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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 ]
 CMP2003
 R. E. Crandall, E. W. Mayer and J. S. Papadopoulos, "The twentyfourth Fermat number is composite," Math. Comp., 72 (2003) 15551572.
Abstract:
We have shown by machine proof that F_{24} = 2^{2^{24}} + 1 is composite. The rigorous Pépin primality test was performed using independently developed programs running simultaneously on two different, physically separated processors. Each program employed a floatingpoint, FFTbased discrete weighted transform (DWT) to effect multiplication modulo F_{24}. The final, respective Pépin residues obtained by these two machines were in complete agreement. Using intermediate residues stored periodically during one of the floatingpoint runs, a separate algorithm for pureinteger 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 Pépin chain. We deposited a final Pépin 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 SelfridgeHurwitz residues. For the sake of completeness, we also generated a Pépin residue for F_{23}, and via the Suyama test determined that the known cofactor of this number is composite.
