# Fermat numbers

If $$F_n$$ denotes the $$n$$th Fermat number, then find the value of $$n$$:

$F_n=\overline{xyzabcde6}$

for some $$\overline {xyzabcde}$$.

Note: Here, $$\overline{xyzabcde6}$$ is not the product of $$\overline{xyzabcde}$$ and $$6$$. It is in accordance with the base-10 positional system.