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

• Redmond-Sun Conjecture in PlanetMath
• Number Theory List (NMBRTHRY Archives) --March 2006
• Sequence A116086 in the On-Line Encyclopedia of Integer Sequences