How many numbers to try to solve the proof-of-work problem
There's no maximum. Instead you can find the formula linking the target and the required number of initial zeroes. Then the average number of hashes you need to calculate is 2^(target number of initial bits). Then you could input the current target to find the average number of hashes.
I don't know the formula for that but for example the block 661657, a recent one, had the target bits as many as about 76, which means it took about 2^76 hashes.