∵ In polar coordinate system, ρ=2cosθ, ∴x=pcosθ, y=psinθ, and p and θ are eliminated.

∴(x- 1)2+y2= 1，

The rectangular coordinates of the center of the circle are (1, 0) and the radius is 1.

∴ The coordinate of point P(2, π3) in the general equation is (1, 3),

∴ The distance from point P(2, π3) to the center of the circle ρ=2cosθ is d=( 1? 1)2+32=3,

So the answer is 3.