From the Wikipedia entry on Erdos-Bacon Number

Daniel Kleitman, a mathematician at MIT, was an advisor for the movie Good Will Hunting and appeared briefly as an uncredited extra. Minnie Driver, who appeared in that movie, also appeared in Sleepers with Kevin Bacon; as such, Kleitman's Bacon number is 2. He also coauthored a paper with Erdős. This gives him an Erdős–Bacon number of 3.

The only ways a lower number could be achieved would be:
- for an individual who had co-authored an academic paper with Paul Erdős to appear in a movie with Kevin Bacon;
- for Bacon to co-author an academic paper with someone with an Erdős number of 1, which would give Bacon an Erdős–Bacon number of 2;
- for anyone who appeared in the documentary N is a Number along with Erdős to appear in a film with Bacon, which would posthumously give Erdős an Erdős–Bacon number of 2;
- for Kevin Bacon to appear in a film that also uses stock footage of Erdős, giving Erdős an Erdős–Bacon number of 1;
- for a heretofore unknown joint academic paper by Bacon and Erdős to be published, giving Bacon an Erdős–Bacon number of 1.
- for Kevin Bacon to be revealed as Paul Erdős in disguise, giving Erdős-Bacon an Erdős-Bacon number of 0.