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Every 10 minutes only 1MB of transactions are been approved, so what happened to the rest of them? Let's say my transaction was not entered into the block, can I be sure that no one is going insert it to the next block?

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Each node on the peer-to-peer network may store the transaction in its mempool, during which time they will continue to relay it to other nodes. After some amount of time, the node will drop it from the mempool. The default time in Bitcoin Core is two weeks but individual nodes are free to use a different value.

Let's say my transaction was not entered into the block, can I be sure that no one is going insert it to the next block?

No, you can't be sure of that. Certainly while the transaction is in most node's mempools, it will continue to be considered for inclusion in new blocks. That's desirable for most people, who would prefer that the transaction get confirmed soon, even if it isn't confirmed immediately.

In principle it's possible that some node sits on your transaction, and that it makes its way into a block a long time later - years, even. The only way to be sure your transaction is never going to confirm is to double-spend it: make a new transaction which spends at least one of the same inputs. If the new transaction is confirmed (with a sufficient number of confirmations, say 6) then the old one can't be, because the block chain isn't allowed to contain conflicting transactions.

  • "make a new transaction which spends at least one of the same inputs." This is not an easy thing to do with a normal wallet because usually you can't control this info. – Mr. Turing Jan 17 '18 at 16:01
  • @Mr.Turing: In general, yes. Though Bitcoin Core has a "coin control" feature where you can choose the inputs for your transaction. Of course, you first have to convince it that those inputs are actually available, and make it forget that it spent them once before. – Nate Eldredge Jan 17 '18 at 18:44

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