Below is my code. If I set W to $10^{55}$, it breaks down and the result is wrong. What do I need to do to use W as large as $10^{200}$?
n = 15;
roots = Table[Sqrt[Prime[i]], {i, n}];
W = 10^45;
A = Table[0, {i, 1, n + 1}, {j, 1, n + 1}];
A[[1, 1]] = 1;
For[i = 1, i <= n, i++, A[[1, i + 1]] = Round[W*roots[[i]]];];
For[i = 2, i <= n + 1, i++, A[[i, i]] = W; ];
b = LatticeReduce[A];
q = Abs[b[[1, 1]]]
The error message is here:
N::meprec: Internal precision limit $MaxExtraPrecision = 50.` reached while evaluating -28254824730949473896127703534134355343731647793777+19979178168491741166272766531031078657045486457686 Sqrt[2].
My version is V9, and my OS is windows 7.
$MaxExtraPrecision
like thisBlock[{$MaxExtraPrecision = 100}, Round[W*#] & /@ roots]
$\endgroup$