GPT-6 Astra proves Linnik's variant of the Goldbach conjecture

ME News reports that on September 21 (UTC+8), Beating AI announced that the anonymous math community account Captain Sude revealed a new proof discovered by GPT-6 Astra, resolving the Liouville version of the Goldbach conjecture. This variant relaxes the classical Goldbach conjecture’s requirement of “two primes” to “two integers with an odd total number of prime factors.” Previously, mathematician Alexander P. Mangerel of Durham University could only prove it under the assumption of the generalized Riemann hypothesis and for sufficiently large even numbers. Astra has now removed both restrictions, proving the statement holds for all even numbers greater than 2. The core approach assumes that a given even number cannot be expressed in this form, then derives mutually contradictory results step by step. The full proof has been formalized in Lean 4; the project compiles successfully, and independent audits have reproduced the results without detecting any `sorry` or additional mathematical axioms. The classical Goldbach conjecture remains unsolved, as the two addends here may still be composite numbers. (Source: BlockBeats)