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The birthday problem means that the number of values you have to choose to have a 50% chance of a collision scales approximately with the square root of the size of the space. [0]

2^(256/2) is way, way bigger than the number of used bitcoin addresses, which is about 33 million according to this csv [1].

[0] https://en.wikipedia.org/wiki/Birthday_attack#Mathematics

[1] https://bitkeys.work/download.php



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