Lecture 31: Using Elliptic Curves to Factor, Part II

William Stein

Date: Math 124 $\quad$ HARVARD UNIVERSITY $\quad$ Fall 2001

I constructed $N = 800610470601655221392794180058088102053408423$ by multiplying together five random (and promptly forgotten) primes $p$ with the property that $p-1$ is not $B$-power-smooth for $B=10^8$. Since $N$ is a product of five not-too-big primes, $N$ begs to be factored using the elliptic curve method.