If \(a\), \(b\), and \(c\) are three prime numbers such that \(abc = 23(a + b + c)\), then the maximum possible value of \(a + b - c\) is

23 divides abc so one prime is 23; with a = 23, bc = 23 + b + c gives (b-1)(c-1) = 24, prime solutions {3,13} and {5,7}. Max a + b - c = 23 + 13 - 3 = 33 (the other set gives 25).