How fast is the Bitcoin mining network compared to other distributed computing networks? ;)
According to Bitcoin Charts, it is equivalent to 127.25 PetaFLOPS currently. This would make it faster than 500 fastest supercomputers in the world (58.9 PetaFLOPS), or Folding@home (4.1 petaFLOPS) [reference]. However, this is only equivalent computation speed, if you would measure actual amount of FLOPS of Bitcoin mining it would be... 0, as Bitcoin does not use floating point operations. Moreover, I'm not exactly sure how Bitcoin Charts computed that figure.
However, objective measure of how fast Bitcoin is in computational sense, would be it's current hashrate - 9.738 Thash/s. At peak rate it was estimated to be over 15Thash/s.
As a side note, one might also be interested in the speed of propagation of blocks in Bitcoin network, which is estimated to be close to 2 seconds.
The Bitcoin network is made up of lots of different types of hardware. The only thing we know for sure is how quickly it can solve blocks by running the sha256 hashing algorithm.
The difficulty is calculated every 2016 blocks (2016 blocks is 6 blocks per hour * 24 hours per day * 14 days, so approximately every 2 weeks) in an attempt to keep the average block generation time being 10 minutes.
Given that, we can calculate the hash rate in Thash/s over the last set of 2016 blocks. At difficulty 1, an average of
2^32 hashes need to be calculated to solve a block. This increases linearly with difficulty. So we can use the following command to look up the current difficulty and use it to calculate the approximate hash rate:
$ python -c "print $(bitcoind getmininginfo | grep difficulty | sed 's/.*: \(.*\),/\1/') * pow(2,32) / 600 / 1e12" 9.87590105239
bitcoind getmininginfo is a new RPC call which is available in the current git HEAD, and will be in the next release of the official Bitcoin client.