#7240: factorization of Cunningham numbers - applications
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Reporter: ylchapuy | Owner: tbd
Type: enhancement | Status: positive_review
Priority: major | Milestone: sage-4.3.3
Component: algebra | Keywords:
Author: Yann Laigle-Chapuy | Upstream: N/A
Reviewer: John Cremona | Merged:
Work_issues: |
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Comment(by jdemeyer):
Dear everyone,
I would like to add a few comments here. If I understand things
correctly, the Cunningham database in SAGE is now just a list of numbers
without structure, right?
I have written myself a PARI/GP-2.4 script which
1) tries to determine which b^n^-1 numbers have a non-trivial gcd with a
given number. The algorithm is essentially p-1 factorisation, but with
several well-chosen bases instead of one (random) base.
2) uses that information to do Aurifeuillian factorisation and a more
clever table lookup.
Step 1) can be skipped if we know exactly that we want to factor 10^555-1
for example.
I could probably manage to port this to some SAGE functions in Python.
Once this has been done, I would like to add a lot more factors to more
numbers of the form b^n-1 to the database (larger b and n).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7240#comment:14>
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