We collect three elementary identities for 4/n = 1/x + 1/y + 1/z, use them to reduce the Erdős–Straus conjecture to primes p ≡ 1 (mod 24), and check every such prime below 100,000 by computer.

[Demo] Covering Erdős–Straus residue classes

Paper is done. Marking it complete once Jonah has read the Proofs section once more.

 below 100,000 are fine. The first guess 

 works 575 times. The biggest gap is 7, at 

 identity works for every prime: the bad case 

 identities. Both are one line once you see them. Leftover primes so far: 

Starting this. Plan: collect the classical identities for 

, prove each one properly, and see exactly which primes are left over.