So, what to explain a block after its prior 10-min block is a 38-minute block? Is it a sudden increase of difficulty?
No.
For mining a block, miners need to solve a mathematical problem which is called proof-of work problem.
This problem is solved through brute-force method. This means that the problem is solved by checking all possible answers. It's possible that the problem is solved in a few seconds. It's also possible that it takes more than an hour until a miner finds the solution.
Yup you are definitely right. for every transcation miners need to solve a mathematical problem and everyday million of transcation had been done. that's why need a long time for complete a transcation block. it take more then 10 minutes
hossienmr93 had the better explanation. coinerer got it wrong on multiple parts
transactions are collated into blocks(batches of data) it doesnt matter if the block contains 1 or 2500 transactions. there is only ONE mathematical problem that is solved per block
on average a block contains about average
1700tx and there is about 144 blocks a day thus there are not millions of transactions a day.