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Extending the Generalized Fermat Prime Number Search Beyond One Million Digits Using GPUs

Iain Bethune, Michael Goetz
EPCC, The University of Edinburgh, James Clerk Maxwell Building, The King’s Buildings, Mayfield Road, Edinburgh, EH9 3JZ, UK
10th International Conference on Parallel Processing and Applied Mathematics, 2013

@article{bethune2013extending,

   title={Extending the Generalized Fermat Prime Number Search Beyond One Million Digits Using GPUs},

   author={Bethune, Iain and Goetz, Michael},

   year={2013}

}

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Great strides have been made in recent years in the search for ever larger prime Generalized Fermat Numbers (GFN). We briefly review the history of the GFN prime search, and describe new implementations of the ‘Genefer’ software (now available as open source) using CUDA and optimised CPU assembler which have underpinned this unprecedented progress. The results of the ongoing search are used to extend Gallot and Dubner’s published tables comparing the theoretical predictions with actual distributions of primes, and we report on recent discoveries of GFN primes with over one million digits.
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