The first genuine discovery target: a short statement with a compact deterministic witness and a natural optimized-search harness.
Open-problem programTried — still open
A divisor-function record beyond 24
Let τ(n) count the positive divisors of n. Is there some n > 24 such that max over m < n of (m + τ(m)) is at most n + 2?
A positive answer is one explicit integer plus a bounded exact divisor-count check.
- Difficulty
- 4/10
- Attempts
- 2
- Last attempt
- 2026-07-20 16:26 UTC
- Source status
- verifiable
- External validation
- none
divisor sieverecord sequence searchbranch and boundOEIS cross-check
Resumable campaign memory
2 epochs · 0 promising · 2 blocked · 0 ruled outResearch map
Independently review or run the reported frontier certificate through approximately 6.16e17.
First action: Independently review or run the reported frontier certificate through approximately 6.16e17.
Stop or redirect when: The planned discriminator resolves the route.
- No open lead is checkpointed.
- unspecified
Exact divisor-incidence sieve with the recurrence R(n+1)=max(R(n), n+tau(n)), independently audited by trial-division factorization and direct maximization. - unspecified
Headless research pass
- Nothing has been rigorously ruled out yet.
Complete history
Attempts on this problem
2026-07-20 16:26 UTCOpen-problem program · 3 min
A divisor-function record beyond 24
Exact divisor-incidence sieve with the recurrence R(n+1)=max(R(n), n+tau(n)), independently audited by trial-division factorization and direct maximization.
What this run accomplished
No candidate was found. The C search exactly checked every n in [25, 10^7], with minimum R(n)-n equal to 3 at n=35. A separate Python trial-division audit agreed through 200,000 and recovered the known terms 5, 8, 10, 12, 24. This does not improve the stronger reported human computational bounds.
No ProgressOpen full record →
2026-07-20 16:21 UTCOpen-problem program · 0 min
A divisor-function record beyond 24
Headless research pass
What this run accomplished
The pass did not produce a valid research result: RuntimeError: Codex failed rc=1: WARNING: proceeding, even though we could not create PATH aliases: Read-only file system (os error 30) Error: failed to initialize in-process app-server client: Read-only file system (os error 30)
ErrorOpen full record →