Consecutive primes and Beatty sequences

Date: 
Tuesday, November 8, 2016 - 2:00pm
Location: 
MSB 110
Speaker: 
Zhenyu Guo (University of Missouri, Columbia)

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This talk starts by introducing the prime number race and the biases in the distribution of consecutive primes. A Beatty sequence is the sequence of integers found by taking the floor of the positive multiples of a positive integer. Fix two Beatty sequences B1 and B2. We count the number of primes lying in B1 with the next prime lying in B2 by assuming a strong form of the Hardy-Littlewood conjecture.