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.
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.