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You don't need to claim the token now, but someday in future after end of the ico you need to claim them, because as far as I understood than they will be frozen and converted into real EOS blockchain token.

Keep also in mind, that their is a risk that the EOS Smart Contract could be hacked. What happens in this case, if somebody else claims your EOS token?

I purchased EOS tokens using MyEtherWallet and the transaction went through no problem. However I have not been able to successfully claim them. I have read every instructions out there that I can find. I have wasted a bunch of fees trying to claim them. I have registered an EOS key twice, which I know is a waste. Can anyone tell me what I am missing or doing wrong? I can see that the purchase transaction went through now a week ago, but I can't seem to claim them. Are my tokens lost? One step I saw in the above tutorial was to enter your private key for your wallet? I always use the keystone file to access my wallet. What is the private key?

Try the claimAll function. They added it some weeks ago.

Do we not want to have real eos blockchain tokens? Or are most people just claiming tokens to play with on the exchanges?