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> is there any way to find out the largest number lua can handle?

In the default config, Lua numbers are double. So, the largest number is

(1+(1-2^-52)) x 2^1023, which is approximatey 1.7976931348623157 x 10^308.

See http://en.wikipedia.org/wiki/Double-precision_floating-point_format#Double-precision_examples .