There are very few pools that reward the miner who finds the block. P2Pool does. The miner who finds the block gets 1/200 of the block reward in addition to any shares he currently has on the chain. Other pools, like mine, might give the miner who finds the block a bonus during certain promotions, but on my pool, that bonus comes from my own pocket.
Some pools do, however, provide statistics on who solved the block. For example, if you take a look at my pool, you can see who has recently solved blocks:
http://www.bravo-mining.com/index.php?page=statistics&action=pool. I know kano also provides this information (but you have to be registered and logged in), as does Eligius. Other pools you'd have to check. Now, just because you can see who solved the block, that doesn't necessarily give you the person's address to which you could send coins. I don't provide that correlation on my pool. Obviously I have access to that data as the pool operator, but it isn't public.
Excellent info, Thanks!
Ok, so it's not public info on your site, but does your site provide a method the miner can use to prove that s/he solved the block?
Is it possible for a miner to place a fingerprint (lets say 8 bytes) into the data of a block so that he can later prove that s/he solved it (by providing a phrase like "my bitcoin address is 1..." the Sha256 hash of which ends with those 8 bytes)?
In pooled mining it doesn't matter who solved the block.
You're on a team. Everyone works with their available effort. Someone finds a block. Everyone on the team is rewarded according to their effort.
Rewarding the device that found the block, relatively more, only increases reward variance for everyone. There's no logical reason to do that.
That extra reward won't make them find more blocks per the amount of work they do.
In fact the person who found the block has no control over it either.
It was only one single hash they did that found the block, out of the 8.6 * 10^16 hashes they do every day per 1THs they have.
Yeah a 1PH miner does almost 10^20 hashes a day.
Currently, it is expected on average that 1 single random hash in almost 10^21 will find a block.
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It's probably more relevant to look at it terms of a comparison:
Someone sent my neighbour a letter. I want to find out who did, so I can reward them for doing that.
No, that's called invasion of privacy, or being a stalker, and frowned upon for good reason.