Where in the Bible it says how much the world is old?

Whole Earth 6000 years old and I keep hearing about. I work with the pastor and asked him and he said there is no place in the Bible, that the age of the world is mentioned. So I just wondering.

The world was created, then some time before Adam was born was expired. We do not know how long expired? And what about the world when Adam and Eve sinned, when he was cursed.

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