Question

What is the sum of any two prime number and composite number

Answer 1

Case 1:

Both composite numbers are even. Then the sum is composite.

Example: 4+10=14

The resultant number 14 is composite.

Case 2:

Both the composite numbers are odd. Then the sum is composite. It is because the sum of two odd numbers is even. All even numbers (barring 2) are composite numbers as they are divisible by 2.

Example: 9+15=24

The resultant number 24 is composite.

Case 3:

One of the composite numbers is even and the other is odd. In this case you can not confidently say whether their sum is composite or not.

Example: 9+16=25

Here the resulting sum is 25 and it is composite.

Now let us take another example.

Example: 9+8=17

The numbers 9 and 8 are both composite but their sum 17 is prime. So it is not composite.