Hello, Also sprach Zarathustra!
Are there any other triples of primes that differ by 2?
Since is the only even prime,
. . any such triple of primes must be consecutive odd numbers.
It can be shown that, in a set of three consecutive odd numbers,
. . one of them will be divisible by 3.
Crank out a list of three consecutive odd numbers:
And we see that is the only such triple of primes.