The exact time depends on the value of each address and time.
The formula the client uses is:
priority = sum(input_value_in_base_units * input_age)/size_in_bytes
If priority is >57,600 there is no transaction fee.
This is an interesting detail for me. Is there a discussion going on somewhere on how to develop on this mechanism? How does the fee count into the equation?
For the network it is bad to have too many transactions and this priority is an effective flood protection ... to a certain extent. With 1M BTC I can still produce 1M transactions per day which is about 50MB (if I don't do weird
1000 addresses to 1000 addresses transactions which might cost the basic fee) per day. For free.
Wouldn't it make sense to completely ignore the input value and take the transaction size for a fixed fee? From the user perspective we want to charge for the service which does not depend on the wealth being transferred but only on the effort to note down some numbers.
Each kB (which is about 2 transactions) will get stored forever on at least 10k computers and not only on the one miner's computer that accept it in the first place. 1kB*10k equals to something like 10MB web space which in turn would justify to charge 0.001$ or 0.0003BTC wouldn't it?
(A TB costs about 20BTC. A kB therefore costs 0.00002BTC=20uBTC.)
Which arguments go against such a fixed fee? With the 50BTC reward we have now, you can easily make it 2uBTC with both a flood-protection effect and a long time model removing all this uncertainty about fees.
Although I myself promoted Bitcoin as a tool for micropayment, it is and will never be fit to be that on a large scale. With 10uBTC fee for my transactions I could still do pretty small payments.
Continuing on that thought why should only the miner who packs a ridiculously large transaction into the block chain be rewarded while all miners have to live with it? I suggest to add all fees to a fee pool in the block chain and miners are allowed to reclaim 1% of that fee pool. Miners would then have an incentive to not build on chains containing blocks like
this one. 330kB for 46 transactions and 0.24BTC fee mostly from old clients 0.02BTC as I suppose.