which file should have my bash prompt, .profile vs .bashrc

I installed bash and have been trying to set up my prompt.  I notice
that if I add

  PS1='# '; export PS1

to my .profile, then I get the prompt when I log in, not when I /sudo
su/ from a regular user.  If I add

  PS1='# '; export PS1

to ~/.bashrc, then I get the prompt when I ``sudo su'', but not when I
log in.  I can add the prompt set up to both files, but I'm asking
myself---how do you guys avoid such redundancy?  (Thanks!)