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I'm new to blockchain and want to start my own private network. I've gotten a lot of information here about coinbase transactions and how they make mining "empty" blocks useful. I would like to get precise answers to one major question and some offshoot questions:

  1. Is the coinbase transaction the one and only means of minting new coins?
  2. Is the coinbase transaction implicated in anyway in the creation of the first initial suppy of bitcoins or the creation of the genesis block?
  3. Since coinbase transaction blocks don't include any previous transaction history (except reward transaction to the miner), is it less computationally expensive to mine than blocks with actual transactions? And does this expense grow with the size of the blockchain or is it constant?
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Is the coinbase transaction the one and only means of minting new coins?

Yes.

Is the coinbase transaction implicated in anyway in the creation of the first initial suppy of bitcoins or the creation of the genesis block?

Yes. Bitcoin was not premined, which means that there was no initial supply created by the creator. All of the Bitcoin in existence came from coinbase transactions produced in the blocks after the genesis block. Additionally, the coins created in the genesis block are also unspendable, so do not actually count to the total Bitcoin supply.

Since coinbase transaction blocks don't include any previous transaction history (except reward transaction to the miner), is it less computationally expensive to mine than blocks with actual transactions?

Technically yes, but the extra computation required is basically negligible. Building a block requires hashing all of the transactions into the merkle root. The more transactions there are, the more hashes that need to be computed. However this only adds a few thousand hashes at worst, so the effect is basically negligible. It can be computed in a second or two at worst.

And does this expense grow with the size of the blockchain or is it constant?

The blockchain being longer has no effect on how difficult it is to mine blocks.

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