You can also arbitrarily launch a new search engine at any time, but that doesn't mean that you will become the next Google. Likewise launching a new social network won't automatically make you the next Facebook. BitCoin already has a strong network of nodes securing the transactions behind it.

Your algorithm only piggybacks on BitCoin, you wouldn't be able to run your scheme without the existing BitCoin infrastructure. Also, the existance of bitcoin prime wouldn't enable you to send bitcoins, so bitcoins would still be unique.

In fact I would like to see you run your scheme. How would you transfer 1000 bitcoin prime to somebody else? Since you don't have the private keys of the real owners of the bitcoins, I don't think you could do it.

Hrrrm. This redefinition, while trivially possible, seems irrelevant. Possession of assets is first and foremost a practical matter. (I think you understand this, but for the benefit of the discussion…)

In the case of primary real-world goods, possession comes from being able to physically access the state of various matter and energy: I physically own a house to the extent that I can reliably live in it and make modifications to it and so forth. I physically own food to the extent that I can make use of it by eating it. Other people can alter the game by acting as environmental forces to change the set of available interactions.

In the case of fiat currency and economic goods, practical ownership (including but not strictly identical to theoretical legal ownership) is similarly determined, but with more of a focus on laws of people rather than the laws of physics; the former are backed by the latter, but usefully form a separate conceptual layer.

The case of Bitcoin is also analogous, but there is now a focus on the laws of mathematics as they apply to the state space in which the Bitcoin system operates, and in particular to the practicalities of computing—a strong cryptographic attack could still destroy the system.

So the reason that owning all the early Bitcoins prime is not useful is the same reason owning all the virtual dollars in a parallel system to the US banks is not useful despite being able to invent whatever such system you want. Because no one will recognize this, the amount this changes your set of available physical interactions with regard to primary goods is very small. (I haven't taken weird social goods into account in the above, but I think a similar argument applies since they also require external recognition.)

That said, I think the GP poster would do well to clarify what ey meant by “unique properties”, and perhaps whether (as I interpret it) “unique” is meant to be “of the set of currently active systems, for some fuzzy activity threshold”, thus excluding Bitcoin prime and the infinite variations thereof.