alpinepony - ds has already started doing that in a low-key way when playing card games at home. he doesn't realise he's doing it, but he knows exactly what's left to play and (probably) who has it. he did start trying to load his own cards, but we've nipped that one in the bud. 
he started nursery a couple of days after his thrid birthday and could do the coins trick - the nursery was a bit freaked out with the 'shop' role play
i would go up to tuck him in and he'd announce a calculation to me, as though he'd just been lying there pondering it whilst waiting.
he's nearly 10 now, and is still number crazy, but is less random about it. i assume it's all still going on in his head, but he discusses it less. still a whizz at math at school.
i dreamt about numbers for the entirety of one christmas. it was when i was a student and had taken a holiday job in a jeweller where you had to input a five or six digit code into the till for each item sold. i found it v easy to memorise the numbers which saved a lot of time (some of the other staff wrote them all down), but the downside was, even when i was sleeping, i was recounting strings of numbers in my head. it was awful.
i wouldn't worry too much about hime being obsessed with his toy numbers or even numberjacks tbh. that is not really any different to any other kid getting a fix on something (usually thomas lol, but anything will do).
oh, prize. that takes me back. i used to listen to the shipping forecast at about 12 and draw up the met charts to get a picture of what the weather was doing. 
hopefully this has reassured you, rather than made you concerned about the bizarre lives of mners, op.
i'm not even close to being a mathlete btw. i'm an english major with an unhealthily woolly leaning towards qualitative research. quant makes me want to kill people.