Benjamin Graham formula: Difference between revisions

Revision as of 02:11, 4 February 2014

In mathematics, the Redmond–Sun conjecture, raised by Stephen Redmond and Zhi-Wei Sun in 2006, states that every interval [x^m, yⁿ] with x, y, m, n ∈ {2, 3, 4, ...} contains primes with only finitely many exceptions. Namely, those exceptional intervals [x^m, yⁿ] are as follows:

[2^{3}, 3^{2}], [5^{2}, 3^{3}], [2^{5}, 6^{2}], [1 1^{2}, 5^{3}], [3^{7}, 1 3^{3}],

[5^{5}, 5 6^{2}], [18 1^{2}, 2^{15}], [4 3^{3}, 28 2^{2}], [4 6^{3}, 31 2^{2}], [2243 4^{2}, 5 5^{5}] .

The conjecture has been verified for intervals [x^m, yⁿ] below 10¹². It includes Catalan's conjecture and Legendre's conjecture as special cases. Also, it is related to the abc conjecture as suggested by Carl Pomerance.

External links

Sequence Physiotherapist Rave from Cobden, has hobbies and interests which includes skateboarding, commercial property for sale developers in singapore and coin collecting. May be a travel freak and in recent years made a journey to Wet Tropics of Queensland. in the On-Line Encyclopedia of Integer Sequences

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-Friends call him Royal. Her husband and her chose to reside in Alabama. What she loves doing is taking part in croquet and she is attempting to make it a occupation. After being out of my job for years I grew to become a production and distribution officer but I strategy on changing it.<br><br>Feel free to visit my page; [http://www.gettingtherefromhere.info/User-Profile/userId/13851 www.gettingtherefromhere.info]
+In [[mathematics]], the '''Redmond–Sun conjecture''', raised by Stephen Redmond and [[Zhi-Wei Sun]] in 2006, states that every interval [''x''<sup>&nbsp;''m''</sup>,&nbsp;''y''<sup>&nbsp;''n''</sup>] with ''x'',&nbsp;''y'',&nbsp;''m'',&nbsp;''n''&nbsp;&isin;&nbsp;{2,&nbsp;3,&nbsp;4,&nbsp;...} contains [[Prime number|primes]] with only finitely many exceptions. Namely, those exceptional intervals [''x''<sup>&nbsp;''m''</sup>,&nbsp;''y''<sup>&nbsp;''n''</sup>] are as follows:
+:<math>[2^3,\,3^2],\ [5^2,\,3^3],\ [2^5,\,6^2],\ [11^2,\,5^3],\ [3^7,\,13^3],</math>
+:<math>[5^5,\,56^2],\ [181^2,\,2^{15}],\ [43^3,\,282^2],\ [46^3,\,312^2],\ [22434^2,\,55^5].</math>
+The conjecture has been verified for intervals [''x''<sup>&nbsp;''m''</sup>,&nbsp;''y''<sup>&nbsp;''n''</sup>] below 10<sup>12</sup>. It includes [[Catalan's conjecture]] and [[Legendre's conjecture]] as special cases. Also, it is related to the [[abc conjecture]] as suggested by [[Carl Pomerance]].
+==External links==
+* {{PlanetMath|urlname=RedmondSunConjecture|title=Redmond-Sun conjecture}}
+* [http://listserv.nodak.edu/cgi-bin/wa.exe?A1=ind0603&L=nmbrthry  Number Theory List (NMBRTHRY Archives) --March 2006]
+* Sequence {{OEIS2C|A116086}} in the [[On-Line Encyclopedia of Integer Sequences]]
+{{DEFAULTSORT:Redmond-Sun conjecture}}
+[[Category:Conjectures about prime numbers]]

Benjamin Graham formula: Difference between revisions

Revision as of 02:11, 4 February 2014

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