for the API design, always check others before rolling your own. E.g. the (three) functions with "Prime" in their name from http://java.sun.com/javase/6/docs/api/java/math/BigInteger.html I hope they are there for a reason. While we're at it - do we have modPow? modInverse? And of course check their implementation as well (should be straightforward, but you never know). J.W.