Preprint Open Access
Gennady Butov
<?xml version='1.0' encoding='utf-8'?> <resource xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://datacite.org/schema/kernel-4" xsi:schemaLocation="http://datacite.org/schema/kernel-4 http://schema.datacite.org/meta/kernel-4.1/metadata.xsd"> <identifier identifierType="DOI">10.15161/oar.it/77083</identifier> <creators> <creator> <creatorName>Gennady Butov</creatorName> </creator> </creators> <titles> <title>Ellipses and hyperbolas of decomposition of even numbers into pairs of prime numbers</title> </titles> <publisher>INFN Open Access Repository</publisher> <publicationYear>2023</publicationYear> <subjects> <subject>prime, primes, number, numbers, even, theory, ellipse, ellipses, hyperbole, hyperboles, decomposition</subject> <subject subjectScheme="pmid">11</subject> </subjects> <dates> <date dateType="Issued">2023-07-01</date> </dates> <language>en</language> <resourceType resourceTypeGeneral="Text">Preprint</resourceType> <alternateIdentifiers> <alternateIdentifier alternateIdentifierType="url">https://www.openaccessrepository.it/record/77083</alternateIdentifier> </alternateIdentifiers> <relatedIdentifiers> <relatedIdentifier relatedIdentifierType="DOI" relationType="IsVersionOf">10.15161/oar.it/77082</relatedIdentifier> </relatedIdentifiers> <rightsList> <rights rightsURI="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0</rights> <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights> </rightsList> <descriptions> <description descriptionType="Abstract"><p>This is just an attempt to associate sums or differences of prime numbers with points lying on an ellipse or hyperbola.<br> Certain pairs of prime numbers can be represented as radius-distances from the focuses to points lying either on the ellipse or on the hyperbola.<br> The ellipse equation can be written in the following form: |p(k)| + |p(t)| = 2n.<br> The hyperbola equation can be written in the following form: ||p(k)| - |p(t)|| = 2n.<br> Here p(k) and p(t) are prime numbers (p(1) = 2, p(2) = 3, p(3) = 5, p(4) = 7,...),<br> k and t are indices of prime numbers,<br> 2n is a given even number,<br> k, t, n &isin; N.<br> If we construct ellipses and hyperbolas based on the above, we get the following:<br> 1) there are only 5 non-intersecting curves (for 2n=4; 2n=6; 2n=8; 2n=10; 2n=16). The remaining ellipses have intersection points.<br> 2) there is only 1 non-intersecting hyperbola (for 2n=2) and 1 non-intersecting vertical line. The remaining hyperbolas have intersection points.<br> Will there be any new thoughts, ideas about this?</p></description> </descriptions> </resource>
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