I have a doubt though. Even to save n number of hashes on your computer's hard drive you have to run the hash function n number of times. After which you fill your hard disk space with all these hashes. It will then be followed by search algorithm that will search some nonce value in those hashes. So time taken to find the hash will be O(hash function + O(search). It sound like a preimage search. I am guessing you will have to do this for every block sent to you because the number of transactions should update what is to be hashed. So unless you can use same list of hashes for some x number of blocks, how does it improve the mining efficiency. Plus now your cpu is hashing and searching. Shouldn't that increase the energy cost? What am I missing here?
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