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 sets A and B are defined which are two subsets of natural numbers. Let k be an arbitrary natural number. k belongs to A implies 6k+1 a composite number, and k not belongs A implies 6k+1 a prime number. k belongs to B implies 6k-1 a composite number, and k not belongs to B implies 6k-1 a prime number. k belongs to A∩B implies 6k+1 and 6k-1 both are composite numbers, and k not belongs to A∪B implies 6k+1 and 6k-1 both are prime numbers. By using the above thesis, theorem (3) is proved. Theorem (3) states that any arbitrary natural number n the two closed intervals
[6(p-n-1)+2, 6p-2] and [6p+2, 6(p+n+1)-2] contains no prime number. where
p=q(62-1)(122-1)(182-1)………...(n262-1) and q is any natural number.
Theorem (4) and Theorem (5) are given without proof. Since proofs of Theorem (4) and Theorem (5) are similar to proof of Theorem (3).
Keywords:
" theory of distribution of prime number"
Cite Article:
"ABOUT THEORY OF DISTRIBUTION OF PRIME NUMBERS", International Journal of Novel Research and Development (www.ijnrd.org), ISSN:2456-4184, Vol.8, Issue 4, page no.b527-b538, April-2023, Available :http://www.ijnrd.org/papers/IJNRD2304175.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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