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Yes. Note that solving the problems is useful to the whole network: it records transactions and secures the network.



What's being solved are not just abstract mathematical problems, but equations that have implications on the whole system?


The "equation" is a simple cryptographic hash performed on a block of data, as described earlier in this thread: http://news.ycombinator.com/item?id=2358396

The equation itself is trivial -- it can be calculated hundreds of thousands of times a second by even a really slow CPU.

An artificially set difficulty is implemented and the result is that only one of those attempts across the entire network will succeed in about ten minutes, which is the targeted time for processing a batch of transactions (a block).




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