AI: Try This One On!

By Shlomo Maital

   A follow up to my previous blog on ‘sentient’ or ‘intuitive’ AI:

    The Microsoft scientists gave an advanced version of their AI Chat GPT4 software (not yet available to the public) a challenge:

Prompt: Can you write a proof that there are infinitely many prime numbers,  with every line that rhymes?

GPT-4: Yes, I think I can,

Though it might take a clever plan.

I’ll start by noting Euclid’s proof,

Which shows that primes aren’t just aloof.

Assume we have a finite list,

Of primes, and that none have been missed.

Multiply them all together,

And add one, just to be clever.

The result will be a number,

That has no prime factors, oh wonder!

But every number has a prime,

That divides it, it’s just a matter of time.

So we’ve found a contradiction,

And our finite list needs eviction.

There must be infinitely many primes,

And that’s the end of my rhyming lines.

  Get it?   It’s a reductio ad absurdum proof.  Assume we have a finite list of all the prime numbers.  Multiply them together.  Add one.  The result will be prime. But we said at the start, we have a finite list of all primes..and now we’ve added another.  Oops.  So our initial assumption must be wrong. Hence, there are an infinite number of primes.   This was Euclid’s proof.    And it rhymes.

    I think as an editor I would change the third last line: And our finite list utterly lacks conviction.  And lines does not rhyme with primes.  Just a quibble.

    But hey!  ChatGPT is cool.  And it deserves its full name.  Chat Generative Pre-trained Transformer. 

    Transformer you bet!

     You can read the entire 150 page scientific paper here: