For Publishers
DiscoveryMetadataPeer reviewHostingPublishing
For Researchers
JoinPublishReviewCollect
Register
Blog
About
Search
Advanced search
My ScienceOpen
Search
For Publishers
For Researchers
Blog
About
112
views
4
references
 Top references
cited by
0
    
0 reviews
 Review
0
comments
 Comment
0
recommends
+1 Recommend
1 collections
    0
    shares
      167
      similar
       All similar

      One-Click Submission System Now Available for SO Preprints, learn more on how this works in our blog post and don't forget to check the video, too!

      scite_
      0
      0
      0
      0
      Smart Citations
      0
      0
      0
      0
      Citing PublicationsSupportingMentioningContrasting
      View Citations

      See how this article has been cited at scite.ai

      scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.

      Version and Review History
      Preprint version 2
      Preprint version 1
       
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Note for the Prime Numbers

      Preprint
      In review
      research-article
      Author(s):   1 ,
      Publication date (Electronic preprint):
      Journal: ScienceOpen Preprints
      Publisher: ScienceOpen
      Keywords: Riemann hypothesis, prime numbers, Riemann zeta function, Chebyshev function
      Bookmark

            Revision notes

            We removed the result that the Cramér's conjecture is false. We considered this result only as a possible extension of this work since the used reference has never been published by a journal under peer-review (it is only available in arXiv despite of it was written by well-known number theorists).  Indeed, we added a Discussion section to include it. For that reason, we changed the Abstract and Keywords.

            Abstract

            Content

            Author and article information

            Journal
            Title: ScienceOpen Preprints
            Publisher: ScienceOpen
            Publication date (Electronic preprint): 28 March 2024
            Affiliations
            [1 ] GROUPS PLUS TOURS INC., 9611 Fontainebleau Blvd, Miami, FL, 33172, USA;
            Author notes
            Author information
            https://orcid.org/0000-0001-8210-4126
            Article
            DOI: 10.14293/PR2199.000744.v2
            SO-VID: d08ab6e6-f475-4264-bd63-f3d432064aa8
            License:

            This work has been published open access under Creative Commons Attribution License CC BY 4.0 , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com .

            History
            Date received : 6 March 2024
            Categories

            Data availability: Data sharing not applicable to this article as no datasets were generated or analysed during the current study.
            ScienceOpen disciplines: Number theory
            Keywords: Riemann hypothesis,prime numbers,Riemann zeta function,Chebyshev function

            References

            1. Connes Alain. An Essay on the Riemann HypothesisOpen Problems in Mathematics. p. 225–257. 2016. Springer International Publishing. [Cross Ref]

            2. Euler's Totient FunctionEquivalents of the Riemann Hypothesis. p. 94–143. Cambridge University Press. [Cross Ref]

            3. Ayoub Raymond. Euler and the Zeta Function. The American Mathematical Monthly. Vol. 81(10)1974. JSTOR. [Cross Ref]

            4. Nicolas Jean-Louis. Petites valeurs de la fonction d'Euler. Journal of Number Theory. Vol. 17(3):375–388. 1983. Elsevier BV. [Cross Ref]

            Comments

            Comment on this article