You are not a randonneur. A randonneur rides organised events sanctioned by the ACP (or BRM).
http://www.audax-club-parisien.com/EN/index.php
Randonneuring involves long distance cycling, but not all long distance rides are randonnees.
I have a list of randonneuring club websites on my Links page so if you're interested in becoming a randonneur, you can look up the club in your area and see what events they have on:
http://www.machka.net/links.htm
That Links page also has links to other (non-randonneuring) long distance events like 24-hour time trials, the RAAM, etc.
As for minimum mileage ... here's what the description of this forum says:
"Do you enjoy centuries, double centuries, brevets, randonnees, and 24-hour time trials? Share ride reports, and exchange training, equipment, and nutrition information specific to long distance cycling. This isn't for tours, this is for endurance events cycling."
So ... a metric century (100 km) is sort of the gateway to long distance cycling, and long distance cycling begins with the imperial century (100 miles).
If you've done 50 mile rides, you should be able to go out and ride a metric next weekend ... you're on your way to being a long distance cyclist.