PPL 089 / 177 permanent IDsPrize Problem Ledger · PPLChecked 2026.07.27
Prize Problem LedgerPPL · Open reward indexAll 177 problems
Prize Problem LedgerZhi-Wei Sun prizesPPL 089Hou–Zeng · A prime, Fibonacci number and Catalan number

Permanent problem IDPPL 089

Source-statedIndependentconjecture

Number theory

Hou–Zeng · A prime, Fibonacci number and Catalan number

Every integer n>4 is the sum of an odd prime, a positive Fibonacci number and a Catalan number.

prime numbersFibonacci numbersCatalan numbers
01

The problem

Every integer n>4 is the sum of an odd prime, a positive Fibonacci number and a Catalan number.

Open since2009exact formulation month
Last checked2026.07.27Catalog verification
02

Reward offers

Offer 01$1,000 proof · $200 counterexampleQing-Hu Hou and Jiang Zeng
Personal offer

US$1,000 is offered for the first positive solution published in a well-known mathematical journal; US$200 for the first explicit counterexample that the sponsors can verify by computer.

Award source ↗
03

Sources & reading

2 unique reference linksPrize terms in Sun’s paper OEIS A154404
04

Related open targets

Number theoryBeal conjecturePPL 005 · $1,000,000 · 33 years openNumber theoryBirch–Swinnerton-Dyer conjecturePPL 006 · $1,000,000 · 61 years openNumber theoryRiemann hypothesisPPL 138 · $1,000,000 · 167 years open