I believe my Erdös number is 5.

I coauthored with Dimitry Leites, who coauthored with Joseph Berstein, who coauthored with Tanya Khovanova, who coauthored with Richard Guy, who coauthored with Paul Erdős.

I have another shortest path of length 5 to Paul Erdős. I coauthored with Andrey Krutov, who coauthored with Véronique Hussin, who coauthored with Hans J. Zassenhaus, who coauthored with Sarvadaman Chowla, who coauthored with Paul Erdős.