On a numerical upper bound for the extended Goldbach conjecture

dc.contributor.author	Quarel, David
dc.date.accessioned	2019-10-10T02:01:43Z
dc.date.available	2019-10-10T02:01:43Z
dc.date.issued	2016
dc.date.updated	2019-10-10T00:54:23Z
dc.description.abstract	The Goldbach conjecture states that every even number can be decomposed as the sum of two primes. Let D(N) denote the number of such prime decompositions for an even N. It is known that D(N) can be bounded above by D(N) C N log2 N Y pjN p>2 1 + 1 p ?? 2 Y p>2 1 ?? 1 (p ?? 1)2 = C (N) where C denotes Chen's constant. It is conjectured [20] that C = 2. In 2004,Wu [54] showed that C 7:8209. We attempted to replicate his work in computing Chen's constant, and in doing so we provide an improved approximation of the Buchstab function !(u), !(u) = 1=u	en_AU
dc.format.mimetype	application/pdf
dc.identifier.uri	http://hdl.handle.net/1885/173607
dc.provenance	Deposited by Mathematical Sciences Institute in 2019.
dc.title	On a numerical upper bound for the extended Goldbach conjecture	en_AU
dc.type	Thesis (Honours)	en_AU
local.contributor.affiliation	Mathematical Sciences Institute, Australian National University	en_AU
local.contributor.supervisor	Trudgian, Timothy
local.identifier.doi	10.25911/5d9efb1b88f6c
local.mintdoi	mint	en_AU
local.type.degree	Other	en_AU

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