Not all guesswork is dignified by the term conjecture though. Part of math school is to learn making and breaking guesses about things mathematical. As noted

Not all guesswork is dignified by the term conjecture though. Part of math school is to learn making and breaking guesses about things mathematical. As noted elsewhere ITT, a conjecture becomes one when there's a community-acknowledged aura of moral rightness about it. So at the very least, a bunch of people have tried to disprove it and failed.