The minimum distance between any two points $$P_1$$ and $$P_2$$ while considering point $$P_1$$ on one circle and point $$P_2$$ on the other circle for the given circles' equations:
$$x^2 + y^2 - 10x - 10y + 41 = 0$$
$$x^2 + y^2 - 24x - 10y + 160 = 0$$ is ________.

The two circles are $$x^2 + y^2 - 10x - 10y + 41 = 0$$ and $$x^2 + y^2 - 24x - 10y + 160 = 0$$.

First circle: $$(x-5)^2 + (y-5)^2 = 25 + 25 - 41 = 9$$. Center $$C_1 = (5, 5)$$, radius $$r_1 = 3$$.

Second circle: $$(x-12)^2 + (y-5)^2 = 144 + 25 - 160 = 9$$. Center $$C_2 = (12, 5)$$, radius $$r_2 = 3$$.

Distance between centers: $$d = \sqrt{(12-5)^2 + (5-5)^2} = 7$$.

Since $$d = 7 > r_1 + r_2 = 6$$, the circles are external to each other. The minimum distance between points on the two circles is $$d - r_1 - r_2 = 7 - 3 - 3 = 1$$.

The minimum distance is 1.