A difficult question and one that you really have to answer on your own, but how badly do you need to know who owns that number?

If you have been receiving nuisance calls then you can just report them to your local police station and let them take care of it. If you trust them to pursue it then that should be the matter resolved. Of course if you really want to make sure that someone is going to take action then you need to get in touch with their phone provider. The police may not have the power to do anything, but their service provider has the power to do a lot more and it could lead to the person making the calls being cut off or worse.

The problem is you can’t phone their service provider without using a reverse phone lookup website as without them then I don’t know of any other way of identifying who they are with (unless you phone their voicemail and they haven’t changed their message then sometimes you can tell from that). Even though there is a small charge involved then you can’t argue that the easiest option is to use one and discover the service provider and the details of their name and address.

Now you are better equipped when you want to go to the police and report them as you can give their name and address, of course you should still go to the phone company too.

Then they can’t escape getting into trouble. That doesn’t necessarily mean the person will stop, they can get a new phone to call you from etc - but if you know the name of the person you at least have the upperhand and if you let them know you are aware it is them then you are no longer being a faceless victim and most people are cowards and will just stop straight away.