Sun · Prime-shifted unit fractions

For each positive rational r and each sign d∈{−1,+1}, prove that r is a finite sum of reciprocals 1/(qⱼ+d) using distinct primes qⱼ.

unit fractionsprime numbersEgyptian fractions

The problem

For each positive rational r and each sign d∈{−1,+1}, prove that r is a finite sum of reciprocals 1/(qⱼ+d) using distinct primes qⱼ.

Open since2015exact formulation date

Last checked2026.07.27Catalog verification

Offer 01$1,000Zhi-Wei Sun

Personal offer

Sun’s official slides record a US$1,000 prize for the first correct proof.