Bitcoin is an electronic currency--a new form of money.
Bitcoins take the form of strings of numbers that can be electronically owned by and transferred among individuals and organizations. For now, the currency is primarily used for payments by fringe retailers or illegal transactions, but it is being accepted at more and more places. And organizations that exchange Bitcoins for standard currency are now being approved to operate as banks.
The premise and promise of Bitcoin--the part that appeals to folks who don't happen to be gold bugs or cryptography geeks--is that the current plan is for only a finite number of Bitcoins to be created.
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