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Can we calculate the number of miners,that we will need in private blockchain in advance and how? for POW algorithm

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  • What do you mean "in advance"? I would think at least one, but to protect against him going offline the actual number should probably be higher. That depends entirely on your preferences.
    – comodoro
    Commented Nov 28, 2016 at 11:03
  • what do you mean by correct?? you mean secure?
    – Badr Bellaj
    Commented Nov 28, 2016 at 11:34
  • @Badr Bellaj I mean secure,faster mining and fault tolerance. Commented Nov 28, 2016 at 12:27

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1 miner is all it takes on a private blockchain, as the difficulty of mining a block is adjusted so that the average sits between 10 - 19 seconds, as described in "How does the Ethereum Homestead difficulty adjustment algorithm work?".

If you are worried blocks will be mined too slowly, you can change the initial mining difficulty on your private chain as described here:

You can set the genesis block difficulty in your private network using the init parameter, but the difficulty will eventually be adjusted according to the algorithm described above.

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