That isn't practical, so let's scale back to primes around 10^20 (around 10^18 different primes) Then, you would need around a thousand terabytes (still assuming that you manage to compress your 64-bit or so primes to fit 1000 of them in 8 bits)
I'll assume you build the machine with those drives, and can do trial divisions in parallel, 1000 CPUs, a billion divisions per CPU per second. you still would need 10^6 seconds to do a complete search over all primes. Rounding down, that is a week.
For comparison, https://sites.google.com/site/bbuhrow/home claims:
"I've seen C90's factored in less than 4 minutes on an 8 core box.
According to what I understand, C90 is tech speak for "90 digits, product of two coprime numbers"
Actually, a million terabytes (an exabyte) is really quite feasible. Not on an individual scale, but I would be very surprised if governments (all of them, really) did not have this sort of thing set up.