My question is that : Why are there so many conjectures in elementary number theory and comparatively less in others? This is particularly weird because every topic in maths should have its equal share of conjectures. On the other hand there are so many conjectures in number theory. Also (most of) these conjectures are so easy to state but literally impossible to prove.
I thought of this question because I myself have two open conjectures in number theory.
I think there are two ways to answer this question.
I am atleast not sure that there are more in number theory in other fields. However as number theory is close to basic arithmetic at times the conjectures are easier to understand and thus they get more famous, so it simply appears as there are more conjectures than in other fields.
If 1. is false i.e. there are more conjectures in number theory than in other fields, this is probably because questions are easy to ask but seem in general quite hard to proove, as we have seen with Golbachs conjecture, Twin prime conjecture and Fermats theorem. Also, most fields rely more or less on numbers and thus number theory appears when doing their calculations which leads to more conjectures.