I guess you have heard about the Erdős number that measures your distance to Paul Erdős in terms of the shortest chain of coauthors of scientific papers. Similarly, the Kevin Bacon number measures your distance to Kevin Bacon in terms of the shortest chain of co-actors in movies. I have determined these and some of my other numbers ...

My Erdős number is 2.
I share this property with over 8,000 other mathematicians and computer scientists. There are several paths of length 2 from Erdős to me, for instance via Noga Alon, via Dieter Kratsch, via Janos Komlos, via Jarik Nesetril, via Janos Pach, and via Zsolt Tuza.

• P. Erdős and J. Pach.
  On a problem of L. Fejes Toth.
  Discrete Mathematics 30 (1980), 103-109.
• J. Komlos, J. Pach, and G.J. Woeginger.
  Almost tight bounds for epsilon-nets.
  Discrete and Computational Geometry 7 (1992), 163-173.

My Andrew Wiles number is equal to 3.

• J. Coates and A. Wiles.
  On p-adic L-functions and elliptic units.
  Journal of the Australian Mathematical Society 26 (1978), 1-25.
• M.K. Agrawal, J.H. Coates, D.C. Hunt, and A.J. van der Poorten.
  Elliptic curves of conductor 11.
  Mathematics of Computation 35 (1980), 991-1002.
• A.J. van der Poorten and G.J. Woeginger.
  Squares from products of consecutive integers.
  American Mathematical Monthly 109 (2002), 459-462.

My Kevin Bacon number is 3.
When I was a student, I was an extra in the movie Pope John Paul II. Parts of this movie that played in the 1950s and 1960s were taken in Graz. I participated as one of the students protesting and demonstrating against Wladyslaw Gomulka. (We got badly beaten up by the Polish police.).
Because of this movie, there are tons of paths of length 3 from Kevin Bacon to me, for instance via Tom Adams and Derek Francis, via Joe Don Baker and Caroline Bliss, via Colin Firth and Patrick Marley, via Marcia Gay Harden and Albert Finney, via Miriam Margolyes and Robert Austin, via Victor Rivers and Nigel Hawthorne, via Michael Shannon and John Forgeham, via Charlize Theron and Sam Dastor, and via Eli Wallach and Marne Maitland.

• Kevin Bacon and Marcia Gay Harden
  Rails & Ties (2007)
• Marcia Gay Harden and Albert Finney
  Miller's Crossing (1990)
• Albert Finney and Gerhard J. Woeginger
  Pope John Paul II (1984)

Finally, my Erdős-Bacon number is 5.
According to the wikipedia your Erdős-Bacon number equals your Erdős number plus your Kevin Bacon number.
Daniel Kleitman has an Erdős-Bacon number of 3.
Also Paul Erdős himself has Erdős-Bacon number 3.