Actually, this doesn't seem quite to be working with the 33-bit large primes; starting with 21.8M relations, it makes a matrix of reasonable-looking size, but then at least the first ten dependencies give an error that I've not seen before:

Code:

Tue Sep 22 02:14:23 2009 reading relations for dependency 8
Tue Sep 22 02:14:23 2009 read 123377 cycles
Tue Sep 22 02:14:23 2009 cycles contain 496240 unique relations
Tue Sep 22 02:14:32 2009 read 496240 relations
Tue Sep 22 02:14:35 2009 multiplying 496240 relations
Tue Sep 22 02:15:33 2009 multiply complete, coefficients have about 20.44 million bits
Tue Sep 22 02:15:33 2009 initial square root is modulo 740671
Tue Sep 22 02:17:51 2009 dependency does not form a congruence of squares!