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One of the biggest issues of Bitcoin blockchain is the ever increasing size. Each address has a weight in bytes or bits. What’s holding someone from creating trillions of different addresses and breaking the block chain this way? Overflowing Bitcoin blockchain by creating addresses? Bitcoin blockchain is unbreakable so I heard. Can it be broken by forcing the size increase and making it unprofitable to run a full node?

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Addresses don't get registered anywhere. You can create as many as you want without having impact on any other network participant.

Addresses only get tracked by others once funds get sent to them. Needing to tie up funds for each address suffices to curb the proposed attack.

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