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The distribution of the prime numbers is generally well behaved: an
accurate rule of thumb is that, near x, the chance of a number being prime
is 1/log_e x. But there are several situations where such probabilistic
interpretations or other numerical evidence can be very misleading. I will
discuss such anomalies, and other surprising facts about the primes, such
as the Hardy-Littlewood Conjecture that no interval [x, x+y] has more
primes in it than the corresponding interval of the same length starting at
2.
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