Sudan function is a fast growing function discovered by Gabriel Sudan. It is similar to the Ackermann function (but less well-known) and formally defined as follows: \(F_0(x,y) = x+y\) \(F_{n+1}(x,0) = x\) (for \(n \geq 0\)) \(F_{n+1}(x,y+1) = F_n(F_{n+1}(x,y),F_{n+1}(x,y)+y+1)\) (for \(n \geq 0,y \geq 0\)) It has been proven that the function is not primitive recursive.