Prime number pairs summing to an odd number

While reading a book (details below), I came across a very nice problem as follows.

Find all pairs of prime numbers that sum up to 999.

As the book says, it involves thinking before actually attacking the problem. Few observations:

• Sum given is odd (999).
• To get sum odd, exactly one of the two numbers have to be even.
• Asked are the pairs of prime numbers.
• Meaning, we want intersection of prime and even which is just the number 2.

So, one of the numbers has to be 2; and thus the other of course is 997. And, that's the only pair of prime numbers which sums up to  999.

Cool indeed! :)

Book details:
Title:  math Charmers - Tantalizing Tidbits for the mind
Author: alfred s. posamentier
Publisher: University Press