Find two different PRIME numbers whose sum is a composite number. Explain the DIVISIBILITY rule that proves the sum is composite.

Answer 1

One example of two different prime numbers whose sum is a composite number is 2 and 5. The sum of 2 and 5 is 7, which is a prime number.

To explain the divisibility rule that proves the sum is composite, we need to understand the concept of divisibility. A number is said to be divisible by another number if it can be divided evenly without leaving a remainder.

When we add two prime numbers, the resulting sum can only be even if at least one of the prime numbers is 2. This is because any odd number added to another odd number always results in an even number. However, the sum of two odd primes will always be an even number since odd + odd = even.

Since 2 is the only even prime number, any other prime number added to 2 will result in an even sum. An even number is always composite because it is divisible evenly by 1, itself, and at least one other number (2).

In the example of 2 and 5, the sum is 7, which is not divisible evenly by any number other than 1 and itself. Hence, the sum is a prime number.

Therefore, to find two different prime numbers whose sum is a composite number, we need to select two odd prime numbers excluding 2.