I organised a 24-hour long performance of "Vexations" in the mid-1980s for basically amateur players to raise money for a charitable purpose. Not many people came to listen, but I think we had a team of about 8 players, not all doing the same length of playing. As I had organised it i had to fill in the required number of hours, which I think came to five, which was not too bad an endurance test. I had also attended years earlier a performance in London given by one pianist (I cannot recall his name), but I stayed for only three hours. What does the initial instruction containing "840" actually mean, then, if not telling the performers the number of repeats?

I'm a bit surprised you managed to organise a performance without apparently understanding the "instruction" ! It translates as follows - "[In order] to play this phrase [motif] 840 times in a row, it will be as well to prepare oneself in advance, and in the deepest silence, through serious immobilities [implying contemplation or meditation]". Orledge's article notes that "Satie's performance indications have been the subject of much speculation" and that his "performance note is not a definite instruction but, rather, a suggestion that if one wants to play this phrase 840 times in a row . . ." Nevertheless, the implication is that there should be a fair number of repetitions.
Orledge's article is of great interest. I posted a link to it in message 1; also a link to the Bryars article about performances, which reveals that the solo version you heard was probably that by Richard Toop.<<<<<<<<From lovedaydewfall: yes, now you've mentioned the name I recall that it was Toop. I'm not sure whether the version of Satie's score that I used actually had that instruction on it. From somewhere or other I got the idea that the piece had to be played 840 times. Somehow or other we figured that 840 divided by 20 was 24, and that hence 20 repetitions were required each hour. We had the music photocopied 20 times, and as a simple method of computing how often it was played the pianist removed a sheet after each play. I had observed that this was how Toop did it, except, I think, he had 840 sheets, although I can't be sure. I only stayed for three hours, and it was ages ago.

Incidentally, there is a full CD of Vexations by Alan Marks (70 minutes - 40 repetitions) - not bad despite the odd mistake and the performer's suspect internal clock.
http://www.amazon.com/Vexations-Erik-Satie/dp/B000AM1TTE