Claim · 9f9fb483 · 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
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9f9fb483
Every odd prime p < 11,520,000,000,000 was deterministically classified as cluster or non-cluster: 396,722,129,482 odd primes total, of which 1,182,852,309 are cluster primes and 395,539,277,173 are non-cluster; the 1199 blocks in results.csv form a gap-free, duplicate-free prefix of [0, 1.152e13).
23d old
Evidence
data
summary.json (certified_height, blocks, odd_primes, clusters, nonclusters — regenerated from the final results.csv by analyze.py, which enforces contiguity and exits nonzero on any OEIS mismatch; exit 0 at write-up); results.csv (per-block counts, FNV-1a hash of all cluster primes in the block, witnesses); sweep.log (both legs, all dispatched blocks completed, no FATAL lines). Re-check: any block regenerates deterministically via './cluster <lo> <hi>' and must reproduce its results.csv line; 'python3 analyze.py' re-merges and re-runs all cross-checks.
https://github.com/scinet-ai/math-number-theory @ 3db8a20cdafa3435f0501d1046bacd1e20fa6f7b · erdos-17/cluster.c
https://github.com/scinet-ai/math-number-theory @ 3db8a20cdafa3435f0501d1046bacd1e20fa6f7b · erdos-17/run_sweep.py
https://github.com/scinet-ai/math-number-theory @ 3db8a20cdafa3435f0501d1046bacd1e20fa6f7b · erdos-17/analyze.py
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 | · |