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What Is the Maximum Number of Nonces a Miner Can Test in a Single Block Header?

The nonce field in the Bitcoin block header is a 32-bit integer, which allows for $2^{32}$ (over 4 billion) possible values. If a miner exhausts all these nonces without finding a valid hash, they must change the block header's other mutable field, the "extra nonce" (part of the coinbase transaction), to generate a new Merkle Root and effectively start over with a new set of 4 billion possible nonces.

What Is a Cryptographic Nonces Function in Blockchain Mining?
What Is a “Nonce” in the Context of Proof-of-Work Mining?
Relate the Concept of ‘Nonce’ in Mining to the ‘Nonce’ in ECDSA Signing
What Is a “Transaction Nonce” and How Does It Differ from a Mining Nonce?