Ticket #191 (closed enhancement: duplicate)
factorization table / database
|Reported by:||was||Owned by:||tbd|
Description (last modified by was) (diff)
It would be very nice if SAGE had a large table/database of integers of special forms whose factorizations are known, since a huge amount of work has already been done on this. The SAGE factor command could consult such a table, before applying other more general techniques.
For example, on the number theory list:
Look in the file http://homes.cerias.purdue.edu/~ssw/bell/r1 for the factorizations of p^p - 1 for most p < 180. (If you change "r1" to "r2", you get the factors of p^p + 1.) For the meaning of the "L" and "M" notation, see the papers at http://homes.cerias.purdue.edu/~ssw/bell/index.html
So a person really wanted to factor some numbers p^p -1, but couldn't with PARI. If SAGE had tables of the factorizations of those numbers, it could have done it via a lookup, and the verbose message could have given the above reference. Something similar would be good for a huge range of classes of prime numbers. This would be an excellent student project.
I believe the Cunningham project has large tables of factored integers of a special form. This might be a useful resource for those wanting to undertake this project.
- Description modified (diff)
- Summary changed from prime table / database to factorization table / database
- Owner changed from was to tbd
- Component changed from number theory to factorization
- Status changed from new to closed
- Resolution set to duplicate
- Report Upstream set to N/A
- Status changed from closed to new
- Resolution duplicate deleted