Others have pointed out how long the computation could potentially take. I think that your math professor is reasonably confident that the problem will not be solved by brute force, in your lifetime.
However, discovery of a new method of factorizing products of large primes could make you a rich man indeed. This is the mathematics that is underlying the RSA algorithm - a general prime factorization algorithm that delivered results quickly, would render RSA crackable. Besides the money you could get from licensing the software, think how much the NSA would pay you to shut up ;).
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