Question 37308: What is the smallest positive integer that cannot occur as the difference between two positive prime numbers.
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! Good problem. Never heard that one before. If you look at the list of primes,
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, etc.,
you find that differences of 1, 2, 3, 4, 5, 6, 8, 9, 10, etc., exist but no 7.
And because all later primes are odd numbers, a difference of seven will not exist there either.
Thus the answer is 7. Good problem.
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