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BitCoin: Need a look at improving Mining Process

I am not a mathematician, but as an engineer am miffed about the high costs of the whole mining process.  I see the high environmental cost (in electricity used) and the number of PC needed as a barrier to massive penetrations, and I hope to find a "poor man's solution" which would not degrade the privacy protections nor the "trustless" nature of BitCoin transactions.

I read that the code for BitCoin is pubic domain. I also saw there are Bookkeepers watching every transaction.

Is the code these Bookkeepers are running also part of the Open Source paradigm? How about the part which generates algorithms which get distributed to those who've committed their machines for "mining" operations?

Please let me know.

Thanks
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I am not so interested in mining BitCoin but need to understand what algorithms are they mining? And how does this relate to making the network Trustless and peer-to-peer?
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I am trying to better understand the purpose of the mining/calculations that are performed.

When algorithms are broken and computations performed by miners, are the answers to these algorithms returned by the miners provide critical information needed as it relates to the BlockChain database updates?
You would have to get a text on this subject. The last post here is way bigger than a 500 point question.
How do I add more points?
Thanks. You cannot add more points. But in here there is a limit to informational offerings beyond which you would need a text book or course or like. A back and forth Live Question in here might suit this.