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Collecting primes with p2-1 827-smooth, or reduced sets for likely solutions to the $620 problem
by
Jon Grantham
IDA/CCS
The problem of finding a number that is simultaneously a Fermat pseudoprime base 2 and a Fibonacci pseudoprime is commonly referred to as the $620 problem. We give some mathematical and historical background.
In the 1980s, Carl Pomerance gave a heuristic which argued that such numbers exist. In the mid-1990s, Red Alford and the author produced a set of primes such that the product of a subset of size 1812 or less was heuristically likely to provide a solution to this problem. In 2003, Chen and Greene produced a list of primes where the size of the likely subset was 1241. We discuss a recently discovered subset of size 1181 and the prospect of further reductions.
Date received: April 14, 2005
Copyright © 2005 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caqa-29.