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First, those that get the coins first aren't "distributing" them into larger circulation. If they generate a block and get the reward, they either save the bitcoins or buy goods/services with them. This is not "distributing", but just normal trade.

Second, how else do you bring coins into the market? Be forced to buy them from the system's founder? I doubt that would catch on. Reserve a set number for each person onthe planet and give it to them when they ask for them? I don't think I could count all of the problems with that idea. Hand them out some arbitrary number of some supply in a first come first serve manner? I don't see how that would be an improvement.

The system needs people to generate blocks in order to provide the security of the system, but generating blocks has costs associated with it (hardware, electricity). Why not reward those block generators that are providing the system's security with new coins for each block they generate, at least until the number of transactions per block grow to a point that block generators can charge transaction fees?

Block generators aren't just generating blocks for the fun of it...they want bitcoins so they can spend them, which means those bitcoins will go to others, who can then further spend them, etc. Anyone can do it. GPU mining is profitable for most who wish to make the investment. There's no central authority choosing who gets to generate new blocks. Each person chooses whether they want to generate blocks or not.

If you don't want to generate blocks, but still want bitcoins, then you offer goods/services for bitcoins.

So far no one has thought of any less arbitrary way to introduce bitcoins into the network while continuing to support the security of the network at the same time.

And the term "proof-of-work" is misleading. They're generating blocks in such a way to deliberately make it difficult for someone else to attack the network by generating replacement blocks in an attempt to double-spend their bitcoins. They're not doing these calculations as an attempt to prove they're not some malicious node. Block generators do the work of creating a block, and if someone wants to double-spend their money, they have to generate that block and every single block that's been generated afterwards with at least the same total difficulty of the other blocks. This can only theoretically be accomplished if they have more processing power than the entire bitcoin network, and even then it would take a long time to do unless they had a lot more. Otherwise they just fall further and further behind as the bitcoin network block generators increase in power and the difficulty increases. Contrary to the opinions of some, these calculations are not wasteful, but are a necessary part of the system's security.



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