Search for good examples of Hall’s conjecture
Stal O. Aanderaa, Lars Bjørlykke Kristiansen, Hans Kristian Ruud · Mathematics of Computation · 2017
A good example of Hall’s conjecture is a pair of natural numbers x , y x,y such that 0 > | x 3 − y 2 | > x 1 / 2 0 > |x^3 - y^2| > x^{1/2} . We have implemented a new algorithm and found nine not previously known good examples. Moreover, we have verified that all good examples with x > 10 29 x > 10^{29} are now found.