Hello,

The exact question is, Prove or disprove that there are three consecutive odd positive integers that are primes, that is, odd primes of the form

,

, and

.

At first glance, I did not realize that this statement was an existentially quantified one, that one example would prove this true--the example being 3, 5, and 7. So, I did a full-fledged proof and am wondering if I did it correctly, notwithstanding its necessity.

Let

be an odd integer that is prime, then

, where

.

p=

this is prime, because the only factors are

and 1.