, the Redmond-Sun conjecture
(raised by Stephen Redmond and Zhi-Wei Sun
in 2006) states that an interval
with only finitely many exceptions. Namely, those exceptional intervals
are as follows:
The conjecture has been verified for intervals below . 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.