You'll typically want a primary key for any of your Views (tables) since having one is critical to performing symmetric aggregates. If you had an explore based on a Table A and decided to join a Table B (that does not have a primary key) onto Table A, Looker would not allow you to use any of Table B's measures in that explore.
In regards to your question about an arbitrary number being your primary key, that is totally fine! You could also instead create a compound primary key that is a combination of two or more other dimensions in your View. Here's an article on how to create a compound primary key:
Hope this was helpful! Let us know if you have any other questions.