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A mnemonic phrase is a list of 12-24 words used to back up a wallet. This phrase is a representation of a seed, which is the data that generates all of the keys in an HD wallet. A mnemonic phrase is also sometimes referred to as a seed phrase or recovery phrase.
Mnemonic phrases are a Bitcoin standard introduced by BIP 39 which most wallets implement. Most wallets will also allow users to add their own unique passphrase onto the end of the list of words to further increase security.
Mnemonic words are chosen from a defined list of 2048 words, and any combination of words is a valid mnemonic phrase which will generate a valid set of keys. Thus, the probability of correctly guessing someone’s mnemonic phrase is 1 in 2048^24 or 2.96 x 10^79 guesses.