What defines a Prodigy?

[mtm]

A little over a month ago, I began teaching a 13 year old boy--with no previous musical experience--the piano.  He knew absolutely nothing about music.  His mom booked him for 30 minute lessons.  
Well, I started him out in the Alfred Adult series---the next week, he came back with about one third of the book learned--and most of it memorized!  He knew all the notes by sight and understood and played the rhythm perfectly.  I thought this was quite startling!
By the 3rd lesson, I handed him a not- so simplied version of Für Elise, By the 4th lesson, he's learned it and almost had it memorized and by the 5th lesson he had it nailed and the following weekend I had him perform it at a recital.
We are now at the 7th lesson, and have switched to a 60 min. lesson--I am giving him some Bach pieces from Anna Magdalena's notebook and other original pieces of some great composers.  I also am trying to fill in the theory at a reasonable pace to keep him up with what he's playing.  He also enjoys composing--he wrote two variations of Brahm's Lullaby this past week and they were quite good!
My question is--as the subject states--Does this sound like a prodigy?
Regardless--does anyone have suggestions for repertoire and perhaps theory or computer programs that might be helpful?
I'd appreciate any ideas . . .  

[Colette]

it sounds like you've got a very talented student. lucky you. i wouldn't worry too much about whether he's a "prodigy" or not, but i would worry about finding the best ways to train him. it sounds like he learns quickly, but don't overwhelm him with big, complicated pieces too soon. many teachers who find themselves with what they deem to be a "prodigy" have an urge to pile the kid with repertoire that is entirely too difficult. keep him at a steady pace, one that is challenging, but balanced.
i'm really not a fan of using the computer as a teaching tool, so i can't be of any help there. i do think it's a good idea to give him some easy bach pieces, then move on (gradually, or speedily at your own discretion) to the inventions. simple clementi sonatas and even some scarlatti sonatas would be great. you can assign these as "challenge" pieces while he's still working through the "level" books (if he's still on them). start him on scales early. they will help him immensely, presently and later on.
it's great that he likes composing. have him write more variations! you should really nurture that interest. on his own time, suggest that he listen to a lot of classical piano and orchestral music if he doesn't already. tell him to check out classical concerts from time to time.  
since you've found a talented student, you'll, of course, want to teach him correctly and carefully from the very beginning. the foundations of learning are absolutely the most important, especially for a gifted student. i don't know if you're an experienced teacher or not, but, after you've taught this kid for a while and if he continues to show huge talent, maybe you should consider introducing him to another, very experienced teacher. this teacher could give you and your student his/her objective opinion on his playing, and suggest what to do next, or even take him on as a personal student. also, talk to your student's parents. tell them how you feel about his progress, and let them know that you are dealing with a "special case." if the parents are informed, you can be sure they'll be pleased and will (most likely) want to take his pianistic future seriously.
also, if you can, give him many opportunities to perform, for other students, teachers, parents, it doesn't matter who the audience is as long as he gets a chance to play frequently.

[sybre]

listen to this 11 year old play!
https://www.clareyeo.com