SMS scnews item created by Andrew Mathas at Fri 24 May 2013 1313
Modified: Fri 24 May 2013 1639
Expiry: 27 May 2013
Calendar1: 27 May 2013 1500-1600
CalLoc1: AGR Carslaw 829
CalTitle1: AGR Seminar: Computation of an Improved Lower Bound to Giuga’s Primality Conjecture
Auth: email@example.com (assumed)
Computation of an Improved Lower Bound to Giuga’s Primality Conjecture
Mr Matt Skerritt, School of Mathematical and Physical Sciences, The University of Newcastle
University of Newcastle (CARMA)
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.
If you would like to attend this seminar in our access grid room then please check to see if the grid is already booked at this time and send an email to firstname.lastname@example.org to let the CSOs know that you would like to attend.