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 \( x^{2} + y^{2} - 10x - 10y + 41 = 0 \) and \( x^{2} + y^{2} - 24x - 10y + 160 = 0 \) is ______________.
