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• One additional enhancement of 5.0c vs 4d-r7a I left out, was that 5.0c now maintains the expressions. Here is some sample output c: ecm ecm-5.0c echo
Message 1 of 2 , Mar 2, 2003
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One additional "enhancement" of 5.0c vs 4d-r7a I left out, was that
5.0c now "maintains" the expressions. Here is some "sample" output

c:\ecm\ecm-5.0c>echo 27.691#+1 | ecm -c 3 -ve 200 -deep 15000
Input number is 27.691#+1 (291 digits)
Using B1=15000, B2=2114895, polynomial x^1, sigma=2214210635
Step 1 took 2313ms
Step 2 took 1522ms
Line=1 Curves=2/3 B1=15000 Factors=0
Input number is 27.691#+1 (291 digits)
Using B1=15000, B2=2114895, polynomial x^1, sigma=579468029
Step 1 took 2414ms
Step 2 took 1532ms
********** Factor found in step 2: 3302513916338587
Found probable prime factor of 16 digits: 3302513916338587
Composite cofactor
2270478349675689184681254371761976795334832608365966034800675383016042
5494115265110948714279402342416540729753940671497012750001602757770976
4024230872996914811635410193141366258313816663972516000113519668852437
273257579884363472903020309122119120061184840304026980285988591553
has 276 digits
Line=1 Curves=3/3 B1=15000 Factors=1
Input number is (27.691#+1 )/3302513916338587 (276 digits)
Using B1=15000, B2=2114895, polynomial x^1, sigma=974840061
Step 1 took 2163ms
Step 2 took 1422ms
Line=1 Curves=4/3 B1=15000 Factors=1

The line "Input number is (27.691#+1)/3302513916338587 (276 digits)
shows this "keeping" of expressions. However, this small example
has also shown me that I missed one (and need to fix it). The
original output of the cofactor is fully expanded, when the
"expression" could have been output.

Jim.
• ... Thanks for adding these features, especially the factorial and multifactorial code! The idea of keeping expressions will also be very handy. I ve run
Message 2 of 2 , Mar 2, 2003
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--- In primenumbers@yahoogroups.com, "Jim Fougeron." <jfoug@k...>
wrote:
> One additional "enhancement" of 5.0c vs 4d-r7a I left out, was that
> 5.0c now "maintains" the expressions. Here is some "sample" output
>
>
> The line "Input number is (27.691#+1)/3302513916338587 (276 digits)
> shows this "keeping" of expressions. However, this small example
> has also shown me that I missed one (and need to fix it). The
> original output of the cofactor is fully expanded, when the
> "expression" could have been output.
>
> Jim.

Thanks for adding these features, especially the factorial and
multifactorial code! The idea of "keeping" expressions will also be
very handy. I've run recently large files for n!+-1 for 600<n<1000
Searching through the output for all the factors was a right pain!!
I've probably made many typos in my lists (at
www.uow.edu.au/~ajw01/curves/ the plus and minus files.)
This will at least help check them all. Does the code sort the factors
in this output?

One other possibility worth considering is adding a definitive
primality test for small factors and cofactors. It should be off by
default with an option to select the maximum digit size for which it
is called. Of course if the AKS conjecture 4 ever gets proved, this
will be feasible for quite decent sizes!

Andrew
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