Redmond-Sun conjecture

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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 $x,y,m,n\in\{2,3,\ldots\}$ 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 $1012$ . 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.