HMMT 2002 U63

Our third and final item comes to us from Germany, I mean Geometry. It is known that a regular $n$-gon can be constructed with straightedge and compass if $n$ is a prime that is 1 plus a power of 2 . It is also possible to construct a $2 n$-gon whenever an $n$-gon is constructible, or a $p_{1} p_{2} \cdots p_{m}$-gon where the $p_{i}$ 's are distinct primes of the above form. What is really interesting is that these conditions, together with the fact that we can construct a square, is that they give us all constructible regular $n$-gons. What is the largest $n$ less than $4,300,000,000$ such that a regular $n$-gon is constructible?