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another interesting tao talk

at UNSW 6pm today

copying from this page:

Abstract: (Tao) Structure and Randomness in the Prime Numbers

God may not play dice with the universe, but something strange is going on with the prime numbers — Paul Erdős.

The prime numbers are a fascinating blend of both structure (for instance, almost all primes are odd) and randomness. It is widely believed that beyond the obvious structures in the primes, the primes otherwise behave as if they were distributed randomly; thispseudorandomness then underlies our belief in many unsolved conjectures about the primes, from the twin prime conjecture to the Riemann hypothesis. This pseudorandomness has been frustratingly elusive to actually prove rigorously, but recently there has been progress in capturing enough of this pseudorandomness to establish new results about the primes, such as the fact that they contain arbitrarily long progressions. We survey some of these developments in this talk.



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