[lancefisher]

The BigInteger is really big.

An i7 does about 109 gigaFLOPS, or 109 operations per nanosecond. [1]

Suppose we can do 1 guess per operation. There are 2^10,000 possible roots. [2]

2^10,000 / 109 nanoseconds is 5.804×10^2991 years. [3]

The stars will burn out before you brute force it.

[1] http://en.wikipedia.org/wiki/FLOPS

[2] http://bit.ly/ZIWkkt (parens in the original link)

[3] http://www.wolframalpha.com/input/?i=2%5E10%2C000+%2F+109+na...

[IvyMike]

I must dryly point out that this does not invalidate the correctness of the algorithm.

[IvyMike]

As an optimist, I must point out that if Moore's law holds for the next 10000 doublings we'll have the answer in 20000 years, plus 9 picoseconds.