Claude Fable 5 and GPT-5.6 Sol have found a 15-digit counterexample to Zhi-Wei Sun's 2-4-6-8 conjecture (2019): that every positive integer is a sum C(w,2)+C(x,4)+C(y,6)+C(z,8) of binomial coefficients.
n = 896,315,812,331,399 has no such representation
Science
A 15-digit counterexample to a 2019 number theory conjecture
Tom Adamczewski of Epoch AI reports that Claude Fable 5 and GPT-5.6 Sol broke Zhi-Wei Sun's 2-4-6-8 conjecture. The number 896,315,812,331,399 cannot be written as the sum of binomial coefficients the conjecture requires.
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- Claude Fable 5, GPT-5.6 Sol
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- Epoch AI
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