I don't know much about this stuff, but based on the fact that a 5870 can get up to 2.7 Teraflops, that would make the government computer 370,370 times faster.  I hear that 5870s get about 300 Mega hash/s so that means that the Exaflop computer would get like 111 MILLION Mega hash/s or 111 Tera hash/s.  That's a block every 59 minutes on average, at the current difficulty level.  Did I do my math right?

The average time to generate a block at 111000000000 Khps, given current difficulty of 109670.13329248 , is 4 seconds