Reference Database
(references for the Prime Pages)
The Prime Pages

Home
Search Site

Largest
Finding
How Many?
Mersenne

Glossary

Prime Curios!
e-mail list

FAQ
Prime Lists
Titans

Submit primes
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 twenty-fourth Fermat number is composite," Math. Comp., 72 (2003) 1555--1572.
Abstract: We have shown by machine proof that F24 = 2^{224} + 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 floating-point, FFT-based discrete weighted transform (DWT) to effect multiplication modulo F24. The final, respective Pépin 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 Pépin chain. We deposited a final Pépin residue for possible use by future investigators in the event that a proper factor of F24 should be discovered; herein we report the more compact, traditional Selfridge-Hurwitz residues. For the sake of completeness, we also generated a Pépin residue for F23, and via the Suyama test determined that the known cofactor of this number is composite.
Prime Pages' Home
Another prime page by Chris K. Caldwell