Consecutive primes and Beatty sequences

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

p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Arial; -webkit-text-stroke: #000000}
span.s1 {font-kerning: none}

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.