Abstract: Prime numbers, the very building blocks of the integers, remain an enigma. Yet we make progress in our quest to understand these very basic objects. This non-stressful talk will highlight recent progress and some of the many problems that are still unsolved.

The speaker: Carl Pomerance is one of the world's leaders in number theory, particularly in the areas of primality testing and factorization of large integers, which have important applications to cryptography. One of his fundamental discoveries is the quadratic sieve algorithm. Carl earned his PhD at Harvard and then went to the University of Georgia, where he rose to the rank of Distinguished Professor. Subsequently he worked at Lucent Technologies for a few years and is currently a Distinguished Professor at Dartmouth. Carl was a visitor here at Illinois in 1978--79. He is the winner of numerous prizes for his research, teaching, and exposition. These include the MAA Chauvenet Prize (1985), the MAA Tepper Haimo Teaching Award (1997), the AMS Conant Prize (2001), and was elected an AAAS Fellow (2004). He is the author of some 150 papers on subjects ranging from recreational math to the forefront of research on factoring.