When looking for information about the nonce property of the genesis file, everything says that it is a 64-bit string hash etc.

But which algorithm is used to generate this hash ?

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There's really no hashing involved in this nonce, the value is arbitrary and the definition "64-bit string hash" is misleading, IMHO.

A better definition for nonce in this specific context can be found in the Ethereum Yellowpaper (page 5, top right). There, the nonce is defined as "A 64-bit value (...)".

It's actually just any value between 0 and 0xFFFFFFFFFFFFFFFF. The nonce itself is just a number represented in hexadecimal format.

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