Seminar

Consider the sequence of primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, . . . and also the differences or gaps between the consecutive primes here: 1, 2, 2, 4, 2, 4, 2, 4, 6, 2, . . . . The most common difference for primes up to x is called a jumping champion, so for example when x=11 the jumping champion is 2. For x>947 the jumping champion is always 6 at least past x= 1,000,000,000,000,000, but nothing beyond this has been proved about jumping champions. Despite this, it is conjectured that aside from 1 the jumping champions are 4 and the primorials 2, 6, 30, 210, 2310. . . . Following up on earlier work of Odlyzko, Rubinstein and Wolf, we will provide some theoretical support for this conjecture.
This is joint work with Andrew Ledoan.