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Exactly when was the first block mined and the first bitcoins generated? How many people knew about the project at this point? Had the project been publicly announced before the first block was mined or did that happen afterwards? Is there anything special about this first block or could anyone have mined it?
I realize that there are a number of questions included here but I don't think that it makes sense to ask them separately.
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Bitcoin's design paper was published on cryptography@metzdowd.com on October 31, 2008, which is considered by most to be the official beginning of the project. On January 3, 2009 at 18:15:05 GMT the Genesis block was established. Six days later, Bitcoin 0.1 was released and announced on the Cryptography Mailing List.
It is hard to estimate the size of the community at any point, especially historically, but there is a decent timeline of the major events in Bitcoin history at the official wiki.
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Exact Bitcoin timeline can be found here.
As far as I understand the first blocks were mined by Satoshi himself (probably to ensure the protocol is working correctly). The only thing special about the genesis block is that it did not link to a previous block (there was none before it), unlike all following blocks. The original block is also distributed with the Bitcoin client, so they can track any following block back to the genesis block.
Anyone can generate their own genesis block, but it will not be accepted as a part of the current block chain. Most notable non-official genesis block is the testnet genesis block. All Bitcoin-spinoff currencies also have their own genesis blocks.
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While this site does not yet have the [closed as general reference] criteria, Stack Exchange sites generally do not host ultra basic questions that can be easily found on Wikipedia and the like. Background here: "This question is too basic; it can be definitively and permanently answered by a single link to a standard internet reference source designed specifically to find that type of information."
– Robert Cartaino – 2011-09-07T16:20:23.7671Some of the details in David's answer are only easily found if you know what to search for and where, i.e. for "Bitcoin history" on the Bitcoin wiki (not Wikipedia). Also, there is more in this question that has not been answered yet: "Is there anything special about this first block or could anyone have mined it?". That information is not easily found. – D.H. - bitcoin.se – 2011-09-07T17:06:14.987
@Robert There is a Meta discussion that you might want to chime in on regarding whether any questions are too basic.
– Michael McGowan – 2011-09-08T20:26:55.547