Erdős-Bacon number

The Erdős-Bacon number of a mathematician or an actor is the sum of their Erdős number (http://planetmath.org/ErdHosNumber) and their Bacon number. Not many professional mathematicians have had film rôles. However, a few important ones have done consulting work for Hollywood films about mathematicians, such as A Beautiful Mind. For example, William Timothy Gowers, who has Erdős number 4, was a consultant for Proof, with Gwyneth Paltrow in the lead rôle. Paltrow was in se7en with Endre Hules, who was in Apollo 13 with Kevin Bacon. Thus Gowers has an Erdős-Bacon number of 7. Daniel Kleitman, consultant for Good Will Hunting, has an even smaller Erdős-Bacon number, 3, since he co-authored a paper with Erdős and the film included Minnie Driver, who starred with Bacon in Sleepers. The smallest likely Erdős-Bacon number would probably be 2, if an Erdős co-author consulted for a movie starring Bacon. It’s also possible that Kevin Bacon could co-author a mathematical paper with an Erdős co-author, but this appears unlikely.