A few days in the past, I used to be occupied with what you wanted to know to make use of ChatGPT (or Bing/Sydney, or any comparable service). It’s straightforward to ask it questions, however everyone knows that these massive language fashions regularly generate false solutions. Which raises the query: If I ask ChatGPT one thing, how a lot do I must know to find out whether or not the reply is right?
So I did a fast experiment. As a brief programming mission, quite a few years in the past I made an inventory of all of the prime numbers lower than 100 million. I used this checklist to create a 16-digit quantity that was the product of two 8-digit primes (99999787 instances 99999821 is 9999960800038127). I then requested ChatGPT whether or not this quantity was prime, and the way it decided whether or not the quantity was prime.
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ChatGPT accurately answered that this quantity was not prime. That is considerably shocking as a result of, if you happen to’ve learn a lot about ChatGPT, you already know that math isn’t one among its sturdy factors. (There’s in all probability a giant checklist of prime numbers someplace in its coaching set.) Nonetheless, its reasoning was incorrect–and that’s much more fascinating. ChatGPT gave me a bunch of Python code that carried out the Miller-Rabin primality take a look at, and stated that my quantity was divisible by 29. The code as given had a few fundamental syntactic errors–however that wasn’t the one downside. First, 9999960800038127 isn’t divisible by 29 (I’ll allow you to show this to your self). After fixing the plain errors, the Python code appeared like an accurate implementation of Miller-Rabin–however the quantity that Miller-Rabin outputs isn’t an element, it’s a “witness” that attests to the actual fact the quantity you’re testing isn’t prime. The quantity it outputs additionally isn’t 29. So ChatGPT didn’t really run this system; not shocking, many commentators have famous that ChatGPT doesn’t run the code that it writes. It additionally misunderstood what the algorithm does and what its output means, and that’s a extra critical error.
I then requested it to rethink the rationale for its earlier reply, and acquired a really well mannered apology for being incorrect, along with a distinct Python program. This program was right from the beginning. It was a brute-force primality take a look at that attempted every integer (each odd and even!) smaller than the sq. root of the quantity below take a look at. Neither elegant nor performant, however right. However once more, as a result of ChatGPT doesn’t really run this system, it gave me a brand new checklist of “prime components”–none of which had been right. Curiously, it included its anticipated (and incorrect) output within the code:
n = 9999960800038127
components = factorize(n)
print(components) # prints [193, 518401, 3215031751]
I’m not claiming that ChatGPT is ineffective–removed from it. It’s good at suggesting methods to resolve an issue, and might lead you to the fitting resolution, whether or not or not it offers you an accurate reply. Miller-Rabin is fascinating; I knew it existed, however wouldn’t have bothered to look it up if I wasn’t prompted. (That’s a pleasant irony: I used to be successfully prompted by ChatGPT.)
Getting again to the unique query: ChatGPT is sweet at offering “solutions” to questions, but when you might want to know that a solution is right, you should both be able to fixing the issue your self, or doing the analysis you’d want to resolve that downside. That’s in all probability a win, however you need to be cautious. Don’t put ChatGPT in conditions the place correctness is a matter until you’re prepared and in a position to do the exhausting work your self.