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# Redmond-Sun conjecture

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

$\left[2^3,,3^2\right], \left[5^2,,3^3\right], \left[2^5,,6^2\right], \left[11^2,,5^3\right], \left[3^7,,13^3\right],$

$\left[5^5,,56^2\right], \left[181^2,,2^\left\{15\right\}\right], \left[43^3,,282^2\right], \left[46^3,,312^2\right], \left[22434^2,,55^5\right].$

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