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Does number of transactions in the block affect it's mining time?

How and why?

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The number of transaction in a block negligibly effects the mining time. The only effect is that more computations need to be done to calculate the merkle root during block construction, but that is a very small fraction of the number of calculations needed to be done during mining itself. Mining only hashes a fixed amount of data so including more or less transactions does not really make a difference.

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