[Cryptography] Has quantum cryptanalysis actually achieved anything?

[Jon Callas]

I have a follow-up and addendum to my missive of last night.

I went over to Google and typed in "factor 2323" -- a four-digit number that my left hand pulled out of its fingers. I've learned that there are enough factoring resources on the web that numbers under six digits or so just pop up. There was a time when I had a file on my laptop of all primes under a million, which meant I could do a primality test with grep. I have apparently stuck that file somewhere safe where I won't lose it. Or find it.

I got back an AI reply, and I'm putting it in text for you, but I saved screen shots. Should you just want to skip ahead, feel free:

---- AI Reasoning Starts, skip ahead if you like ----

AI Overview

What you're solving for
Finding the prime factorization of the number 2323.

What's given in the problem
The number to factor: 2323

How to solve
Find the prime factors of 2323 by trial division.

Step 1
Find the smallest prime factor

Divide 2323 by the smallest prime number, 2.
2323 is not divisible by 2 because it is not even.

Divide 2323  by the next smallest prime number, 3.
2+3+2+3=10, which is not divisible by 3, so 2323 is not divisible by 3.

Divide 2323 by the next smallest prime number, 5.
2323 does not end in 0 or 5, so it is not divisible by 5.

Divide 2323 by the next smallest prime number, 7.
2323÷7≈331.86, so it is not divisible by 7.

Divide 2323 by the next smallest prime number, 11.
2323÷11≈211.18, so it is not divisible by 11.

Divide 2323 by the next smallest prime number, 13.
2323÷13=179, so 13 is a factor.

[I'm not going to bore you with Step 2, which does the same iteration to show that 179 is prime.]

Step 3
…
Write the prime factorization
The prime factorization of 2323 is 13 × 179.

Solution
The prime factorization of 2323 is 13 × 179.

Generative AI is experimental. Answers might be inaccurate or misleading. Double-check for accuracy.

---- AI Reasoning Ends, actual answer a few lines up ----

Got that? Answers might be inaccurate or misleading, so we need to check.

Before we do that, right below the AI answer was another section of text on the page:

Properties of the number 2323
Factorization	23 * 101

So which is it, 13 * 179, or 23 * 101?

I shall leave that as an exercise for you, gentle reader, with a hint that the number is twenty-three hundred and twenty-three.

    Jon