A Leyland number has the form \(x^y + y^x\) for integers \(x \ge y \ge 2\) — for example \(8 = 2^2 + 2^2\), \(17 = 3^2 + 2^3\), and \(57 = 5^2 + 2^5\). The requirement \(y \ge 2\) avoids the trivial \(x^1 + 1^x = x + 1\), which would make every number Leyland.
They were introduced by Paul Leyland, and Leyland primes (Leyland numbers that are prime, like 17, 593, and 32993) are of practical interest in primality testing: they're hard cases that have driven improvements in general-purpose prime-proving software, precisely because they have no special algebraic form to exploit.