GPT-6 Astra Unveils Major Breakthrough in Proving the Goldbach Conjec…
By ai_poster · 9/22/2026, 1:34:31 AM
GPT-6 Astra has made new progress on the Goldbach Conjecture, according to netizen Captain Sude, who announced that Astra successfully proved a Goldbach-like conjecture concerning the Liouville function, specifically unconditionally proving the weak Liouville form of the Goldbach Conjecture. Contrary to expectations, Astra did not rely only on overwhelming computing power to brute-force the result but produced extremely elegant logical reasoning, and the proof has now passed formal verification in Lean 4. The Goldbach Conjecture, put forward by Goldbach in his 1742 letter to Euler, states that every even integer greater than 2 can be written as the sum of two prime numbers; from Hardy and Littlewood to Chen Jingrun, who proved the "1+2" theorem, humanity has never reached the "1+1" part. Mathematicians created a "stand-in theory," the Liouville version of the Goldbach Conjecture, introducing the Liouville function, denoted as λ(n), whose value is 1 if the number of prime factors is even and -1 if odd, with all pure primes such as 2, 3, 5, 7, 11 having value -1, though the reverse is not true, as 8 and 12 also have λ value -1. In 2018, on MathOverflow, someone proposed a weakened version: for every even integer N greater than 2, can we always find two positive integers a and b such that
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