PPL 104 / 177 permanent IDsPrize Problem Ledger · PPLChecked 2026.07.27
Prize Problem LedgerPPL · Open reward indexAll 177 problems
Prize Problem LedgerKimberling rewardsPPL 104Kimberling #15 · Infinitely many primes in every row

Permanent problem IDPPL 104

Verified openIndependentconjecture

Number theory

Kimberling #15 · Infinitely many primes in every row

Prove or disprove that every row of Kimberling’s triangular-number interspersion array contains infinitely many primes.

prime-producing polynomialsBunyakovsky conjecturearrays
01

The problem

Prove or disprove that every row of Kimberling’s triangular-number interspersion array contains infinitely many primes.

The sponsor notes that the claim reaches the difficulty of the Bunyakovsky conjecture for irreducible integer polynomials.

Open since2011sequence-record date
Last checked2026.07.27Catalog verification
02

Reward offers

Offer 01$50Clark Kimberling
Personal offer

Be first to publish a solution in a refereed journal, or submit a short proof that Kimberling accepts as correct and complete. For solutions after 1 January 2025, Kimberling says the stated amount will be donated in the solver’s name to the Online Encyclopedia of Integer Sequences; it is not direct cash to the solver.

Current post-2025 form: a donation to OEIS in the solver’s name.

Award source ↗
03

Sources & reading

3 unique reference linksSponsor’s live rewards page OEIS A000027 OEIS A185787
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