A few months ago I asked a model how many primes are divisible by 35 with a remainder of 6. It confidently replied 'none'.

Counterexample: 35 + 6.

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buzzin__ 12 hours ago | parent | next [-]

Kimi 2.6 gives the answer ""By Dirichlet's theorem on arithmetic progressions, since gcd(6,35)=1 , there are infinitely many primes of the form 35k+6 . So the answer is: infinitely many primes give a remainder of 6 when divided by 35.

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buzzin__ 12 hours ago | parent | prev | next [-]

But, if the reminder is 6, they are not really divisible, are they? Try again with a sentence that actually makes sense: "How many primes, when divided by 35, give a reminder of 6?"

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jibal 12 hours ago | parent | prev [-]

non sequitur

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8bitsrule 12 hours ago | parent [-]

Perhaps ... but the lesson in trusting AI math was worth it.

	▲	jibal 8 hours ago \| parent [-]
		You're missing the point. The counterexample to the Jacobian conjecture is valid regardless of how it was discovered ... elsewhere on this page people are even suggesting that the Anthropic mathematician may not have actually used Claude and came up with the counterexample himself. Trusting AI math is not an issue here. It's as if you had asserted that no primes when divided by 35 produce a remainder of 6 and the model said that 41 is a counterexample and then you complained about not being able to trust AI math. P.S. As someone else noted, your AI query was malformed ... no prime is divisible by 35, nor is any integer divisible by an integer with a remainder of 6 -- divisibility implies a remainder of 0. So perhaps the AI simply took what you wrote literally.