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The bigger problem is that everyone has a incentive to run their computers day and night cranking out solutions, which burns up lots of natural resources and processor time for a zero-sum result.

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The economics in this regard are the same as for gold. With gold only the most efficient gold mines can make a profit, so only those profitable operate -- nobody tries to mine all the gold in the world. With bit gold, only those with the most efficient processors and most spare time will be able to make a profit, so again there will just be a handful of a few powerful computers, or many small computers but just using the spare CPU cycles (like SETI@home), solving the mathematical puzzles to generate the bit gold.

But an algorithm is easier to share than a gold mine. Fixed and marginal costs are lower.

If you could find gold by scraping your bathroom tiles or filtering water for gold dusta gold standard would be terribly inefficient.

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