# For which block sizes are certain hash algorithms proven to not have collisions? [closed]

CRC32 has hash collisions for the inputs "plumless" and "buckeroo". What's the smallest data length for collisions in MD4, MD5, SHA-1, and the recently accepted SHA-3 (Keccak)? We know that lim_len n->infty p(collision) = 1.0, but I'm curious how large your data has to be before a particular hash algorithm actually experiences a collisions.

Can MD4 collide on blocks less than 100 byes? 1000? 10^10? 10^20? ...

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## closed as off topic by rschwieb, Rudy the Reindeer, Thomas, sdcvvc, Jason DeVitoOct 13 '12 at 3:06

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The probability of collision is rather small. If you generate, say, $2^{50}$ random hashes, then it is very unlikely that there will be any collisions. –  Yuval Filmus Oct 4 '12 at 2:40