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)
Let
G ={x | x∈N and 6x-1, 6x+1, 6x+5 & 6x+7 are all prime numbers}
In other word,
G = {x | x∈(A∪B)c and x+1∈(A∪B)c}
Where A and B are two subsets of set of natural numbers as defined in my second article IJNRD 2304175. Set of natural numbers as universal set.
i.e
G = {17, 32, 137, 247, 312, 347, 542, 577, 942, 1572, ………………………}
In this article, Theorem states that,
n( [6b+1, (b-1)(6b+1)-1]∩G )
≈ (b-2)(6b+1)(1/5)(3/7)(7/11)(9/13)………….((Pr-4)/Pr).
Where Pr is greatest prime number such that Pr ≤ 6(b-1)+1.
Infiniteness of pairs of two consecutive pairs of twin prime numbers in the form 6k-1 & 6k+1 and 6k+5 & 6k+7 is the immediate consequence of the above theorem.
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Cite Article:
"Article 6 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.e200-e219, May-2023, Available :http://www.ijnrd.org/papers/IJNRD2305420.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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