2026-07-20 16:26 UTCgpt-5.6-terra · high

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.

No Progress

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.

Strategy and discriminator

Legacy attempt

Hypothesis: Not recorded.

Test: Not recorded.

Rationale

The sieve counts tau(x) by its defining divisor incidences, and the record recurrence is an exact identity. The audit uses a distinct tau implementation and direct maximum. Both checks are bounded only.

Claims requiring scrutiny

The executed C program excludes every n with 25 <= n <= 10^7: max_{m<n}(m+tau(m)) >= n+3.
The independently audited range 25 <= n <= 200000 has no candidate.

Evidence and scope

/root/proof-factory/research/erdos-647/workspace/search.c; command: cc -O3 -std=c11 -Wall -Wextra -pedantic search.c -o search && ./search 10000000
/root/proof-factory/research/erdos-647/workspace/audit.py; command: python3 audit.py 200000
/root/proof-factory/research/erdos-647/workspace/RESULTS.md
UndefinedBehaviorSanitizer run passed through 10^6; AddressSanitizer's LeakSanitizer could not run under the traced environment.

Computational experiments

None recorded.

Independent checker

Not provided.

Contribution gate

legacy attempt

No structured gate reasons were recorded in this legacy attempt; see the adjudication ledger.

Original model outcome: no_progress
Public classification: no_progress

Cross-domain transfers tested

None recorded.

Established facts

None recorded.

Ruled out in this epoch

None recorded.

Open leads

None recorded.

Continuation checkpoint

Objective:

First action:

Stop condition:

Next moves

Independently review or run the reported frontier certificate through approximately 6.16e17.
Formalize the record recurrence and the finite sieve certificate, then investigate the reported prime-chain reduction rather than extending an already dominated raw scan.

Citations

Tool disclosure

Used web search/opening for source and literature checks; wrote C and Python code; compiled with cc; ran Python 3 and UndefinedBehaviorSanitizer. No CAS, proof assistant, SMT/SAT solver, external data set, or sub-agents used.

Duration: 190.3s
Review state: not a result claim
Attempt ID: erdos-647-20260720-162607-f232b3

Human review ledger

No human review recorded.