On a SS holy cow!
Longest I managed "fresh" here at home is about 530km inside 24 and could have continued albeit not for too much longer.
Longest I rode without a proper rest (but an odd micro nap) was on TCR to make the CP in Poland from Slovenia. It was 675km, headwinds and bloody hilly. Not something I would ever want to repeat.
I have a loose goal of trying for a 700km 24 hour TT before my 60th, so a few years to refine it. Id need to use a faster set up than my endurance outfit though.