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).
All the primes are of the form 6k+1 or 6k-1,except for 2,3. because 6k+2 is divisible by 2, 6k+3 is divisible by 3, 6k+4 is divisible by 2 and finally 6k+5=6*(k+1)-1. So, if they are prime pair, they have same k value, the middle number will be 6k. So, the number between them is divisible by 6.
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