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Their point is that the PoW is wasteful because the redundant work is useless. See primecoin.io for an example of more useful PoW.

• VMG 11y ago
  So in primecoin I can mine on any block and generate a useful byproduct? What stops me from attacking that network by mining on my private chain with a double spend? I have no opportunity cost.
  • taejo 11y ago
    > What stops me from attacking that network by mining on my private chain with a double spend? Nothing stops you mining on a private chain, but since you have a small minority of the compute power, the network doesn't care about your private chain. The same is true in Bitcoin. > I have no opportunity cost. You could be mining blocks that generate useful byproducts and currency.
    • VMG 11y ago
      > Nothing stops you mining on a private chain, but since you have a small minority of the compute power, the network doesn't care about your private chain. Right, this is not an issue for small miners. But if you have a significant part of mining power, it's important that there is a significant opportunity cost mining on the wrong chain. That can only be ensured by using a PoW that is wasteful outside the currency you're mining.
  • bduerst 11y ago
    That's because if it was valuable to you as a miner it would incentivize you to mine the wrong chain. Network value is different from individual value.