- CARMA OANT SEMINAR
- Speaker: Matt Skerritt, School of Mathematical and Physical Sciences, The University of Newcastle
- Title: Computation of an Improved Lower Bound to Giuga’s Primality Conjecture
- Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
- Access Grid Venue: CARMA [ENQUIRIES]
- Time and Date: 3:30 pm, Mon, 27th May 2013
Our most recent computations tell us that any counterexample to Giuga’s 1950 primality conjecture must have at least 19,907 digits. Equivalently, any number which is both a Giuga and a Carmichael number must have at least 19,907 digits. This bound has not been achieved through exhaustive testing of all numbers with up to 19,907 digits, but rather through exploitation of the properties of Giuga and Carmichael numbers. We introduce the conjecture and an algorithm for finding lower bounds to a counterexample, then present our recent results and discuss challenges to further computation.
- [Permanent link]