Computation of an Improved Lower Bound to Giuga’s Primality Conjecture

Host Institution:

University of Newcastle

Title of Seminar:

Computation of an Improved Lower Bound to Giuga’s Primality Conjecture

Speaker's Name:

Matt Skerritt

Speaker's Institution:

School of Mathematical and Physical Sciences, The University of Newcastle

Time and Date:

Monday 27 May, 3.30pm (AEST)

Seminar Abstract:

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.

Seminar Convenor:

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