Actually there are 4722 valid identities.
As for the "crazy growth" of the network, I doubt it, since the reward is getting smaller and smaller with the network growth, so many will leave. Maybe this will change in the future since we are on a semi-mainnet (semi-testnet) phase.
^Is that so? I think the more people who join the network, the more rewards the user can get. It seems that I was wrong.
^I have downloaded Idena, but until now I haven't received the code

Yeah, the reward/block is fixed, so the more people join the network the less rewards we all get. Not that this is a bad thing tho.
BTW, if you still need an invite I have one for you, just PM me.
2 invites left here, if anyone needs any.