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This is the Prime Pages' interface to our BibTeX database.  Rather than being an exhaustive database, it just lists the references we cite on these pages.  Please let me know of any errors you notice.
References: [ Home | Author index | Key index | Search ]

Item(s) in original BibTeX format

@article{CMP2003,
	author={R. E. Crandall and E. W. Mayer and J. S. Papadopoulos},
	title={The twenty-fourth {Fermat} number is composite},
	abstract={We have shown by machine proof that $F_{24} = 2^{2^{24}} + 1$ is composite.
		The rigorous P{\'e}pin primality test was performed using independently developed
		programs running simultaneously on two different, physically separated
		processors. Each program employed a floating-point, FFT-based discrete
		weighted transform (DWT) to effect multiplication modulo $F_{24}$. The
		final, respective P{\'e}pin residues obtained by these two machines were in
		complete agreement. Using intermediate residues stored periodically during
		one of the floating-point runs, a separate algorithm for pure-integer negacyclic
		convolution verified the result in a ``wavefront'' paradigm, by running
		simultaneously on numerous additional machines, to effect piecewise verification
		of a saturating set of deterministic links for the P{\'e}pin chain. We deposited
		a final P{\'e}pin residue for possible use by future investigators in the event
		that a proper factor of $F_{24}$ should be discovered; herein we report
		the more compact, traditional Selfridge-Hurwitz residues. For the sake
		of completeness, we also generated a P{\'e}pin residue for $F_{23}$, and via
		the Suyama test determined that the known cofactor of this number is composite.},
	journal= MC,
	volume={72},
	year={2003},
	pages={1555--1572}
}

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