Redmond–Sun conjecture

In mathematics, the Redmond–Sun conjecture, raised by Stephen Redmond and Zhi-Wei Sun in 2006, states that every interval [x ^m, y ⁿ] with x, y, m, n ∈ {2, 3, 4, ...} contains primes with only finitely many exceptions. Namely, those exceptional intervals [x ^m, y ⁿ] are as follows:

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.