Strange Mobile device tried to connect to my iMac via Bluetooth! Should I be concerned?

Question

I woke up this morning with a pop-up message saying that a mobile device tried to pair with my system but was rejected most likely from an incorrect password. I've always had "bluetooth" enabled. Never used it though, I have a wired mouse and keyboard. I never thought about possible threats occuring from this until now. I originally had all default settings turned on for bluetooth but no sharing enabled. I clicked off "discoverable" and turned bluetooth off altogether. My concern is that I am seeing a "T-Mobile myTouch Q" Smartphone in the list. I don't own this type of phone. I've never had a t-mobile phone or know anybody who does. I tried to "browse" the device but I get an error. I am unable to remove the device from my list.
It doesn't appear to be connect or ever have been connected to my knownledge but I would like it taken off.
Is there any way somebody can hack your iMac via a mobile device? I went on a researching rampage this morning but am unsure of what to think at this point. If bluetooth only operates up to 30 feet of range, who could possibly have wanted to connect at 4-5 am in the morning? Also, if they were paired, exacly what information can they gain from being paired via bluetooth to a mobile device?
Should I be concerned about this? I have Mac firewall enabled in stealth mode. Have Sophos installed and up to date and running. All sharing is turned off. What else can I do and how can I remove this device from the list so I can use bluetooth in the near future without any worries?
Thanks for any help!

Answer 1

WZZZ wrote:
Csound1 wrote:
Bluetooth is very limited, in range (20 to 40ft on a good day)....
The Bluetooth on my wife's iPad, before I turned it off, put out a signal much further than that. Out of curiosity, I took it down to the lobby of our building, easily a hundred feet or more--just guessing--through one floor and a number of walls. It was still getting a healthy signal there. Maybe the Mac's Bluetooth isn't so powerful. Probably depends on the device being used. I know if I move my mouse not far away from the Mac the connection is quickly lost.
That is an extraordinary connection distance for BlueTooth, did you happen to investigate the data rate at that range?
This really only applies to older Blutooth devices (so should exclude an iPad)
Many USB Bluetooth adapters or "dongles" are available, some of which also include an IrDA adapter. Older (pre-2003) Bluetooth dongles, however, have limited capabilities, offering only the Bluetooth Enumerator and a less-powerful Bluetooth Radio incarnation.[citation needed] Such devices can link computers with Bluetooth with a distance of 100 meters, but they do not offer as many services as modern adapters do.[clarification needed]
The spec for Bluetooth is a bit vague but here is some general info.
But wireless is a bit like playing Roulette