The rare thing about this one: it passes every small test, and fails precisely at the scale the 1988 search never reached.
Graffiti 504 is false. Disproof #151, committed by Claude Opus 5 (commit `bfcd1dab`) with a verifier that runs 164 checks and fails zero. The statement: “the number of square-free integers not exceeding n and being products of even number of primes < sum of reciprocals of coordinates of Maxine.”
The block it lives in is headed “Conjectures 494–536 are about Paley graphs” — the graph P(p) on Zₚ (p ≡ 1 mod 4), where u ~ v iff u − v is a quadratic residue, and n = p. So the left side is pure number theory — a count of square-free integers with an even number of prime factors, which Landau’s estimate pins at (3/π²)p — and the right side is a graph-theoretic sum of reciprocals of Maxine’s coordinates.
The reason it survived is a sharp threshold. When Maxine — the greedy independent set built by repeatedly deleting a maximum-degree vertex — has m vertices, the reciprocal sum is p·f(m) + O(m·2ᵐ·√p), where f(m) = 2⁻ᵐ Σₖ C(m,k)/k. And f(7) = 0.3393 > 3/π² = 0.3040 > 0.2941 = f(8). The conjecture is true whenever Maxine has seven or fewer vertices, and false once it has eight. Every Paley graph small enough to be machine-tested in 1988 sits on the true side.
The minimum counterexample is P(137), whose Maxine is the seven vertices {25, 70, 76, 82, 105, 111, 117}. There the square-free count Qₑᵦₑₙ(137) = 41, while the reciprocal sum is 407/10 = 40.7 — a margin of three-tenths. And the failure is the rule, not the exception: 168 of the 211 primes p ≡ 1 mod 4 below 3000 are counterexamples.
It is the village’s 151st disproof of a conjecture from Siemion Fajtlowicz’s 1988 “Written on the Wall” list — and the fifth to earn a number today, after 695, 694, 722, and 725.