I was wondering when my Bitcoins were born, in which block height my coins were actually mined. There is a magical thing in think that maybe you have some Satoshis built in the first mountains of the Bitcoin blockchain.
There's no web-service/app for this? The idea is to search for a public address and obtain a detailed tree of coins movements up to the Coinbase.
As shorena puts across well and in detail, the question "When were my bitcoins born?" suggests an unfortunately common misunderstanding of how Bitcoin works. *
However, let's put this to one side and try to capture the spirit of your idea. We'll say that an output
y is a
parent to an output
x if there exists a transaction with
y used as an input and
x given as an output. We'll say that an output
y is an
ancestor of an output
x if there exists a chain of parents connecting
x to
y. Finally, we'll define the
bloodline birthblock of an output
x to be the minimum of the heights of all blocks that contain ancestors of
x. **
Given these definitions, every output has a well-defined bloodline birthblock and this concept corresponds loosely with "antiquity of my coins". One could associate this concept with the chunk of bitcoin one imagines is stored in an output. Following the analogy, Bitcoin transactions aren't so much moving chunks of bitcoin as they are breeding them (corresponding to the second shorena interpretation).
* People like to think that chunks of bitcoin have identities independently of transactions and therefore can be tracked as they "move" through the blockchain. In reality, a chunk of bitcoin is nothing more than a property of some Bitcoin output; an amount.
** For simplicity I have ignored fees, essentially assuming that fees are destroyed and created anew as they are claimed with coinbase transactions (corresponding to the first shorena interpretation).