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
)
Since the smaller prime is greater than six, it must be odd. Any number greater than an odd number by one must be divisible by two.
In any three consecutive numbers, you'll get one that is of the form 3a, one that is of the form 3b + 1, and one that is of the form 3c + 2. Since neither of the primes are multiples of three, the middle one must be divisible by three.
Any number that is evenly divisible by three and by two must be divisible by six.
Solution
