The Erdos Number is a humorous mathematical norm. The wikipedia article is most informative. If mathematicians are vertices on a graph, then draw an edge between them if they have co-authored a paper.

This is really due to Erdos's lifestyle. He never lived in the same place for very long, but changed from house to house every few days, writing mathematics papers with his hosts, who were usually faculty members.

The hop-count distance metric on a graph is a distance metric. (i.e. since you can get from Carl Pomerance to Paul Erdos by only one step, the distance is 1. But to get from Henri Gilbert to Erdos requires going through at least 1 other mathematician (in this case A. Odlyzko) and so that is distance 2).

The Erdos Number is the distance between any particular mathematician and Erdos.

• Paul Erdos has Erdos Number 0 by definition.
• Andrew M. Odlyzko has Erdos number 1 from:
P. Erdos and A. M. Odlyzko: ``On the density of odd integers of the form (p-1)/2^k and related questions.'' J. Number Theory, 11 (1979), pp. 257-263.
• Henri Gilbert has Erdos number 2 from
Henri Gilbert, Dipankar Gupta, Andrew M. Odlyzko, Jean-Jacques Quisquater: ``Attacks on Shamir's `RSA for Paranoids'.'' Inf. Process. Lett. 68(4): 197-199 (1998)
• Nicolas Courtois has Erdos number 3 (or lower) from
C. Berbain, O. Billet, A. Canteaut, N. Courtois, H. Gilbert, L. Goubin, A. Gouget, L. Granboulan, C. Lauradoux, M. Minier, T. Pornin, and H. Sibert: ``SOSEMANUK, a fast software-oriented stream cipher.'' Proc. Symmetric Key Encryption Workshop 2005.
• Gregory Bard has Erdos number 4 from
N. Courtois, and G. Bard. ``Algebraic Cryptanalysis of the Data Encryption Standard.'' Published in Springer's Lecture Notes in Computer Science