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| In [[mathematics]], the '''Redmond–Sun conjecture''', raised by Stephen Redmond and [[Zhi-Wei Sun]] in 2006, states that every interval [''x''<sup> ''m''</sup>, ''y''<sup> ''n''</sup>] with ''x'', ''y'', ''m'', ''n'' ∈ {2, 3, 4, ...} contains [[Prime number|primes]] with only finitely many exceptions. Namely, those exceptional intervals [''x''<sup> ''m''</sup>, ''y''<sup> ''n''</sup>] are as follows:
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| :<math>[2^3,\,3^2],\ [5^2,\,3^3],\ [2^5,\,6^2],\ [11^2,\,5^3],\ [3^7,\,13^3],</math>
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| :<math>[5^5,\,56^2],\ [181^2,\,2^{15}],\ [43^3,\,282^2],\ [46^3,\,312^2],\ [22434^2,\,55^5].</math>
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| The conjecture has been verified for intervals [''x''<sup> ''m''</sup>, ''y''<sup> ''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]].
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| ==External links==
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| * {{PlanetMath|urlname=RedmondSunConjecture|title=Redmond-Sun conjecture}}
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| * [http://listserv.nodak.edu/cgi-bin/wa.exe?A1=ind0603&L=nmbrthry Number Theory List (NMBRTHRY Archives) --March 2006]
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| * Sequence {{OEIS2C|A116086}} in the [[On-Line Encyclopedia of Integer Sequences]]
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| {{DEFAULTSORT:Redmond-Sun conjecture}}
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| [[Category:Conjectures about prime numbers]]
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