They aren't useless the secure the network.
If you decide to open a bank so you pay a contractor a lot of money to build a secure vault, and then you install lots of cameras, pay for an alarm system, and hire security guards .... and then the bank never gets robbed (maybe because the security is too tight) was it a waste of resources?
So are you saying that the process of mining is purely validating transactions? I apologise for my question if that is the case, I had the impression most mining calculations were akin to brute force calculations looking for special numbers that match the formula - similar to hunting for prime numbers. Have I got this all wrong then?
Mining isn't to validate transactions, every node tries to validate a transaction when it receives it. Mining is to wrap a set of transactions in a tamper-proof layer, called a block. The point of the calculations is that if someone wants to alter the transaction-history, he has to redo the calculations in order for it to be accepted by the network. And he has to redo these calculations while trying to beat the network of honest users that is trying to extend the block chain with honest blocks.
The precise algorithm used for these calculations is not important as long as it satisfies the following conditions:
- The puzzle/solution has to depend on the transactions in the block. Change the transactions and the puzzle should change.
- The puzzle/solution can be tweaked automatically to be more difficult if the network increases in computational power. And vice versa.
- It is hard to find a solution, but very easy and fast to verify that a given solution is correct. Other nodes in the network should be able to check the validity of a block efficiently.