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<records>
  <record>
    <language>eng</language>
    <publisher>Science and Education Publishing</publisher>
    <journalTitle>Turkish Journal of Analysis and Number Theory</journalTitle>
    <eissn>2333-1232</eissn>
    <publicationDate>2020-07-19</publicationDate>
    <volume>8</volume>
    <issue>3</issue>
    <startPage>52</startPage>
    <endPage>56</endPage>
    <doi>10.12691/tjant-8-3-1</doi>
    <publisherRecordId>TJANT2020831</publisherRecordId>
    <documentType>article</documentType>
    <title language="eng">An Elementary Proof of the Twin Prime Conjecture</title>
    <authors>
      <author>
        <name>B. Gensel</name>
        <email>b.gensel@fh-kaernten.at</email>
        <affiliationId>1</affiliationId>
      </author>
    </authors>
    <affiliationsList>
      <affiliationName affiliationId="1">Berndt Gensel, Carinthia University of Applied Sciences, Austria</affiliationName>
    </affiliationsList>
    <abstract language="eng">It is well known that every prime number  has the form  or  We will call  the generator of  Twin primes are distinghuished due to a common generator for each pair. Therefore it makes sense to search for the Twin Primes on the level of their generators. This paper present a new approach to prove the Twin Prime Conjecture by a sieve method to extract all Twin Primes on the level of the Twin Prime Generators. We define the --numbers  as numbers for which holds that  and  are coprime to the prime  By dint of the average distance  between the --numbers we can prove the Twin Prime Conjecture indirectly.</abstract>
    <fullTextUrl format="pdf">http://pubs.sciepub.com/tjant/8/3/1/tjant-8-3-1.pdf</fullTextUrl>
    <keywords language="eng">
      <keyword>twin prime</keyword>
      <keyword>primes</keyword>
      <keyword>number theory - MSC2010: 11A41</keyword>
    </keywords>
  </record>
</records>