There exist quite some alternatives to bitcoin that are partially based on it, and I'm sure their creators all are convinced they improve upon something. But are there any serious drawbacks in bitcoin that can or will probably never be fixed?

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I don't think there are severe drawbacks of Bitcoin. Certainly none that other coins are solving.

However, Bitcoin has certain properties that could be replaced with some other. Most altcoins to just that. Popular properties that altcoins change are:

  • replace PoW with something else

Some altcoins do not use a PoW mechanism or use a hybrid mechanism. PeerCoin (originally named PPCoin) was the first altcoin to use the Proof-of-Stake mechanism, which basically requires miners to hold a certain amount of currency in order to mine new. PeerCoin uses a hybrid of PoS and PoW. Nxt is an altcoin that uses pure PoS.

  • the PoW algorithm

Bitcoin uses SHA-256, which is a hash algorithms that almost entirely requires CPU cycles to calculate. This means that it is easy to create custom hardware to perform this calculations. There are many altcoins that use Scrypt as the PoW algorithm. Scrypt is more memory-intensive and therefore harder to implement in custom hardware. The first altcoin to implement Scrypt is Litecoin. Primecoin requires miners to calculate large prime numbers as a PoW mechanism.

  • the total amount of coins that can be mined

Bitcoin has a 21 million coin limit. Some altcoins raise this limit, such as Dogecoin, others lower it, such as 42.

  • the rate at which new blocks are created

Bitcoin blocks are mined at an average rate of one block every 10 minutes. Many merchants require that a transaction has been confirmed by several blocks before they accept it. With a confirmation time of 10 minutes (in fact, the recommended amount of confirmations to wait for is 6) can be quite cumbersome in certain use cases. Litecoin has a confirmation time of 2.5 minutes.

  • the time it takes before the maximum amount of coins is created

Block rewards usually have a halving time. Every halving time the block reward halves until it is too low to represent using the maximum precision and it becomes zero. With Bitcoin it will take until 2140 until the block reward becomes zero. Some coins shorten this period. Sometimes they shorten it so much that the creator (who mines first, of course) is accused of pre-mining because he can mine very fast and easy in the beginning of the existence of the coin.

  • Thanks! PoS sounds interesting, and I like the idea of primecoin trying to calculate something actually (slightly) useful instead of brute-hashing. Personally, I consider changing the amount of total coins nonsense though, since that is equivalent to changing the scale (apart from, maybe, changing for how long miners get a reward in addition to fees). – Tobias Kienzler Jan 26 '14 at 9:08
  • Well, take care with PoS though. I once read a post from one of Bitcoin core devs (yeah I lost the post and can't find it anymore) that PoS is not at all as safe as PoW is. And about increasing the amount, the Dogecoin community quite enjoys talking in big numbers :) It sounds better that you can say I own 10k doge instead of 1 BTC, right? – Steven Roose Jan 26 '14 at 20:22
  • Well, I could say I own a billion nano-Satoshi :P But PoS alone does indeed sound a bit risky - if one party does manage to hold the majority of altcoins they'd most likely increase their lead forever, and there seems to be no mechanism to prevent that. Though, I start having an idea - one could track which part of a given transaction was already "used" as PoS (via it's history) and only unused parts, to be included (in the respective fraction) in the coinbase transaction, would count – Tobias Kienzler Jan 27 '14 at 7:49
  • I think that's somehow the principle of how it works. But I thought the main issue was that there was much less incentive for minders to only work on the current branch. The way of gaining your PoS share is by being lucky to be picked and you will get your stake * the time you are holding it without PoS share. But because no "work" is involved, it would make sense to keep trying to append your self after any recent block to try having more luck there. It was something like that. Could result in regular forks and orphaned blocks. – Steven Roose Jan 27 '14 at 14:27

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