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https://hdl.handle.net/2142/86936
Description
Title
Prime and Quasi-Prime Number Races
Author(s)
Sneed, Jason P.
Issue Date
2009
Doctoral Committee Chair(s)
Hildebrand, A.J.
Kevin Ford
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
"We review the body of work done on prime number races, specifically the results involving infinitely many lead changes in prime number races. We describe a computational way of showing that any race has infinitely many lead changes and greatly expand the known results in this area. An extension of the traditional prime number race problem is discussed where we race ""quasi-primes"" or composite numbers that are the product of two odd primes modulo 4. We then consider what ""percentage"" of the time that the residue class 1 leads the residue class 3 in this ""quasi-prime"" race modulo 4."
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