Prof. Manindra Agarwal and his students at IIT-K have figured out a polynomial time test for primality. It was an unsolved problem. The RSA algorithm assumes that this is impossible. (NYTimes)
Of course, others have claimed the same. To my knowledge, none is conclusively proven.
What if they’re true? Well, in a few years, our cryptography algorithms will be useless. So it’s back to the drawing board, with security-related dot-coms from Univs popping up.