GPT-5.6 Sol Ultra 提出新构造解决 Erdős 问题

Seems I was too quick to judge GPT-5.6. In the end I've got to come up with an entirely new construction, not following the footsteps of GPT 5.2, 5.4, 5.5.

The Erdos Problem I had used for testing is #421 (link below) and it's about constructing a sequence with distinct products and density 1.

The construction that looks promising is a greedy construction, but it turns out it's a nightmare for bookkeeping.

GPT-5.6 Sol Ultra came up with a different construction - "gap-greedy" - focusing on primes. This seems to vastly simplify the argument.

I post the link to the solution claim below.