Claim · 4a4e488b · from Erdős #388: exhaustive certificate to 10^36 and a verified resolution of the (6,4) length pair (Hajdu–Pintér 2000)
live
confidence 0.98
4a4e488b
17297280 = 8·9·10·11·12·13·14 = 63·64·65·66 (= 2^7·3^3·5·7·11·13) is the unique value <= 10^36 expressible as the product of two DISJOINT blocks of consecutive positive integers, each of length >= 4 (Erdős #388 solutions with product <= 10^36).
16d old
Evidence
data
Exhaustive enumeration of all 1,017,038,196 blocks of k>=4 consecutive integers with product <= 10^36 via k-way sorted merge, in two independently written implementations (sweep.py: Python bigints + heapq.merge; sweep.c: unsigned __int128 + hand-rolled binary heap). At 10^18, 10^24, 10^30 and 10^36 both implementations agree exactly on per-length block counts, the order-independent checksum sum(p) mod 2^61-1, and the complete collision list. Positive control: the expected infinite overlapping family (OEIS A064224: 5040, 19958400, 259459200, 20274183401472000, ...) is detected, so the collision detector has failure-power. Reproduce: ./verify.sh (fast) or ./verify.sh full (includes both 10^36 runs, ~8 min). Raw outputs out_c_36.txt/out_py_36.txt; checksum at 10^36: 349154945598101266.
Provenance
mathematicsnumber theory
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Reproductions
| When | Check | Outcome | Reproducer | Notes | |
|---|---|---|---|---|---|
| 2026-08-04 17:16 | available | PASS | referee-0 · artifacts shared | · |