Probability table Birthday problem

the white fields in table show number of hashes needed achieve given probability of collision (column) given hash space of size in bits (row). using birthday analogy: hash space size resembles available days , probability of collision resembles probability of shared birthday , , required number of hashed elements resembles required number of people in group . 1 of course use chart determine minimum hash size required (given upper bounds on hashes , probability of error), or probability of collision (for fixed number of hashes , probability of error).

for comparison, 6982100000000000000♠10 6985100000000000000♠10 uncorrectable bit error rate of typical hard disk. in theory, 128-bit hash functions, such md5, should stay within range until 7011819999999999999♠8.2×10 documents, if possible outputs many more.