I had thought that the value of the "processed" during a sync was the block number, but the number goes far beyond the latest block.
What is the meaning of this number?
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Imported new state entries count=384 flushed=0 elapsed=1m51.659s processed=2507 pending=20431 duplicate=0 unexpected=227
Imported new state entries
Those are the number of "state entries", rather than blocks themselves. You can think of them as items in Ethereum's state database.
Each block can contain many transactions. Each transaction can bring about many changes in the state database, which is why the "processed" count can be higher than the latest block number.