Question

Is the sum of two prime numbers always even?

Answer 1

Hint: We first discuss the prime and how even numbers are related. We take 2, the only possible even prime number and find the sum with another prime. Then we conclude the given statement.

Complete step-by-step answer:
We first discuss the condition of prime numbers and its relation with even numbers.
Every natural number can be categorised into two parts of prime and composite numbers.
We first discuss the characteristics of the prime and composite numbers.
The numbers which have only two factors as 1 and that number itself are called prime numbers. The prime numbers are only divisible by 1 and that number.
For example, the numbers 5, 7, 11 are the prime numbers.
All other natural numbers other than prime numbers are called composite numbers.
All even numbers are composite numbers except 2. There aren’t enough smaller numbers than 2 to form the factors of 2. Therefore, it’s considered as prime numbers. All the other even numbers are composite numbers.
Therefore, if we take sum of 2 and any other prime number then the sum isn’t even.
For example, $2+5=7$. Therefore, the sum of two prime numbers isn’t always even.

Note: Sum of two odd numbers is always even. All prime numbers except 2 are odd. So, if we are taking a sum of two prime numbers other than 2 then we'll always have an even number as the sum.