When we do mining in bitcoin does it solve any computational problem? I mean all these machines running around the world working to generate bitcoins, so the hashing work they do, does it solve any problem?
For e.g. some of you might have heard about GIMPS which is about finding next highest Mersenne prime number. Now to do that a software is run like bitcoin which does the computation for you. So basically people all around the world running that software to find the next Mersenne prime number. As you can see running that sofware (which does computation like bitcoin client) results in solving problem which is Mersenne prime number.
So is there some benefit of doing all this bitcoin mining other then it being used as a currency?