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From the wallet FAQ:

In order to ensure that only you got access to your iotas you ought to create a sufficiently complex seed. This means a randomized 81 character seed consisting of latin letters and the number 9.

I've heard that if you make your seed longer that 81 trytes, it's not actually more secure. Why is 81 the magic number?

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IOTA uses 81-tryte (243-trit) addresses. We assume that 81-tryte seeds (shorter seeds can be considered as 81-tryte seeds after being padded with "9") map to 81-tryte addresses uniformly and hence longer seeds would give several seeds mapping to the same address (because of https://en.wikipedia.org/wiki/Pigeonhole_principle). To "hack" an address one needs to try random seeds, a single attempt can succeed with 1/(27^81) probability because it depends on the number of the addresses, not on the number of the seeds. This means that seeds longer than 81 trytes don't increase address security.

The above is a version for people not specializing in Math. We say that longer seeds don't increase the security to avoid necessity to explain complex things. Actually, longer seeds do increase address security, though not significantly because 81-tryte seeds are already secure enough for any practical scenario. If one wants to assess how much security is added by longer seeds I suggest to start from https://en.wikipedia.org/wiki/Random_permutation_statistics.

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