Formulation of a set of even numbers and generation of pairs of odd numbers for application in proving strong Goldbach's conjecture/ (Record no. 88544)

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fixed length control field 03159nam a22001937a 4500
003 - CONTROL NUMBER IDENTIFIER
control field KE-MeUCS
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20240429155127.0
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 240411b xxu||||| |||| 00| 0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 000000
040 ## - CATALOGING SOURCE
Transcribing agency KE-MeUCS
Modifying agency KE-MeUCS
050 ## - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA241.S26 2023
100 ## - MAIN ENTRY--PERSONAL NAME
Personal name Sankei Daniel Njoroge
245 ## - TITLE STATEMENT
Title Formulation of a set of even numbers and generation of pairs of odd numbers for application in proving strong Goldbach's conjecture/
Remainder of title Daniel Njoroge Sankei
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Place of publication, distribution, etc Meru
Name of publisher, distributor, etc Daniel Njoroge Sankei
Date of publication, distribution, etc 2023
300 ## - PHYSICAL DESCRIPTION
Extent xi, 82p
500 ## - GENERAL NOTE
General note A thesis submitted in partial fulfillment of the requirements for conferment of the Degree of Master of Science in Pure Mathematics of Meru University of Science and Technology
520 ## - SUMMARY, ETC.
Summary, etc The Strong Goldbach's conjecture also known as the Binary Goldbach conjecture (BGC) is one of the oldest and best-known unsolved problems in Number theory and all of mathematics. It states that every even integer greater than 2 can be expressed as the sum of two primes. A Goldbach number is a positive even integer that can be expressed as the sum of two odd primes. Since 4 is the only number greater than 2 that requires the even prime 2 to be written as the sum of two primes, another form of the statement of the Strong Goldbach's Conjecture is that all even integers greater than 4 are Goldbach numbers. The BGC has set a persistent challenge to the exploration of the foundations of mathematics in general and Number theory in particular as it remains unproven for foundations of mathematics in general and Number Theory in particular as it remains unproven for almost 250 years despite considerable efforts by mathematicians throughout history. The best known result so far is that of Chen proving that every sufficiently large even integer N can be written as the sum of a prime and the product of at most two prime numbers. The known algorithms for attempting to prove or verify the BGC on a given interval [a, b] consist of finding two sets of primes Pi and Pj such that Pi + Pj cover all the even numbers in the interval [a, b]. The traditional representation of an even number is 2k for k∈N and this formulation has not provided mathematicians with a direct pathway to easily obtain all Goldbach partitions for any even number of this form. This study introduces a new formulation of a set of even numbers as an integer E of the form Eij = ni+nj=(nj-ni) n for all n ∈ N. The proof that this new formulation holds ∀n< ∞ is provided. This new definition will have two consequences: (1) using the new formulation of a set of even numbers, it has proved that any even number say Eij can be partioned into all pairs of all odd numbers whose sum is Eij, and (2) from these set of pairs of odd numbers, it has been shown that there exists at least one Goldbach partition for Eij. Finally, a rigorous proof of the Strong Goldbach's conjecture is provided. The study further recommends the exploration of the method of partitioning any even number into all pairs of odd numbers so as to find a new method of attacks to the Twin Prime Conjecture and the Weak Goldbach Conjecture.
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Source of classification or shelving scheme Library of Congress Classification
Koha item type Thesis
Cataloguer Intern
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Withdrawn status Lost status Source of classification or shelving scheme Damaged status Not for loan Home library Current library Shelving location Date acquired Source of acquisition Cost, normal purchase price Cataloger Total Checkouts Full call number Barcode Date last seen Price effective from Koha item type
    Library of Congress Classification     Meru University Meru University Periodical Section 11/04/2024 - 0.00 Intern   QA241.S26 2023 24-37881 11/04/2024 11/04/2024 Thesis

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