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Erschienen in:
2014 | OriginalPaper | Buchkapitel
Computation of an Improved Lower Bound to Giuga’s Primality Conjecture
verfasst von : Matthew Skerritt
Erschienen in: Mathematical Software – ICMS 2014
Verlag: Springer Berlin Heidelberg
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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 Borwein, Borwein, Borwein, and Girgensohn. We present the algorithm used, and discuss technical challenges and challenges to further computation.