not 1 or 5 then it is NOT a prime number ¤ If the remainder is 1 or 5 then it CAN be a prime number ¤ Divide the number by all prime numbers from 2 to Sqrt(n) and check if it is divisible by any of these numbers ¤ If the number is divisible by ANY of the prime numbers from 2 to Sqrt(n) then it is NOT a prime number ¤ If the number is NOT divisible by ALL the prime numbers from 2 to Sqrt(n) then it is a prime number
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Sample Problems
Q1. Check if a 123 is prime number or not
Solution:
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¤ 123 divided by 6 gives 3 as remainder which is NOT 1 or 5 ¤ 123 is NOT a prime number
Q2. Check if a 127 is prime number or not
Solution:
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¤ 127 divided by 6 gives 1 as remainder ¤ 127 CAN be a prime number ¤ We need to divide 127 by all prime numbers from 2 to Sqrt(127) and check if it is divisible by any of these numbers ¤ Closest integer to Sqrt(127) is Sqrt(121) = 11. So prime numbers from 2 to 11. 2,3,5,7,11 ¤ 127 is NOT divisible by ALL the prime numbers 2,3,5,7,11. ¤ 127 is a prime number