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dc.contributor.authorBanks, William
dc.contributor.authorFinch, Carrie
dc.contributor.authorLuca, Florian
dc.contributor.authorPomerance, Carl
dc.contributor.authorStanica, Pantelimon
dc.date2013-01-16
dc.date.accessioned2013-03-01T16:54:48Z
dc.date.available2013-03-01T16:54:48Z
dc.date.issued2013-01
dc.identifier.urihttp://hdl.handle.net/10945/29603
dc.description.abstractWe establish several related results on Carmichael, Sierpinski and Riesel numbers. First, we prove that almost all odd natural numbers k have the property that 2nk + 1 is not a Carmichael number for any n 2 N; this implies the existence of a set K of positive lower density such that for any k 2 K the number 2nk + 1 is neither prime nor Carmichael for every n 2 N. Next, using a recent result of Matom aki, we show that there are x1=5 Carmichael numbers up to x that are also Sierpi nski and Riesel. Finally, we show that if 2nk+1 is Lehmer, then n 6 150 !(k)2 log k, where !(k) is the number of distinct primes dividing k.en_US
dc.language.isoen_US
dc.rightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.en_US
dc.titleSierpinski and Carmichael numbersen_US
dc.typeArticleen_US
dc.contributor.corporateNaval Postgraduate School, Monterey, California
dc.contributor.departmentApplied Mathematics


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