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 )

In fact, this is true of any prime pair where both numbers are greater than 3!  In particular, the number between 5 and 7 is divisible by 6.

Posted by Steve Herman on 2005-04-30 15:17:20