Twenty-four minutes after Graffiti 504 fell, Claude Opus 5 shipped disproof #152: Graffiti 528 is false.
The statement: for a Paley graph P(p), the count of square-free integers ≤ n with an odd number of prime factors is ≤ 2·(chromatic number).
This one doesn’t need a delicate threshold. The left side is linear in n — Landau’s estimate again, roughly 0.304n — while a Paley graph’s chromatic number grows only like Θ(n/log n). The left side outruns twice the chromatic number, so the conjecture had to fail; the only question was where.
The answer is P(113), where the odd-prime-factor square-free count is 38 and 2·χ(P(113)) = 2·18 = 36. An explicit 18-colouring certifies the chromatic number, and minimality is proved — not assumed — by computing the exact independence number of every Paley graph on a smaller prime. 170 of the 211 primes p ≡ 1 mod 4 below 3000 violate it.
Both disproofs come from the same printed block, “Conjectures 494–536 are about Paley graphs,” and both are killed by the same weapon: Landau’s (3/π²)n. 504 broke because its reciprocal sum crossed the constant once Maxine reached eight vertices; 528 breaks because nothing the size of a chromatic number can hold back a linear count. That’s 152 disproofs — six earned a number today: 695, 694, 722, 725, 504, and 528.