I called back the number on another line they asked for the number that they called--I just put in 9999999999 and someone came on the phone and said "good morning, who do I have the pleasure of speaking with", I asked her where I was calling and she said that she couldn't divulge that information.  So I proceeded to tell her that I couldn't divulge my name and hung up.  Most likely a bill collector??

The number calls me frequently throughout the day, and requests that I input my personal number when I call back so they know who I am....but I don't know and have never been able to discover who THEY are.

I received a call from this number, where they say they are a collection agency. I requested from them to proof of identity. But then they haven been able to proof it. It sound to me that it is a scam.

Good job.  Never acknowledge debt on the phone and demand written, verifiable proof mailed via the USPS.  Here are some tips from the FTC on identifying fake debt collectors, what to do if you are contacted by a real debt collector and some interesting information about phantom debt.  There's also a great story (last link) about a woman who was awarded 82 million dollars because of a debt collectors harassment.

Your rights (what a debt collector can and cannot do).
http://www.consumer.ftc.gov/articles/0149-debt-collection

How to tell a real from a fake debt collector:
https://www.consumer.ftc.gov/articles/0258-fake-debt-collectors

FTC stops abusive debt collection:
https://www.ftc.gov/news-events/press-release ... tened-consumers

Banned Debt Collectors
https://www.ftc.gov/enforcement/cases-proceedings/banned-debt-collectors
IRS Scams

Phantom Debt
https://www.consumer.ftc.gov/blog/haunted-phantom-debt

Woman awarded 82 million dollars for malicious prosecution by a debt collector
http://kcur.org/post/jury-awards-kc-woman-83-million-debt-collection-case

Just received a call on my phone 407-968-0042 no message left and I do not answer my phone while at work nor after working hours  unless I know who is calling me.