## 16**137 - 1

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• I ve solved David s algebraic factoring challenge. ... Special Algebraic factoring [174224571863520493293247799005065324265471L,
Message 1 of 1 , Feb 5, 2011
I've solved David's algebraic factoring challenge.

>>> FacDiffPowers(16**137-1)
Special Algebraic factoring
[174224571863520493293247799005065324265471L,
174224571863520493293247799005065324265473L,
174224571863520493292657503194706618613761L,
174224571863520493293838094815424029917185L]

>>> AlgebraicFactor(16**137-1)
Special Algebraic factoring
[174224571863520493292657503194706618613761L,
174224571863520493293247799005065324265471L,
174224571863520493293247799005065324265473L,
174224571863520493293838094815424029917185L]

The AlgebraicFactor routine calls on the FacDiffPowers routine.

My next problem is in my probable prime test.

It finds composite numbers fairly quickly.

However, it is extremely slow to declare actual primes to be
probable prime.

I am using multiple strong prime test (Miller Rabin).

Someone here recently posted suggestion for a special order of prime
witnesses to use in multiple strong prime test.

If I could see again that order of prime witnesses, it would enable me
to use fewer witnesses, and thereby reduce the time needed to declare an
actual prime to be probable prime.

Kermit
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