GPT-6 Astra solves Liouville's version of the Goldbach conjecture, with independent verification and approval by Lean.
59 minutes ago
Insight Beating AI Flash News: Anonymous math community account Captain Sude has released a new proof discovered by GPT-6 Astra, solving the Liouville version of the Goldbach problem. This problem relaxes the "two primes" condition in the classic Goldbach conjecture to "two integers with an odd total number of prime factors". Previously, Durham University mathematician Alexander P. Mangerel could only prove this under the assumptions that the Generalized Riemann Hypothesis holds and the even number is sufficiently large. Astra has now removed both constraints, proving that all even numbers greater than 2 satisfy the condition. The core approach is to first assume that a given even number cannot be split in this way, then derive contradictory results step by step. The full proof has been written in Lean 4. The project compiles successfully, and independent audit repositories have successfully reproduced the result, with no `sorry` statements or additional mathematical axioms found. The classic Goldbach conjecture itself remains unsolved, as the two addends here can still be composite numbers.
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