Yes, there are quite a few papers of this kind. Of course, if proving the implication to known theorems or between the various conjectures is interesting and challenging then this is "ordinary". If the paper contains only a statement of the conjectures then this is indeed more special. There are papers who have short note sections or problem sections appropriate for such papers. (I published a couple of papers with just conjectures in such sections.)

As a general rule, it always makes sense to try other journals, to consult with friends, colleagues and teachers, to put the paper on the arxiv, and to try to improve the paper.

Yes, there are quite a few papers of this kind. Of course, if proving the implication to known theorems or between the various conjectures is interesting and challenging then this is "ordinary". If the paper contains only a statement of the conjectures then this is indeed more special. There are journals which have short note sections or problem sections appropriate for such papers. (I published a couple of papers with just conjectures in such sections.)

As a general rule, it always makes sense to try other journals, to consult with friends, colleagues and teachers, to put the paper on the arxiv, and to try to improve the paper.

Yes, there are quite a few papers of this kind. Of course, if proving the implication to known theorems or between the various conjectures is interesting and challenging then this is "ordinary". If the paper contains only a statement of the conjectures then this is indeed more special. There are papers who have short note sections or problem sections appropriate for such papers. (I published a couple of papers with just conjectures in such sections.)

As a general rule, it allwyas make sense to try other journals, to consult with friends/colleagues/teachers, to put the paper on the arxive, and to try to improve the paper.

Yes, there are quite a few papers of this kind. Of course, if proving the implication to known theorems or between the various conjectures is interesting and challenging then this is "ordinary". If the paper contains only a statement of the conjectures then this is indeed more special. There are papers who have short note sections or problem sections appropriate for such papers. (I published a couple of papers with just conjectures in such sections.)

As a general rule, it always makes sense to try other journals, to consult with friends, colleagues and teachers, to put the paper on the arxiv, and to try to improve the paper.