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RE: Bitcoin mining will exist only if the Bitcoin price goes up!
Miners make decisions based on the profitability of mining. BTC price is only 1 factor in profitability. Other factors are BTC transaction fees, increasing hash rates from next generation mining hardware and more miners entering the market. The beauty is that a market driven equilibrium will be reached driven by profitability. When mining profitability drops for whatever reason, some miners will exit the market and the remaining miners will see their profits increase. As long as people continue to transact in BTC, independent of price, some number of miners will exist.
Believe me if the price drops at 500$ with this complexity of Proof of Work algorithm to create a new block ... almost no one will mine .. of course you made a good point
You can make the calculation .. this complexity , with 500 usd for 1btc (which means low transaction fee) .. who will invest in new generation miners ?
Remember, the mining difficulty will automatically adjust downward as miners exit. Also, people won't need next gen hardware if there is a precipitous drop in BTC price...current gen hardware and fire-sale used mining hardware (from people exiting the market) will work fine
Please look at the formula which define difficulty. Mathematical task which miners needs to solve in order to be rewarded doesn't relate to the number of miners. On the other hand check this https://en.bitcoin.it/wiki/Target
The BTC difficulty setting (aka target) applied to the BTC SHA256 hashing function depends on the network hashrate, which depends on the number of miners. If miners leave the mining business, the network hashrate drops and the BTC software self adjusts the difficulty target to ensure that blocks are solved on average every 10 minutes.
Blockchain will not exist correcty withour miners(or 'transaction processors'). Although It seems to be possible. Instread of proof of work there is a chance of using Proof of Stake as an alternative. In that case, we don't need 'miners' to solve a cryptographic tasks. The main tasks for Miners is to check if all is good with Blockchain. I know that we have "audiotors" as well but Miners are mainly important because their purpose is to: provide a decentralized mechanism for determining which version of history to accept