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If the Hash Rate Suddenly Doubles, How Soon Will the Next Difficulty Adjustment Occur?

The difficulty adjustment will still occur after 2016 blocks have been mined, regardless of how quickly that happens. If the hash rate instantly doubles, the average block time would drop from 10 minutes to approximately 5 minutes.

This means the 2016 blocks will be mined in about 7 days (2016 blocks 5 minutes/block), causing the adjustment to happen in half the expected two-week time frame.

How Does the Difficulty Adjustment Mechanism Relate to SHA-256’s Output?
How Often Does the Bitcoin Network Typically Adjust Its Mining Difficulty?
How Does the Settlement Finality Time on Layer 2 Solutions Compare to Traditional Financial Market Settlement Times?
What Happens to the Block Discovery Time If the Network Hash Rate Suddenly Drops?