J.C. Saunders, Department of Pure Mathematics, University of Waterloo
“Jumping Champions: Gaps Between Primes”
We explore the behaviour of the differences between consecutive prime numbers. Hardy and Littlewood conjectured an asymptotic formula for the number of twin primes and more generally k-tuples of primes of a specific configuration where there is no obvious divisibility condition that would rule out the configuration. Odlyzko, Rubinstein, and Wolf studied the problem of the most common gap between consecutive primes, which they termed a jumping champion. They conjectured that these jumping champions take on the values of 4 and the primorials. Here we define the nth primorial to be the product of the first n primes. We look at their evidence for this conjecture, which is based on the HL k-tuple conjecture, as well as a similar argument put forth by Goldston and Ledoan.
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