...given that people want to have some coins 
Why would they want that?Just in case you asked this question not sarcastically
I don't know? Why do people want to have gold?
The only things you _really_ need are air to breathe, something to drink and something to eat.
All other things are just wanted beause they make life more comfortable, interesting, enduring, more fun, whatever.
Some people play raffle, others gather cryto coins; some people participate in seti@home or folding@home, others might join primecoin
So some might want primecoins just because they want the coins, others might want to find cunningham chains and the primecoins are a kind of fall-out for them...
Bitcoins have value because you can buy stuff with them and they now have a track record of enabling both on and off the record 'fiscal' transactions.
Finding cunningham chains for fun while generating primecoins as a by product does not produce a *demand* to purchase coins- which is what is required to drive price - but merely increases *supply*.
What the prime aspect does is make Primecoin marginally more interesting to mine than other altcoins, which could translate to more mining power and in turn a more secure network, which could then increase the value of the coin.