What does it mean for one conjecture to be stronger than another?

[UncertaintyAjay]

So, I was reading the Wikipedia page for Legendre's Conjecture and I came across this:
"Two stronger conjectures, Andrica's conjecture and Oppermann's conjecture"
My question is this: What does it mean for one conjecture to be 'stronger' than another?

 

[fresh_42]

Usually it means that if the stronger conjecture is true then the weaker one is true as well. But they are not equivalent.