In the Bitcoin system, a new coin is produced whenever a computer can calculate an answer to a difficult problem, and then attaches that answer to a digital record of every transaction of every Bitcoin ever traded — a breathtakingly large amount of information to carry around in order to buy a pack of gum, but in a time when information can zip around the Internet, not too much to ask. Anyone would be free to create a new coin, within proscribed supply limits, by having a computer do the work needed to prove that it was in fact a valid Bitcoin.

“The incentives are right, they are a check that everyone is following the rules,” said Mr. Andresen. “Early adopters want it to succeed, because they already own the currency. And if you generate Bitcoins no one thinks is valid, you have wasted a lot of computer time.”

In fact, Bitcoin is a rarity for a currency in that it is neither a so-called fiat currency — one like dollars, which are valuable because the government says they are — nor is it a specie currency, one that gets its value because it can be converted into a precious metal like silver or gold.

But why would a Bitcoin have value if it is only a stream of numbers, unsupported by government fiat or by some underlying asset?

“Why does any tool have value?” Mr. Andresen asked. “It is valuable because it is useful.”

Starting almost as soon as the coins were introduced, they have been traded for dollars at online exchanges, serving as a crude measure of the currency’s popularity and health (and also giving a market where owners can trade in Bitcoins for real dollars).

After two years, there are seven million of these “coins” in circulation and the rate of increase — currently 50 coins are added every 10 minutes — will slow each year until the number tops out at 21 million coins around 2025. The coins, which trade for about $17 each at online exchanges, have a cumulative value of about $100 million. “I do think of it as the market cap of Bitcoin,” said Mr. Andresen. Today, a list of businesses that accept Bitcoin currency is a motley collection of companies on the fringe of the computer world, groups that conduct gambling or the like, and, notably, the antisecrecy group WikiLeaks, which accepts contributions in Bitcoins. You certainly can’t stock the pantry or furnish your home with Bitcoins.

When reached by phone, a bookstore owner on the list, Sonny Saul, from Woodstock, Vt., said that he had had the account for only a week and a half and that he had “no practical experience with it yet, other than your phone call.”