The Erdos Number of a person is defined as being 1, plus the minimum of
Erdos numbers of people he co-authored with; Paul Erdos has Erdos numeber 0.
You may want to visit the
Erdos Number Project
homepage.
My current Erdos number is 3, in two different ways:
Uzi Vishne -- Alex Lubotzky
Alex Lubotzky -- Laszlo Pyber
Laszlo Pyber -- Paul Erdos
and also
Uzi Vishne -- Boaz Tsaban ([5] in my list)
Boaz Tsaban -- Saharon Shelah
Saharon Shelah -- Paul Erdos