Blockchain – Bitcoin Blocktime Analysis Combined with Propagation

For both scenarios described below, we make two assumptions:

• Network propagation for a block is always 6 seconds.

• We start the analysis at time = t0 and at that t0 all nodes have the same exact chain.

Scenario 1: Block Time = 10 minutes

If the block time is 10 minutes and miner A solves blockD at time t0 + T and shares immediately, it can solve its own block that other miners were working on during times t0+T and t0+T+6. Let’s call the variable “X” how many miners solve this during this time.

Scenario 2: Block Time = 4 minutes

If the block time is 4 minutes and miner A solves blockD at time t0 + T and shares it immediately, he can solve his block that other miners were working on during times t0+T and t0+T+4. Let’s call the variable “Y” how many miners solve it during this time.

As a result, Y > X.

Question 1: Am I correct in saying that Y will be greater than X? Of course, it’s not a 100% case, but it’s a probability.

Question 2: How can I check if Y > X is mathematically true? I know it’s about the challenges and how the goals are set. The lower the difficulty, the higher your chances of solving a block in 6 seconds. (Note the word: “all”). This is important because we don’t know exactly when minerA will solve a block. However, as I have read, there is a probability that Y > How many minutes, 10 minutes, whatever. What is the mathematical approach to this? So I believe this.