-----BEGIN PGP SIGNED MESSAGE----- Theodor Schlickmann and Peter Trei have expressed some skepticism regarding the 2048-bit number which I believe can be factored. I confess that I do not know the exact method required, but I am pretty sure it exists. Hint 1: The method will not work to factor 2048-bit numbers in the general case. Hint 2: There is an observation which suggests the number may be factored. A one word hint will reveal this observation. (I want to hold off on Hint 3 for a little while in case somebody is already working on the problem. If anybody wants me to withhold Hint 3, please post a message to the list and I may do so. It seems to me that it will be more fun to solve without Hint 3.) Wouldn't it be neat to actually factor a 2048-bit number which was the product of two large primes? Monty Cantsin Editor in Chief Smile Magazine http://www.neoism.org/squares/smile_index.html http://www.neoism.org/squares/cantsin_10.htm -----BEGIN PGP SIGNATURE----- Version: 2.6.2 iQEVAwUBNHMvmpaWtjSmRH/5AQHWVQf+KvPxxNw8bHWhxVq//I7ic8dwtmVa2AS6 zpl77qI6vkeMfjFv0UxP5XXIEDH13cy7nlgOHjmvSc/IjC2A0+twQEgxUBzLV5pe Ltpnbw/RM/vqs5wX7d7KhY+kUxQR77ElUANVVve5sQNn1cDPAIQcQnC7UL7oAk0B Wo2/xlCoTncUkXwPX94PLk1hjdARimpvcoBYmtYcE0mnwNZfzTTU4ExgxAbiOq5H /oosTwnEjb+bDU7uPr9H/XxUkdGxa4PfWEw9C+folUbEtjFjJznfn78c45fz2IYs 6S/oywGnKlWEU9xS9Yg8fnIDCWB1V6tTEW3PGJDp5fwi3x06i298eQ== =sJgk -----END PGP SIGNATURE-----