It's very clever, but obnoxiously slow. It's useful for code golf and as a pretty impressive party trick. But like your banker will not be impressed with your college funding plan of pulling a quarter out of his ear, this is not going to make it in any real use.
Imagine naive absolute-beginner-programmer trial division. This is worse. Now add the overhead of counting via regex backtracking and integer comparison via matching strings. A fair number of regex engines will also start using enormous amounts of memory.
AKS is of theoretical interest, but not really a "normal test." It's very slow in practice, being beat by even decent trial division for 64-bit inputs (it's eventually faster, as expected, but it takes a while). But it is quickly faster than this exponential-time method. The regex is in another universe of time taken when compared to the methods typically used for general form inputs (e.g. pretests + Miller-Rabin or BPSW, with APR-CL or ECPP for proofs).
As others have noted, "has been popularized by Perl" is because it was created by Abigail, who is a well-known Perl programmer (though almost certainly a polyglot). It's also been brought up many times, though it's a nice new blog article. I hope the OP found something better when "researching the most efficient way to check if a number is prime." In general the answer is a hybrid of methods depending on the input size, form, input expectation, and language. The optimal method for a 16-bit input is different than for a 30k-digit input, for example.
It is a proven deterministic test of primality. We already had those before AKS, and they are significantly faster than AKS (even the various improvements). But they don't check all the boxes that are useful for stating things in computational complexity proofs without a paragraph of weasel words. So from the theory side of things, it's great since we don't particularly care about the actual execution time, but the asymptotic behavior and whether it is solidly shown to be in P.
Lots of math packages have deterministic primality tests, but none use AKS as a primary method, because AKS offers no benefits over other methods and is many orders of magnitude slower.
For inputs of special form, there are various fast tests. E.g. Mersenne numbers, Proth numbers, etc.
The fastest method depends on the input size and how much work you want to put in. For tiny inputs, say less than 1M, trial division is typically fastest. For 32-bit inputs, a hashed single Miller-Rabin test is fastest. For 64-bit inputs, BPSW is fastest (debatable vs. hashed 2/3 test). The BLS methods from 1975 are significantly faster than AKS up to at least 80 digits, but ECPP and APR-CL easily beat those. ECPP is the method of choice for 10k+ digit numbers, with current records a little larger than 30k digits.
Imagine naive absolute-beginner-programmer trial division. This is worse. Now add the overhead of counting via regex backtracking and integer comparison via matching strings. A fair number of regex engines will also start using enormous amounts of memory.
AKS is of theoretical interest, but not really a "normal test." It's very slow in practice, being beat by even decent trial division for 64-bit inputs (it's eventually faster, as expected, but it takes a while). But it is quickly faster than this exponential-time method. The regex is in another universe of time taken when compared to the methods typically used for general form inputs (e.g. pretests + Miller-Rabin or BPSW, with APR-CL or ECPP for proofs).
As others have noted, "has been popularized by Perl" is because it was created by Abigail, who is a well-known Perl programmer (though almost certainly a polyglot). It's also been brought up many times, though it's a nice new blog article. I hope the OP found something better when "researching the most efficient way to check if a number is prime." In general the answer is a hybrid of methods depending on the input size, form, input expectation, and language. The optimal method for a 16-bit input is different than for a 30k-digit input, for example.