What are Prime Numbers?

What are Prime Numbers?

A prime number is defined as a natural number greater than 1 and is divisible by only 1 and itself....

Some interesting facts about Prime Numbers:

Except for 2, which is the smallest prime number and the only even prime number, all prime numbers are odd numbers. Every prime number can be represented in form of 6n + 1 or 6n – 1 except the prime numbers 2 and 3, where n is any natural number. 2 and 3 are only two consecutive natural numbers that are prime. Goldbach Conjecture: Every even integer greater than 2 can be expressed as the sum of two primes. Wilson Theorem: Wilson’s theorem states that a natural number p > 1 is a prime number if and only if...

Properties of Prime Numbers:

Every number greater than 1 can be divided by at least one prime number. Every even positive integer greater than 2 can be expressed as the sum of two primes. Except 2, all other prime numbers are odd. In other words, we can say that 2 is the only even prime number. Two prime numbers are always coprime to each other. Each composite number can be factored into prime factors and individually all of these are unique in nature....

Prime Numbers and Co-prime numbers:

It is important to distinguish between prime numbers and co-prime numbers. Listed below are the differences between prime and co-prime numbers....

How to check whether a number is Prime or not?

Naive Approach: The naive approach is to...