Reply-To: Richard E Crandall
Sender: Number Theory List
From: Richard E Crandall
Subject: F_22 is composite
Comments: To: NmbrThry@vm1.nodak.edu
To: Multiple recipients of list NMBRTHRY
F_22 was shown composite in October 1993 by R. Crandall, J. Doenias,
C. Norrie, and J. Young. The run was done on an Amdahl mainframe and
partly on a Cray. The multiply algorithm used the discrete weighted
transform (DWT) of Crandall and B. Fagin, (to appear in Math. Comp.).
The computation took about six Amdahl months.
This may have been the longest computation ever performed for a
non-trivial 1 bit result. The number of CPU ops spent was about
10^16.
The group also verified independently the original F_20 compositeness
result of Young and D. Buell (1988). For both of these numbers (and
some other large Fermat cofactors also shown to be composite during
these runs) some rigorous checking schemes were implemented. First,
Norrie developed a "wavefront" scheme, in which the mainframe does the
classical Pepin primality test (which does successive squaring) and a
host of workstations follow the mainframe's results by checking
squarings from the a-th to the b-th, for various small (b-a). In this
way the deterministic character of the mainframe's Pepin run is
verified. Norrie used a *different* program, in fact a different
multiply algorithm, for the a-to-b verifications. All this time,
Young, at Cray, verified various partial runs and attacked other
numbers such as F_19, F_21 and their cofactors.
All of these results will be put in print as soon as some final F_n
verifications are performed; but F_22 is hereby announced as
composite.