Assignment:
A classic unsolved problem in number theory asks if there are infinitely many pairs of `twin primes', pairs of primes separated by 2, such as 3 and 5, 11 and 13, or 71 and 73. Prove that the only prime triple (i.e. three primes, each 2 from the next) is 3, 5, 7.
Provide complete and step by step solution for the question and show calculations and use formulas.