He has held a chair at the University of Bonn's Hausdorff Center for Mathematics since 1992.
Franke's research has covered various problems of number theory, algebraic geometry and analysis on locally symmetric spaces.
Franke attended the University of Jena, where he earned his PhD under Hans Triebel in 1986.
In recent years, Franke worked on an implementation of the Number Field Sieve algorithm for prime decomposition.
In May 2007, he and his colleague Thorsten Kleinjung announced the factorization of M1039, the 1,039th Mersenne number.