Click here for a rather technical outline of the situation! There's even a suggestion that it is infinite - which seems absurd - but I'll leave you to decide for yourself whether that's possible.
My answer yesterday wasn't very helpful, so today - if you click here - you will find a Wiki Answers website which suggests the relevant distance is claimed to be 18,838 kilometres. That's 11,705 miles. I have no idea how accurate that is, however.
I know your question is a week old now, but I wondered whether you had watched today's 1 o'clock BBC News. A young man from Portland was interviewed on his journey planned to go all the way around Britain's coast. He was doing this with sponsorship to help pay the �20,000 it had cost to rescue him from a boat he'd stolen a year or two ago.
Anyway, the interviewer said he'd covered 900 miles and still had over 5,000 to go. So, there's yet another figure for your consideration!