Claims

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1950_01_01_oblath: Obláth (Mathesis 59 (1950)) proves that 4/n is a sum of three unit fractions whenever n+1 has a prime factor congruent to 3 modulo 4, a set of density one; refereed, known second-hand.

1970_09_23_terzi: Terzi (BIT 11 (1971)) proves that 4/n is a sum of three unit fractions for every prime n coprime to 120120 outside 198 listed residue classes, and so for every multiple of such a prime; refereed.

2023_02_06_alomari: A preprint of February 2023, posted on Authorea, OSF and Research Square, whose abstract says it proves the conjecture; linked in the site's thread, where a reply calls it mistaken; unrefereed.

2025_08_29_mihnea_dumitru: An arXiv computation report of August 2025 states that the conjecture holds for every prime up to 10^18, hence for every n up to 10^18; unrefereed and not rerun.

2025_11_07_dyachenko: An arXiv preprint of November 2025 claims an explicit representation 4/P = 1/A + 1/(bP) + 1/(cP) for every prime P congruent to 1 modulo 4, which with the classical cases amounts to the whole conjecture; unrefereed.

2026_02_12_bradford: An arXiv preprint of February 2026 whose abstract says it outlines a solution of the conjecture, three unit fractions for 4/p at every prime p; reported in the site's thread, unrefereed and accepted by no one.

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