New Passport and Residente Permanente

While my RP card doesn't show a passport number on it, when it was issued my passport was part of the process and guessing it resides somewhere in INM's records.

When I renew my passport and get a new number, do I need to notify INM?

I know that you are supposed to notify INM if your Mexican address changes, or if you work here, if you change employment venue, but I never heard anything about giving them a new passport number.
As Ferret said, if you leave the country and reenter, they scan your passport, so it would be in their database. Your RP isn't tied to your passport number, or I think they would have that on our RP cards.

From the INM site:

"Todo extranjero con Condición de Estancia de Residente Temporal, Residente Temporal Estudiante o Residente Permanente, está obligado a comunicar al INM, los cambios de estado civil, nombre o nacionalidad, domicilio o lugar de trabajo, dentro de los 90 días naturales posteriores a que ocurra dicho cambio."

Nothing about new passports.

I have a Global Entry card and it doesn't have my passport number on it, but it is in their record and I am obligated to update it when I get a new passport number.  

When I enter and leave MX I present both my RP and passport so that's why I was wondering if a new passport number will be an issue with INM when my account pops up on their screen.

I know they scan my US passport at INM, but can't recall if they also scan or enter the RP data at the same time.  

Guess I'll find out soon enough as i get ready to renew my passport.