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If I delete the Bitcoin wallet from my HD, my Bitcoins will be still alive inside the Bitcoin network, right? Is there any way to remove my bitcoins from the network in a permanent way?

  • Bitcoin is a closed system, so it is not possible to remove a Bitcoin balance from the system. What are you trying to achieve: Do you want to prove they are not in your possession anymore, or do you just want to make sure they are lost to everyone? – Murch Feb 3 '14 at 15:03
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If you don't use them, nobody will be able to use them, so in a sense they will have disappeared. If you wish for them to be publicly, permanently destroyed, you could try one of the approaches at What is the Bitcoin equivalent of /dev/null?, such as sending them to the address 1111111111111111111114oLvT2, which is the address of an all-zeroes hash. There are technically many private/public keys that correspond to the address, but finding one is practically impossible.

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If you delete your wallet and have no other copies around, this means those bitcoins are gone forever because no one has the private keys to move them.

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