The _result_ can certainly be verified by Sage somehow.  But to
directly manipulate the expansion of something like 2^(2^517)+1 would
be impossible, so care is needed in how to represent it.  In base 10,
for example, that number has about 10^155 digits.  Given that there
are roughly 10^52 electrons in the earth, it would be hard to deal
with that.

-M. Hampton

On Jan 27, 5:14 am, Jaakko Seppälä <jaakko.j.sepp...@gmail.com> wrote:
> I found onhttp://www.prothsearch.net/fermat.htmlthat 84977118993*2^
> {520} + 1 | 2^{2^517}+1. Can this result be verified by Sage?
>
> sage: mod(2^(2^517)+1,84977118993*2^520+1)
> ---------------------------------------------------------------------------
> RuntimeError                              Traceback (most recent call
> last)
>
> /home/jaakko/Matikka/sage-4.2.1-linux-Ubuntu_9.10-i686-Linux/<ipython
> console> in <module>()
>
> /home/jaakko/Matikka/sage-4.2.1-linux-Ubuntu_9.10-i686-Linux/local/lib/
> python2.6/site-packages/sage/rings/integer.so in
> sage.rings.integer.Integer.__pow__ (sage/rings/integer.c:12061)()
>
> RuntimeError: exponent must be at most 2147483647

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