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I have made an estimate on when the total hash rate will be high enough that we might observe blocks that have a hash with complete zeros.

000000001aeae195809d120b5d66a39c83eb48792e068f8ea1fea19d84a4278a <-- Block 50000  (04/10)
00000000000000000006834ff0dd4567d98352d077bf045ea3f13c4041b582f5 <-- Block 709798 (11/21)
                                |   
                                | ( some years later if we assume
                                |   similar hashrate growth)
0000000000000000000000000000000000000000000000000000000000000000 <-- Block ?? in ~2070

It is a very rough estimate base only on two data points. From logarithmic total hashrate plots it seems that the multiplicative growth rate (slope in logaritmic plot) is not constant but seems to decline over time. But if we still assume that the hashrate is increasing with the same multiplicative rate as it did between those two observations, i.e. that we will have that many more leading zeros every 11 years (note that we have hexadecimal digits representing 4 binary digits, I only do a rough estimate), we will run into problems around 2070.

Did I make a mistake or is it true that these kind of problems (block hash collision, difficulty adjustment will first have low resolution and finally can't prevent blocks from being mined too fast) are not too far away? Are there already plans to circumvent such issues (harder POW hashing algorithm, concatenate two hashes to have more bits)?

EDIT

My estimates are based on the assumption that the hash rate growth rate will continue to be exponential (i.e. constant slope in logarithmic plot). Despite the fact that in the recent two years the hashrate growth seemed to be approximately linear, I think that it is reasonable to assume that in the long run, the total hashrate will grow exponentially. This assumption is backed by Moore's law. Here are two logarithmic plots of the number of transistors and the supercomputer power (FLOPS) over time and indeed, the logarithmic growth rate is linear here. Moore's Law FLOPS So I think that indeed we can assume that the total hashrate is exponential in time, i.e. that the number of leading zeros in block hashes is linear in time in the long run and that this will be a problem for Bitcoin sooner or later.

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No, it's not reasonable to expect that the hashrate will continue to grow exponentially (sustained exponential growth is generally unlikely for pretty much anything). See this chart of the hashrate growth since inception on a logarithmic scale: Total  computation speed on logarithmic scale via bitcoin.sipa.be

As you can see, hashrate growth has been slowing down. Bitcoin's hashrate was increasing very quickly at first, because mining hardware went from CPU to GPU to FPGA to ASIC to miniaturized ASIC. For a while each generation of hardware was obsoleted in less than a year after release. Meanwhile, ASICs have caught up the state of the art of chip production, and improvements will be more gradual.

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  • Well, it could still be exponential growth from now on - just with respect to a smaller base :) Especially since you are saying that now ASICs have caught up, i.e. before that we had a phase where state-of-the-art technological capacity was not fully exploited, and from now on we have more gradual improvements = pure Moore's law growth without superposition of strong miniaturization effects.
    – phinz
    Nov 16 '21 at 7:38
  • I doubt it, but who knows. Either way, block 50 000 to block 709 798 would not be representative, though, since 50 000 was even before GPU mining was publicly available.
    – Murch
    Nov 16 '21 at 11:33
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  1. Bitcoin targets are not actually evaluated as a count of leading zeroes.

  2. If we look at a chart of Bitcoin difficulty we can see that the long term trend in recent years looks much more linear than exponential. There have additionally been significant periods of decrease rather than increase.

Bitcoin difficulty in recent years

  1. It seems unlikely that Bitcoin will still exist if it ever becomes computationally feasible for a mining consortium to force a double SHA256 hash of real data to a single desired target value.
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  • Thank you, I didn't realize that enforcing a hash of zeros is basically equivalent to find a double SHA256 preimage of a desired 32 bit value.
    – phinz
    Nov 15 '21 at 10:36
  • 2.: You say the growth rate is rather linear: I updated my question to justify the exponential growth. 3.: Saying Bitcoin will not survive until then is similar to the thoughts that will lead to the Year 2038 problem where people thought unix would not survive until then. Admittedly, there will be enough time to fix it when we approach that day.
    – phinz
    Nov 15 '21 at 11:41

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