  Let $n \ge 2$ be an integer and consider the defining ideal of the Fermat
configuration of points in $\mathbb{P}^2$:
$I_n=(x(y^n-z^n),y(z^n-x^n),z(x^n-y^n)) \subset R=\mathbb{C}[x,y,z]$. In this
paper, we compute explicitly the least degree of generators of its symbolic
powers in all unknown cases. As direct applications, we easily verify
Chudnovsky's Conjecture, Demailly's Conjecture and Harbourne-Huneke Containment
problem as well as calculating explicitly the Waldschmidt constant and
(asymptotic) resurgence number.
