What Is the Farthest One Human Being Has Ever Been from Another?

Randall Munroe, the roboticist and artist behind the webcomic xkcd, operates the blog “What If?” In it, he responds to strange scientific queries by readers. Most recently, reader Bryan J. McCarter asked Mr. Munroe:

What is the furthest one human being has ever been from every other living person? Were they lonely?

Mr. Munroe suspects that it was either Mike Collins, Dick Gordon, Stu Roosa, Al Worden, Ken Mattingly or Ron Evans. These are astronauts who stayed in the Apollo command module in lunar orbit while other astronauts landed on the surface of the moon. While on the opposite side of the moon, these men would have been 3,585 kilometers from any other human.
But, Mr. Munroe explains, there are also other possible candidates. An individual Polynesian during the migration of those peoples across the Pacific Ocean might have become isolated at a great distance from other human beings. A hypothetical shipwrecked sailor in the Eighteenth Century south Atlantic Ocean might also qualify.
But these are speculations. We can be sure about only the isolation of Apollo astronauts.
Were they lonely? Probably not. Mike Collins from the Apollo 11 mission described his experience:

Far from feeling lonely or abandoned, I feel very much a part of what is taking place on the lunar surface ... I don't mean to deny a feeling of solitude. It is there, reinforced by the fact that radio contact with the Earth abruptly cuts off at the instant I disappear behind the moon.
I am alone now, truly alone, and absolutely isolated from any known life. I am it. If a count were taken, the score would be three billion plus two over on the other side of the moon, and one plus who knows what on this side.