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Can someone work out the math that occurs with Bitcoin and Litecoin when the target changes to the hard coded minimum and maximum value, with respect to time?

In other words, if a lot of hashpower is added to the network and target increases by 4x, that is the upper bound. How many blocks can be created right before the throttle of 4x is taken by the network?

I'm trying to calculate the affect throttling has on the number of blocks generated per hour.

Question

What is the average time per block, right before the network adjusts to the 4x limit, when the hash power is added to the network?

If I were to guess, right before that 4x limit was reached, 1 block is generated every 2.5 minutes for Bitcoin, and 1 block every 45 seconds for litecoin.

Furthermore any hashpower added (or removed) beyond the 4x multipler will not cause a network adjustment and infinitely many blocks may be created in that interval.

Why I want to know this...

If a lot of hashpower is added to the Litecoin network, which already generates blocks (one every 2.5 minutes) then there will be more blocks generated, increasing the risk of a chain split.

I ultimately want to understand how the chain split will cause wasted computation by peers as their blocks are discarded by the longest chain.

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The network doesn't "throttle" the blocks found. Rather, it simply doesn't change the difficulty by a factor of more than x4 in every adjustment (which is once every 2016 blocks). There is no limit on the rate of block generation.

Let's say you were in an equilibrium where a block is found every 10 minutes. Right after a difficulty adjustment, more power joins the network and the hashrate is x100 the original. The difficulty didn't change yet so now a block will be found every 6 seconds. This will go on for 2016 blocks (~3 hours) and then the difficulty will go up by x4. Now a block will be found every 24 seconds; after 2016 more blocks (~13 hours) the difficulty will go up again by x4. Then a block will be found every 96 seconds, for 53 hours; then a block will be found every 384 seconds, for 215 hours; then the hardcoded limit will not be active, the difficulty will go up by a factor of (600/384), and now a block will be found every 10 minutes.

In those times that the total hashrate is too high for the current difficulty, the level of forking will be as if the time constant was shorter. So forking will indeed be high if the total hashrate has just rapidly increased.

  • Maybe I should rephrase, and ask: What is the total anticipated hash rate change implied by the arbitrarily chosen 4x limit by the developers? Why would they chose 4x? Could that be in relation to the average block generation of 1 per 10 min? Since that is a "time-bound" criteria, what "time" does the 4x imply? (interval between blocks) ... before it is unbounded as you describe? – goodguys_activate May 23 '13 at 14:01
  • @makerofthings7: Still not sure what you're asking. If in the Bitcoin network 2016 blocks are generated at a rate of 2.5 min each, the difficulty will go up by x4. If they are created faster than that the difficulty will still increase by x4 because this is the upper bound. The value of x4 was chosen because it balances resilience to disruption in extreme situations with quick response to genuine changes in hashrate. – Meni Rosenfeld May 23 '13 at 15:36
  • My goal is to take your previous comment, and put it in the context of Litecoin, and figure out what the resilience to disruption in extreme situations would be. – goodguys_activate May 23 '13 at 15:45
  • @makerofthings7: The choice of the figure "x4" basically means "If the network hashrate grows by more than x4 in two weeks, something weird is going on". This doesn't have much to do with the time constant 10 min (2.5 for Litecoin). It does have something to do with the difficulty retarget constant (14 days for Bitcoin, 3.5 days for Litecoin). However, that effect is fairly small, and I'd say x4 is a good figure for Litecoin as well. – Meni Rosenfeld May 23 '13 at 17:58

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