INTERNATIONAL JOURNAL OF NOVEL RESEARCH AND DEVELOPMENT International Peer Reviewed & Refereed Journals, Open Access Journal ISSN Approved Journal No: 2456-4184 | Impact factor: 8.76 | ESTD Year: 2016
Scholarly open access journals, Peer-reviewed, and Refereed Journals, Impact factor 8.76 (Calculate by google scholar and Semantic Scholar | AI-Powered Research Tool) , Multidisciplinary, Monthly, Indexing in all major database & Metadata, Citation Generator, Digital Object Identifier(DOI)
In this article, two theorems and one corollary about theory of distribution of prime numbers are
given with proof.
For arbitrary natural number b ˃ 1.
Theorem (1) states that Number of prime numbers in the form 6k+1 contained in the closed interval
[36b+11, 6(b-1)(6b+1)+1] is almost (approximately) equal to
(b-2)(6b+1)(4/5)(6/7)(10/11)(12/13)(16/17)(18/19)……………((Pr-1)/Pr)
Theorem (2) states that Number of prime numbers in the form 6k-1 contained in the closed interval
[36b+11, 6(b-1)(6b+1)+1] is almost (approximately) equal to
(b-2)(6b+1)(4/5)(6/7)(10/11)(12/13)(16/17)(18/19)……………((Pr-1)/Pr)
Corollary states that Number of prime numbers contained in the closed interval [36b+11, 6(b-1)(6b+1)+1]
is almost (approximately) equal to
2(b-2)(6b+1)(4/5)(6/7)(10/11)(12/13)(16/17)(18/19)……………((Pr-1)/Pr)
Where Pr is the greatest prime number such that Pr ≤ 6(b-1)+1.
Keywords:
Cite Article:
"Article 5 About Theory Of Distribution Of Prime Numbers ", International Journal of Novel Research and Development (www.ijnrd.org), ISSN:2456-4184, Vol.8, Issue 5, page no.b411-b425, May-2023, Available :http://www.ijnrd.org/papers/IJNRD2305153.pdf
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ISSN:
2456-4184 | IMPACT FACTOR: 8.76 Calculated By Google Scholar| ESTD YEAR: 2016
An International Scholarly Open Access Journal, Peer-Reviewed, Refereed Journal Impact Factor 8.76 Calculate by Google Scholar and Semantic Scholar | AI-Powered Research Tool, Multidisciplinary, Monthly, Multilanguage Journal Indexing in All Major Database & Metadata, Citation Generator
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