(*A proxy for the prime numbers satisfy this linear program*)
(*start*)
nn = 42;
TableForm[
L1 = Table[
LinearProgramming[
Table[1/n, {n, 1, k}], {Table[If[n == 1, k, 1], {n, 1, k}]}, {{1,
0}}, Table[
If[n == 1, {-1, 1}, {-2 (n - 1), 2 (n - 1)}], {n, 1, k}]], {k,
1, nn}]];
b=Table[Sum[-Sign[-1 + Sign[L1[[n, k]]]], {k, 1, n}], {n, 1, nn}]
(*end*)
(*Setting one of the bounds to zero gives a square root bound*)
(*start*)
nn = 42;
TableForm[
L2 = Table[
LinearProgramming[
Table[1/n, {n, 1, k}], {Table[If[n == 1, k, 1], {n, 1, k}]}, {{1,