Home - News ( United States | United Kingdom | Italy | Germany ) - Football scores

Showing content from https://link.springer.com/article/10.1007/s11253-008-0034-7 below:

Re-extending Chebyshev’s theorem about Bertrand’s conjecture

In this paper, Chebyshev’s theorem (1850) about Bertrand’s conjecture is re-extended using a theorem about Sierpinski’s conjecture (1958). The theorem had been extended before several times, but this extension is a major extension far beyond the previous ones. At the beginning of the proof, maximal gaps table is used to verify initial states. The extended theorem contains a constant r, which can be reduced if more initial states can be checked. Therefore, the theorem can be even more extended when maximal gaps table is extended. The main extension idea is not based on r, though.

This is a preview of subscription content, log in via an institution to check access.

Springer+

from €39.99 /Month

• Starting from 10 chapters or articles per month
• Access and download chapters and articles from more than 300k books and 2,500 journals
• Cancel anytime

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

1. G. Mosaheb, Elementary Number Theory, Vol. 2, Pt. 2, Soroush Press, Tehran (1980).

   Google Scholar 

2. P. Ribenboim, The New Book of Prime Number Records, Springer, New York (1995).

   Google Scholar 

3. C. K. Caldwell, http://www.utm.edu/research/primes/notes/GapsTable.html.

4. J. Young and A. Potler, “First occurrence of prime gaps,” Math. Comput., 53, 221–224. (1989).

   MathSciNet  Google Scholar 

5. T. Nicely, “New maximal prime gaps and first occurrence,” Math. Comput., 68, 1311–1315 (1999).

   Article  MATH  MathSciNet  Google Scholar 

6. T. Nicely and B. Nyman, First Occurrence of a Prime Gap of 1000 or Greater, Preprint, http://www.trnicely.net/index.html.

Download references

1. The University of Manchester, Manchester, UK

   A. Shams

2. Ferdowsi University of Mashhad, Mashhad, Iran

   A. Shams

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 12, pp. 1701–1706, December, 2007.

Shams, A. Re-extending Chebyshev’s theorem about Bertrand’s conjecture. Ukr Math J 59, 1914–1921 (2007). https://doi.org/10.1007/s11253-008-0034-7

Download citation

• Received: 13 June 2006

• Revised: 18 January 2007

• Published: 11 July 2008

• Issue Date: December 2007

• DOI: https://doi.org/10.1007/s11253-008-0034-7

RetroSearch is an open source project built by @garambo | Open a GitHub Issue

Search and Browse the WWW like it's 1997 | Search results from DuckDuckGo

HTML: 3.2 | Encoding: UTF-8 | Version: 0.7.4