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Abstract: Last August, Agrawal, Kayal, and Saxena, all from the Indian Institute of Technology in Kanpur, announced a new algorithm to distinguish between prime numbers and composite numbers. Unlike earlier methods, their method is completely rigorous, deterministic, and runs in polynomial time. Previous results, some of them quite deep, were close to this ideal in various ways, so, perhaps, it was not such a great surprise that such a result should exist. But the relatively easy algorithm and proof is stunning. In this talk, the new algorithm will be described as well as some more recent developments.
This talk will be accessible to graduate students.
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