If you just recorded the smallest primitive roots I'll bet the database would get a lot smaller:-) Do you need all the prim roots in the CrypTool tutorial for a particular purpose, eg discrete logs?
I'd guess a database of the smallest prim roots mod p for all primes out to a million (for starters) would be interesting to some number-theorists. I did a google search and could not find much online. I did find Western, A. E. and Miller, J. C. P. Tables of Indices and Primitive Roots. Cambridge, England: Cambridge University Press, pp. xxxvii-xlii, 1968, although I couldn't find what it had, and this page http://www.ieeta.pt/~tos/p-roots.html has a link to some related data. Hope these are useful. On Fri, Jul 31, 2009 at 3:49 AM, Minh Nguyen<[email protected]> wrote: > > Hi folks, > > I have been playing around with primitive roots lately in an effort to > get more Sage code into the CrypTool tutorial. A result of this is > that I have computed all the primitive roots modulo p, for each prime > p between 1 and 100,000 inclusive. All Sage code and results are up at > > http://sage.math.washington.edu/home/mvngu/doc/primitive-roots/ > > In particular, the generated database of such primitive roots is > > http://sage.math.washington.edu/home/mvngu/doc/primitive-roots/primroots.dat.bz2 > > Even after compression, it's about 285 MB; it's 1.0 GB uncompressed. > The whole database took about one day to generate on sage.math. At the > moment, I'm not aware that Sage has a function to compute all > primitive roots modulo a prime p so I created ticket #6467 > > http://trac.sagemath.org/sage_trac/ticket/6467 > > in order to get this implemented. I'm not at all well-versed in > mathematics, nor number theory for that matter, so I'm not sure what > anyone can do with the above database of primitive roots. Or is it > just one of those long and pointless uses of Sage like Carl Witty's > build [1] of Sage on a G1 cell phone? :-) > > [1] > http://groups.google.com/group/sage-devel/browse_thread/thread/243dfd4ab25a2779/3cc58c39cc9cadff > > -- > Regards > Minh Van Nguyen > > > > --~--~---------~--~----~------------~-------~--~----~ 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-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
