The Kauffman model is the archetypal model of genetic computation. It highlights the importance of criticality, at which many biological systems seem poised. In a series of advances, researchers have honed in on how the number of attractors in the critical regime grows with network size. But a definitive answer has remained elusive. We prove that, for the critical Kauffman model with connectivity one, the number of attractors grows at least, and at most, as (2/sqrt[e])^{N}. This is the first proof that the number of attractors in a critical Kauffman model grows exponentially.