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COMPUTATION OF AN IMPROVED LOWER BOUND TO GIUGA’S PRIMALITY CONJECTURE

Borwein, Jonathan M. and Maitland, Christopher and Skerritt, Matthew (2013) COMPUTATION OF AN IMPROVED LOWER BOUND TO GIUGA’S PRIMALITY CONJECTURE. Integers, 13 .

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    Abstract

    Our most recent computations tell us that any counterexample to Giuga’s 1950 primality conjecture must have at least 19,908 decimal digits. Equivalently, any number which is both a Giuga and a Carmichael number must have at least 19,908 decimal digits. This bound has not been achieved through exhaustive testing of all numbers with up to 19,908 decimal digits, but rather through exploitation of the properties of Giuga and Carmichael numbers. This bound improves upon the 1996 bound of one of the authors. We present the algorithm used, and our improved bound. We also discuss the changes over the intervening years as well as the challenges to further computation.

    Item Type: Article
    Subjects: UNSPECIFIED
    Faculty: UNSPECIFIED
    Depositing User: Mrs Naghmana Tehseen
    Date Deposited: 06 Jan 2015 10:12
    Last Modified: 06 Jan 2015 10:12
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1511

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