I wish to roundly thank all those that responded to our need for verification. We had several excellent responses. The primes have now been better verified using Miller-Rabin with different platforms, and with separately coded math libraries. More exhaustive testing is ongoing. Thanks are due to Wei Dai and Frank A Stevenson, as well as independent math libraries by Rich Schroeppel and Eric Young. Bill.Simpson@um.cc.umich.edu Key fingerprint = 2E 07 23 03 C5 62 70 D3 59 B1 4F 5E 1D C2 C1 A2