Shortest distance was 0km for my son's travelbug The Kozzy Bug-gy that we placed last august. Path5inder found it a few days after we placed it and he has not been logged since.
In addition to shortest distance, you at least got "a few days" so I can beat that with a few hours. We placed one in the Niagara Falls area. Someone took it a few hours later and it was never heard from again!
My very first purchase was a poppy geocoin. After activating it, I placed it in a puzzle cache in front of a neighbor's house (like 7 houses away). It was grabbed a few days later and logged by the cacher...and never moved or seen again. So it lasted for 2 days and made it 7 houses away... Grrr
