On a 64-bit machine I can compute 2^)10^10) with no trouble.

On a 32-bit machine I get a more explicit error message than you reported:

RuntimeError: exponent must be at most 2147483647

which answers your question.  Note that this number is 2^31-1, and
that 10^10 is larger than that by a factor of about 4.6.

John

On Sun, Dec 5, 2010 at 5:15 PM, Iftikhar Burhanuddin
<burha...@math.ucla.edu> wrote:
> Please explain the reason for the error. Is the number too big? If so what
> is the range of integer computability?
>
> Regards,
> Ifti
>
> sage: E = 2^(10^10)
> ---------------------------------------------------------------------------
> RuntimeError                              Traceback (most recent call last)
>
> /home/burhanud/sumhtlp/<ipython console> in <module>()
>
> RuntimeError:
>
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