I've been receiving calls from "LLM Services" (this is what shows on the caller ID). We screen all of our calls with caller ID and an answering machine. We do not actually pick up unless we know exactly who it is calling. Only a select few people have our number - it is unlisted, and was recently changed in late March 2008.
The person or persons calling either leave a blank message, or something of the nature of "Hello, are you there?" or something to that effect, they do not leave a real message (name, callback #, reason for calling, etc.)
They just called this morning at about 8 am while my wife and I were getting ready to leave for work. The number from the caller was 602-281-4730. The 602 is Phoenix AZ area code and therefore did not show up on the caller ID so I know that it was a local call.
I have been getting these type of calls for a while now and I'm getting tired of them - they are more of an annoyance than anything. I am going to use the Internet, including sites like this one, to get to the bottom of this.