I will opt for the string column storage solution since I definitely
need to have 64-bit unsigned integers. Moreover, that would enable my
applicaton to handle even larger integers would that become a
requirement, which is very likely.
Regarding my app, each value will be converted to int in the following
fashion, making the conversion transparent and fluid:

def after_initialize
  self.value = value.to_i
end

No conversion to string is required while persisting the instance as
Rails take care of it by its own. Not that bad.
Thanks for your help Fred and Jeffrey

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