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There is a node that will always relay every transaction, regardless of whether its amount is acceptable and whether a fee was paid. This node is described in the Free Transaction Relay Policy page on the Bitcoin wiki.

There are no miners listed though which will always include these transaction.

Microtransactions for amounts worth just a few cents would not be able to pay a fee and even the minimum fee causes Bitcoin to no longer be "near free", as the amount on a percentage basis can become quite high.

Are there any miners which will include these microtransactions with no fee? Do any of them connect to the node listed in the free relay policy page, or are the IP addresses for these shown anywhere?

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    Even if there currently are such miners, they'll disappear once the block size limit is hit. Raw bitcoin transactions simply aren't a good fit for micro transactions.
    – CodesInChaos
    Jul 27, 2012 at 6:36
  • Not necessarily; I can see a lot of the network deciding to mine at least partially based on transaction age, possibly to the extend that you'd include a free transaction. This would guarantee that Bitcoin is useful even for small transactions, as such transactions usually don't need much speed.
    – Daniel H
    Aug 28, 2012 at 4:19
  • I would, if I knew how.
    – Kinnard Hockenhull
    Dec 31, 2012 at 4:50

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Yes. All miners using the default Bitcoin Core settings will include some free transactions in their blocks based on priority.

Let's say you have a microtransaction-sized 5,000 satoshi input (about $0.01 USD presently). According to Bitcoin Core 0.10.0's estimatepriority RPC, you currently need 59985719 priority to get a zero-fee transaction mined within 25 blocks (~4 hours). That means you'll only have to wait until your input is about 46 years old:

satoshis * blocks per year * years / tx size > priority
5000     * 52596           * 46    / 200     > 59985719

That's because priority is computed by input amount in satoshis, times the number of blocks since it was received, divided by the number of bytes in the transaction.

I haven't heard of any miners that have free transaction policies that are more generous than the Bitcoin Core defaults.

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