How to update integer primary key adding 1000?
Yes, you can do that, however if you need to do this regularly, then something is probably bad in your DB or software design.

The purpose of the primary keys is to identify the records. They should not have any additional information. This rule may be stepped over on the some optimization reasons, or in special cases (like DB merge, refactor) but that is all.

Furthermore, typically the primary keys are referred by external parts of your software (either by foreign keys from other tables, or by non-db parts of your software). Be careful, changing a primary key requires to change it everywhere where they are referred. The CASCADE parameter of the foreign keys may help a lot, if you are using MySQL.

Put this additional information in alternate columns, you will spare a lot of pain on the longterm with that.