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This question already has an answer here:

Bitcoin-Qt initial sync can take a day to complete. You should make sure that you have enough bandwidth and storage for the full blockchain size.

What happens with wallet synchronization when blockchain gets infinitely large?

marked as duplicate by Stephen Gornick, Nick ODell, o0'., cdecker, kirian Apr 2 '13 at 13:28

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The block chain will never get infinitely large. In fact, nothing will ever get infinitely large.

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