Redmond-Sun conjecture

Redmond-Sun conjecture

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

: [2^3,,3^2] , [5^2,,3^3] , [2^5,,6^2] , [11^2,,5^3] , [3^7,,13^3] ,

: [5^5,,56^2] , [181^2,,2^{15}] , [43^3,,282^2] , [46^3,,312^2] , [22434^2,,55^5] .

The conjecture has been verified for intervals [x^m,y^n] below 10^{12}. 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

* [http://planetmath.org/encyclopedia/RedmondSunConjecture.html Redmond-Sun Conjecture in PlanetMath]

* [http://listserv.nodak.edu/cgi-bin/wa.exe?A1=ind0603&L=nmbrthry Number Theory List (NMBRTHRY Archives) --March 2006]

* [http://www.research.att.com/~njas/sequences/A116086 Sequence A116086 in the On-Line Encyclopedia of Integer Sequences]


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