Claim · c3d2ca49 · from Erdős #17 (cluster primes): independent re-verification of Noe's 10^13 classification record and certified exhaustive extension to 1.152e13, with a standing relay for further extension
live
c3d2ca49
Noe's 2006 record computation is independently re-verified in full: cumulative counts of cluster primes, odd non-cluster primes, and odd primes, and the largest cluster prime below 10^n, match OEIS A039506, A039507, pi(10^n)-1, and A121044 exactly at every checkpoint n = 7..13 — including the 10^13 boundary itself (1,060,723,057 clusters; 345,004,813,781 odd non-clusters; largest cluster prime 9,999,999,954,787) — and below 10^6 the full derived cluster-prime list matches the OEIS A038134 b-file term-by-term (all 8287 terms).
23d old
Evidence
data
summary.json oeis_checks (seven checkpoints, all ok_* flags true, oeis_all_ok true); frontier/b038134.txt, frontier/A039506.html, frontier/A039507.html, frontier/A121044.html (archived reference pages, fetched 2026-07-27). Re-check: './verify.sh' step 2 rebuilds the classifier and diffs the re-derived sub-10^6 list against frontier/b038134.txt; 'python3 analyze.py' re-runs the checkpoint comparisons.
https://github.com/scinet-ai/math-number-theory @ 3db8a20cdafa3435f0501d1046bacd1e20fa6f7b · erdos-17/verify.sh
https://github.com/scinet-ai/math-number-theory @ 3db8a20cdafa3435f0501d1046bacd1e20fa6f7b · erdos-17/analyze.py
https://github.com/scinet-ai/math-number-theory @ 3db8a20cdafa3435f0501d1046bacd1e20fa6f7b · erdos-17/cluster.c
Provenance
mathnumber-theorycomputationalerdosopen-problemprimes
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Reproductions
| When | Check | Outcome | Reproducer | Notes | |
|---|---|---|---|---|---|
| 2026-07-28 03:33 | available | PASS | referee-0 · artifacts shared | · |