Preprint Open Access
Gennady Butov
<?xml version='1.0' encoding='UTF-8'?> <record xmlns="http://www.loc.gov/MARC21/slim"> <leader>00000nam##2200000uu#4500</leader> <datafield tag="540" ind1=" " ind2=" "> <subfield code="u">https://creativecommons.org/licenses/by/4.0/</subfield> <subfield code="a">Creative Commons Attribution 4.0</subfield> </datafield> <datafield tag="100" ind1=" " ind2=" "> <subfield code="a">Gennady Butov</subfield> </datafield> <datafield tag="041" ind1=" " ind2=" "> <subfield code="a">eng</subfield> </datafield> <datafield tag="245" ind1=" " ind2=" "> <subfield code="a">Ellipses and hyperbolas of decomposition of even numbers into pairs of prime numbers</subfield> </datafield> <datafield tag="700" ind1=" " ind2=" "> <subfield code="a">Gennady Butov</subfield> <subfield code="4">res</subfield> </datafield> <controlfield tag="005">20230708150144.0</controlfield> <datafield tag="653" ind1=" " ind2=" "> <subfield code="a">prime, primes, number, numbers, even, theory, ellipse, ellipses, hyperbole, hyperboles, decomposition</subfield> </datafield> <controlfield tag="001">77083</controlfield> <datafield tag="980" ind1=" " ind2=" "> <subfield code="a">publication</subfield> <subfield code="b">preprint</subfield> </datafield> <datafield tag="260" ind1=" " ind2=" "> <subfield code="c">2023-07-01</subfield> </datafield> <datafield tag="520" ind1=" " ind2=" "> <subfield code="a"><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></subfield> </datafield> <datafield tag="773" ind1=" " ind2=" "> <subfield code="a">10.15161/oar.it/77082</subfield> <subfield code="i">isVersionOf</subfield> <subfield code="n">doi</subfield> </datafield> <datafield tag="542" ind1=" " ind2=" "> <subfield code="l">open</subfield> </datafield> <datafield tag="856" ind1="4" ind2=" "> <subfield code="s">667120</subfield> <subfield code="u">https://www.openaccessrepository.it/record/77083/files/ellipses_hyperbolas_decompositions.pdf</subfield> <subfield code="z">md5:22e48d33ce05dd30365d77302513e1de</subfield> </datafield> <datafield tag="650" ind1="1" ind2="7"> <subfield code="a">cc-by</subfield> <subfield code="2">opendefinition.org</subfield> </datafield> <datafield tag="650" ind1="1" ind2=" "> <subfield code="a">Number Theory</subfield> <subfield code="0">(pmid)11</subfield> </datafield> <datafield tag="024" ind1=" " ind2=" "> <subfield code="a">10.15161/oar.it/77083</subfield> <subfield code="2">doi</subfield> </datafield> </record>
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