<?xml version="1.0" encoding="UTF-8"?>
<article article-type="Research Article">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher">journal-of-discrete-mathematical-sciences-and-cryptography</journal-id>
      <journal-title-group>
        <journal-title>Journal of Discrete Mathematical Sciences and Cryptography</journal-title>
      </journal-title-group>
      <issn publication-format="electronic">2169-0065</issn>
      <issn publication-format="print">0972-0529</issn>
      <publisher>
        <publisher-name>Taru Publications</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.47974/JDMSC-2011</article-id>
      <title-group>
        <article-title>On using of weird number sequence in counting Beurling prime systems</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Hussein</surname>
            <given-names>Hussein A.</given-names>
          </name>
          <aff>Department of Mathematics, College of Education for Pure Science, University of Babylon, Babylon, Iraq</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Al-Maamori</surname>
            <given-names>Faez A.</given-names>
          </name>
          <aff>Department of Security, College of Information Technology, University of Babylon, Babylon, Iraq</aff>
        </contrib>
      </contrib-group>
      <volume>27</volume>
      <issue>5</issue>
      <fpage>1695</fpage>
      <lpage>1704</lpage>
      <pub-date date-type="pub">
        <day>26</day>
        <month>08</month>
        <year>2024</year>
      </pub-date>
      <abstract>
        <p>Beurling introduces the generalisation of the primes in the third decade of last century. He said in his work that any positive , increasiy real sequences {ri}∞i=1 with r1 precisely qreatar than one called Beurling  primes the fundamental Furthermore, the series of Beurling integers (or B-integers) could be generated by using the F-T-A. This work adapted the generalization  Balanzarios work “Exampls of the generalised prime system“ where using the sequence of weird numbers to show that size of |N(x) – ax|, a &gt; 0 is always less that the asymptotic behavior of πq(x).</p>
      </abstract>
      <kwd-group>
        <kwd>F-T-A and B-prime systems</kwd>
      </kwd-group>
      <custom-meta-group>
        <custom-meta>
          <meta-name>access</meta-name>
          <meta-value>open</meta-value>
        </custom-meta>
        <custom-meta>
          <meta-name>retracted</meta-name>
          <meta-value>no</meta-value>
        </custom-meta>
      </custom-meta-group>
    </article-meta>
  </front>
</article>
