Pairs of primes separated by a single number are called prime pairs. Examples are 17 and 19. Prove that the number between a prime pair is always divisible by 6 (assuming both numbers in the pair are greater than 6).

(From http://www.ocf.berkeley.edu/~wwu/riddles/intro.shtml )

Here's the way I figured it.

In the three consecutive numbers (the one divisible by 6 and the two primes), there must be at least one number divisible by 2 and one number divisible by 3. Since neither of the primes can be divisible by 2 or 3, the middle one must be.

Posted by Gamer on 2003-10-11 17:11:29