Question

The sum of two prime numbers is the prime number 89,563. Find the smaller of the two addends.

I attempted the problem but I'm not sure if it is right. 89,561 is a prime number and so is 2. So is the answer 2?

Answer 1

Yes

Answer 2

The logic behind this is very interesting.

All prime numbers except the number 2 are odd
the sum of any tow odd numbers is even.

Since 89563 is odd, it must have been the sum of an even and an odd.
So it had to be 2 and 89561