Verifying the jumping champion conjecture

Autoren Rahul Athale
TitelVerifying the jumping champion conjecture
NoteInvited Abstract at Talks Foundations of Computational Mathematics (FoCM'02). Minneapolis, Minnesota, August 2002

In this paper, we present the results of computational verification of jumping champion conjecture made by Odlyzko et. al. in the paper Jumping Champions. They have given heuristics and computational results for two intervals of size 107, claiming that 210 takes over as jumping champion from 30 somewhere between 10425 and 10426. In one of those two intervals, starting from 10450, 210 was not a dominant gap. This motivated us to verify the conjecture computationally. We considered intervals of size 107 starting from 10410, 10420, …, 10550 and in many of them 210 did not appear as a dominant gap. Therefore we continued our experiments with intervals of size 108. We present the results of these experiments. We used computer algebra system Mathematica™ (Mathematica™ is a product of Wolfram Research, Inc.) for the computation.