prime divisor, primitive divisor, recurrence sequence, marsenne prime, polynomial sequence
We examine results concerning the generation of primes in certain types of integer sequences. The sequences discussed all have a connection in that each satisfies a recurrence relation. Mathematicians have speculated over many centuries that these sequences contain an infinite number of prime terms, however no proof has been given as such. We examine a less direct method of showing an infinitude of primes in each sequence by showing that the sequences contain an infinite number of terms with primitive divisors.
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Master of Science (M.S.)
College of Arts and Sciences
Length of Campus-only Access
Masters Thesis (Open Access)
Russell, Richard, "On Prime Generation Through Primitive Divisors Of Recurrence Sequences" (2006). Electronic Theses and Dissertations. 879.