“what makes them valuable is the time spent in looking for them and their limited number,is that it?”
Basically yes. That is also the reason gold is so valued. Gold has little useful intrinsic value but it is rare, easy to verify and hard to find/create.
You don't go looking for the coins. You create them but it requires computing resources. The architecture of the system always keeps the creation cost near the value of the coins. So just like with the “gold standard”, nobody can flood the market with cheap, easily obtained currency.
If enough people in the world use such a system, IMO it is much more secure than the paper fiat currency most people use today. The only issue is that it requires a global network to always be online (internet). Unlike gold, you can't store the “bits” under your mattress if the power goes out.