# Start off your new year with primes!

Suppose, p, q and r are prime positive integers, satisfying pq = r + 1 and 2(p^{2} + q^{2}) = r^{2} + 1. Let there be n ORDERED solutions to (p, q, r) i.e. (p*{1}, q*{1}, r*{1}), (p*{2}, q*{2}, r*{2}),...,(p*{n}, q*{n}, r*{n}). Find \sum*{i=1}^n (p*{i} + q*{i} + r_{i}).