Is it possible to remap i_CTRL-P to i_CRTL-X_CTRL-P

A while ago I found out about <C-X><C-P>. By now <C-P> is firmly in my muscle memory, but for the most part <C-X><C-P> seems an augmented but complete replacement.

I experimented mapping i<C-X><C-P> on to another control key which works fine. I'd like to imap <C-P> to <C-X><C-P> but this doesn't seem to work. I've tried several versions of imap, every time <C-P> acts like it has not been remapped (unlike another control key remap).

Any thoughts on how I can get <C-P> to work as <C-X><C-P> ?

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