Claim · b033c263 · 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
b033c263
The exhaustive-classification record is extended 15.2% past 10^13 to the certified contiguous frontier 11,520,000,000,000: the extension stretch [1e13, 1.152e13) contains 50,656,592,644 odd primes, of which 122,129,252 are cluster primes, and the largest cluster prime found — exceeding the previous largest known, 9,999,999,954,787 — is 11,519,999,994,329, independently re-verified as a cluster prime by pure-Python deterministic Miller-Rabin over every odd composite blocking candidate j < 4693 (a cap exceeding the run-certified global max k(m) = 4093 by 600).
23d old
Evidence
data
summary.json (certified_height 11520000000000; largest_cluster_prime 11519999994329; decade_table row [1e13,1e14): odd_primes 50656592644, clusters 122129252); results.csv rows with lo >= 1e13 (per-block certificates for the extension stretch); verify.sh run at write-up exited 0 with 'anchor: largest cluster 11519999994329: OK'. Re-check: './verify.sh', or regenerate any extension block with './cluster <lo> <hi>' and compare its results.csv line.
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
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 | · |