Claims

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1981_01_01_erdos: Erdős's example 3·4 ≡ 5·6·7 ≡ 1 (mod 11), from a letter of 31 October 1979 reported in Guy's problem A15, settles the case k = 2.

1983_01_01_makowski: Mąkowski's 1983 note in Elemente der Mathematik gives three adjacent intervals whose products are each 1 modulo 17, the case k = 3; refereed.

2007_05_04_andersen: Andersen's computations on Prime Puzzles give, for each k from 10 to 14, the least prime with k adjacent intervals of product 1, the k = 14 witness at p = 10428007 settling every k from 2 to 14.

2026_06_03_agustin_aquino_hernandez_santiago: Agustín-Aquino and Hernández Santiago prove that infinitely many primes p have four distinct n with n! ≡ 1 (mod p), which gives the case k = 3 for infinitely many primes; with a Lean formalization.

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