Claims

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2025_01_16_sampaio: No integer n has greatest prime factor 19 while n plus one is a power of 2, so the statement fails for the pair 19 and 2; the site's remarks record the observation and extend it to primes above 13 with 2 as a primitive root.

2025_01_16_tong: For every prime p there are infinitely many primes q such that no integer n has greatest prime factor p while n plus one has greatest prime factor q; the elementary disproof the site's remarks record and credit to Tong.

2026_02_07_alexeev: Infinitely many primes q such that no n at least 2 has P(n)P(n+1) equal to 2q: the 2020 Romanian Master of Mathematics argument, formalized in Lean by ChatGPT, Aristotle and Boris Alexeev; accepted on Lean built here.

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