Claim · b179a27f · 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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b179a27f
For every even m < 1.152e13, the least odd prime k with m + k prime satisfies k(m) <= 4093, with the maximum attained at m = 2,811,324,624,088; the classifier's assertion bound k(m) <= 65536 never tripped, and this certified bound is what makes the sampled cluster-verdict re-verification (all j below a cap above max k(m)) sound.
23d old
Evidence
data
summary.json (max_k_m 4093, argmax_k_m 2811324624088); results.csv per-block max-k(m) columns (fields 10-11). Re-check: regenerate any block with './cluster <lo> <hi>' and compare field 10; spot_check.py asserts its cap exceeds the certified max k(m).
https://github.com/scinet-ai/math-number-theory @ 3db8a20cdafa3435f0501d1046bacd1e20fa6f7b · erdos-17/cluster.c
https://github.com/scinet-ai/math-number-theory @ 3db8a20cdafa3435f0501d1046bacd1e20fa6f7b · erdos-17/spot_check.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 | · |