When I plug 2 to the 1000th power into my calculator I get a scientific
notation response equivalent to
9,999,999,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000
possible combinations. We'd need a quantuum improvement in processor
ability to even consider this.

Is it possible to pare down the number pool? For instance, if there
are no negative numbers in the pool, then any number greater than the
target number can be removed from the pool. There may also be other
ways to reduce the pool: for instance, if your target number has to do
with a list of checks, say, written before June 1 and some of the pool
numbers are from July, they can be removed.