Noob question - mining and generationg partial bitcoins

[DeathAndTaxes]

There isn't magical about a super computer.  It can't hash faster than its hashrate.  All that matters is the hashrate and today many ASIC farms are magnitudes faster than supercomputer at performing SHA-256 hashes.

There is no known shortcut to finding hashes.  If there was that would mean SHA-256 is broken and most forms of cryptography not just Bitcoin rely on it.  Everything from protecting nuclear launch codes, to making sure ATM are "talking" to the real bank and not an attackers computer.