Transcript The numbers 3, 5, and 7 are three consecutive odd numbers that are prime.

The numbers 3, 5, and 7 are three consecutive odd numbers that are prime. How
many other triplets of consecutive odd numbers greater than 1 consist entirely of
primes?
(a)
None
(b)
One
(c)
Two
(d)
Three
(e)
More than three
Correct Answer: A
Explanation:
You can look at some triplets of consecutive odd numbers greater than 1:
5, 7, 9
11, 13, 15
25, 27, 29
53, 55, 57
93, 95, 97
You should quickly observe that any triplet of consecutive odd numbers would
have one multiple of 3. (The numbers that are multiples of 3 are italicized.)
Therefore, the only triplet of consecutive odd numbers greater than 1 that
contains all primes is 3, 5, 7. The correct answer is (A).