Acknowledgement of submission to the Annals of Mathematics Does the Annals of Mathematics always to reply every submission within a few days? I submitted a few times to them before, and every time I hear back from the  editorial office very soon (within three days). But this time there has been no response to my submission for more than one week.

Is this normal? Or I should inquire about the status of my paper?
A week is not so different from three days, especially if that week includes the July 4th holiday in the U.S.  If several weeks pass and you still have been given no indication that the paper was received, then it would be worth asking if they got it, but in the meantime I don't think you need to worry.