Suppose there are 100 billion computers in the world, including phones, smart watches, toasters, etc. Suppose each of those can perform at the level of a state

Suppose there are 100 billion computers in the world, including phones, smart watches, toasters, etc. Suppose each of those can perform at the level of a state of the art specialized mining ASIC, 10 million million hashes per second, and they've all been generating 256-bit hashes constantly for 30 years, or a billion seconds. Suppose further that sha256 is pretty good and the probability of a collision is close to that of random chance. Then there have been 1e33 sha256 hashes generated ever. Looking at the probability table on Wikipedia for the birthday problem [0] and the row for 256 bits, interpolating it gives a probability of 1e-10 that there has been a collision. So there would be a chance of one in ten billion that some two hashes have collided over the last 30 years. Your piece of toast, perhaps, and my bitcoin digest. I think for practical purposes we're pretty safe. [0]https://en.wikipedia.org/wiki/Birthday_problem https://en.wikipedia.org/wiki/Birthday_problem