True. I was just thinking that why Sage won't use the law of congruences to evaluate the expression. 84977118993*2^520+1 is not too large number to fit into the memory. Therefore one can use laws of congruences to evaluate mod(2^(2^517)+1,84977118993*2^520+1).
On Jan 27, 5:21 pm, Marshall Hampton <[email protected]> wrote: > 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 <[email protected]> wrote: > > > I found onhttp://www.prothsearch.net/fermat.htmlthat84977118993*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 -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
