Brocard's problem and Brown numbers

Brocard's problem asks for solutions to a simple Diophantine equation. Only three are known. Are there any others? My other YouTube channels: The Science Fiction Rock Experience ( the music show I produce):    / @sciencefictionrockexperience   My science and music channel::    / @drdaviddarling   Science World (with Emrah Polat):    / @scienceworld1   My website: https://www.daviddarling.info My latest book is available here: https://oneworld-publications.com/wor...