Yes, there are a lot of hashes with low enough values to be acceptable. Precisely, there are
target + 1 hashes which are acceptable.
The target varies over time and is adjusted every 2016 blocks (called a "difficulty period") so that with the then-current hashing power of the network, the average block time of the next difficulty period would be 10 minutes.
About every block explorer should be able to show you the block hashes. The hash of the current block (block 453794) is
You can see this in the table of the block explorer of your choice:
The difficulty cannot be shown by all block explorers, but by some. It currently is
440779902286.5892. The difficulty merely is an easier-to-read version of the target. You can learn more about it on https://en.bitcoin.it/wiki/Difficulty.
I haven't calculated the current target but it got to be at most
because otherwise, the current top block wouldn't be a valid block.
Every hash smaller than that is also accepted. Note that the representation of the hash in in hexadecimal which is the most common way of representing hashes.
You can just ask WolframAlpha what that number is in decimal. It's this monster:
Because 0 is also valid, there are at least
Or in a more sane notation:
For comparison: You're probably made up of somewhere around
7*10^27 atoms and Earth's circumference is about
8.01*10^11 times the width of a human hair. So, yeah ... quite a few options to choose from.