Can a two-block-sized chain override the main chain?

Question

After i read this:

Honest generators only build onto a block (by referencing it in blocks they create) if it is the latest block in the longest valid chain. "Length" is calculated as total combined difficulty of that chain, not number of blocks, though this distinction is only important in the context of a few potential attacks. A chain is valid if all of the blocks and transactions within it are valid, and only if it starts with the genesis block. https://en.bitcoin.it/wiki/Block_chain

Would it be possible to mine a block after the genisis block, which has a higher difficulty then all blocks in the mainchain together and override the blockchain with my own one? --- just hypothetical, i know that such a difficulty is ismost impossible to reach... but with some luck?

Answer 1

No, it would have to be much longer.

Besides the fact that there are checkpoints, the difficulty of a block is defined by its target value, not the actual value of the block hash. The block hash just has to be less than that target value. So you would need to make the target value be very small (i.e. make the difficulty very large). In order to do this, you would need to mine at least 2016 blocks to trigger a difficulty adjustment. But difficulty adjustments are capped at being no more than 4 times harder (and no less than 4 times easier) than the previous difficulty. So you would need to trigger many difficulty adjustments in order to get your difficulty up to the necessary value.

Once you get your difficulty high enough, yes then you could mine a block which has a higher difficulty than the sum of the entire blockchain's difficulty, and then nodes will accept your blockchain (assuming you started from the last checkpoint).

However doing this would be extremely computationally infeasible. In order to mine said block, you would need to have the sum of all the mining power at each block in order to mine one of these large difficulty blocks. What this means is that if block 1 was mined by one machine, and block 2 was mined by the same machine, then you would have to have at least two of those machines in order to mine a replacement block 1 that has a higher difficulty than the sum of the difficulties of blocks 1 and 2.