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Primecoin is a fun, new and rapidly growing form of digital currency. This form of digital currency is called "cryptocurrency"; a type of digital currency. Cryptocurrency is completely anonymous, decentralized, and extremely secure. Primecoin is used with a wallet on your computer, your smartphone, or a website. You can use it to buy goods and services, or trade it for other currencies (both other cryptocurrencies or traditional currency like US dollars).
One of the most popular uses for Primecoin is "tipping" fellow internet-goers who create or share great content. Think of it as a more meaningful "like" or upvote, with real value that can be used all across the internet. Bitcoins is a payment system introduced as open-source software in 2009 by developer Satoshi Nakamoto. The payments in the system are recorded in a public ledger using its own unit of account, which is also called Bitcoins. Payments work peer-to-peer without a central repository or single administrator, which has led the US Treasury to call bitcoin a decentralized virtual currency.Although its status as a currency is disputed, media reports often refer to bitcoin as a cryptocurrency or digital currency.

When comparing Primecoin with today's most widely spread cryptocurrency called bitcoin some notable differences are:
Scarcity is governed by the nature of prime number distribution
Almost all cryptocurrencies in existence define their scarcity properties merely by a set of predefined values in source code, whereas scarcity of Primecoin is based purely on a relationship of a simple function and mathematical property of natural occurrence of prime chains in the set of whole numbers that are.
No predefined ultimate number of coins
Instead of having hard-set ultimate number of coins in its code like many other alternative cryptocurrencies, number of Primecoins released per block is always equal to 999 divided by the square of the difficulty. There has been some attempts at approximating this number. The number of Primecoins that will be mined will be determined by the progress of its adaptation by the mining community, improvements that will be done to the mining algorithms and ultimately by Moore's law.
Difficulty adjustment is more frequent
Primecoin protocol adjusts its difficulty slightly after every block. The difficulty change that occurs each block is targeted at achieving target of one new block created once per minute. As comparison the bitcoin protocol adjusts its difficulty every 2016 blocks, or approximately every two weeks.
Faster transaction confirmations
Since Primecoin blocks are generated 8 to 10 times as fast as bitcoin blocks on average, Primecoin transactions are confirmed approximately 8 to 10 times as fast.