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Their goal is to find a hash that has at least a certain number of leading zeroes. That constraint is what makes the problem more or less difficult.

More leading zeroes means fewer possible solutions, and more time required to solve the problem. Every 2, blocks roughly two weeks , that difficulty is reset. If it took miners less than 10 minutes on average to solve those 2, blocks, then the difficulty is automatically increased. If it took longer, then the difficulty is decreased.

Miners search for an acceptable hash by choosing a nonce, running the hash function, and checking. When a miner is finally lucky enough to find a nonce that works, and wins the block, that nonce gets appended to the end of the block, along with the resulting hash.

Her first step would be to go in and change the record for that transaction. Then, because she had modified the block, she would have to solve a new proof-of-work problem—find a new nonce—and do all of that computational work, all over again.

Again, due to the unpredictable nature of hash functions, making the slightest change to the original block means starting the proof of work from scratch. But unless the hacker has more computing power at her disposal than all other bitcoin miners combined, she could never catch up.

She would always be at least six blocks behind, and her alternative chain would obviously be a counterfeit. She has to find a new one. The code that makes bitcoin mining possible is completely open-source, and developed by volunteers.

But the force that really makes the entire machine go is pure capitalistic competition. Every miner right now is racing to solve the same block simultaneously, but only the winner will get the prize. In a sense, everybody else was just burning electricity. Yet their presence in the network is critical. But it also solves another problem. It distributes new bitcoins in a relatively fair way—only those people who dedicate some effort to making bitcoin work get to enjoy the coins as they are created.

But because mining is a competitive enterprise, miners have come up with ways to gain an edge. One obvious way is by pooling resources. Your machine, right now, is actually working as part of a bitcoin mining collective that shares out the computational load. Your computer is not trying to solve the block, at least not immediately. It is chipping away at a cryptographic problem, using the input at the top of the screen and combining it with a nonce, then taking the hash to try to find a solution.

Solving that problem is a lot easier than solving the block itself, but doing so gets the pool closer to finding a winning nonce for the block.