Primes Question - AMTI Inter Level Finals
Find the sets of primes \(x\), \(y\) and \(z\) that satisfy the condition above. Submit your answer as the sum of all possible values of \(x\), \(y\) and \(z\).
Note: If all the possible solutions are, for example, \((3, 4, 5)\), \((5, 12, 13)\) and \((9, 12, 15)\), then the sum will be \(3+4+5 + 5+12+13 + 9+15\). (The last 12 is omitted since \(y\) only has two possible values; 5 still appears twice since it appears for different variables \(x\) and \(y\).)