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Old 2018-09-29, 17:23   #1
didgogns
 
Mar 2014
South Korea

24 Posts
Default On the efficiency of SNFS for "dirty" numbers

Hi,

This time I want to factor (2^300-1)*10^91+2^299-1 and similar numbers.
The number is very close to 2^300*10^91 and a reasonable SNFS polynomial will be something like 10*x^5+2^299-10^91-1, where x=2^60*10^18.
Now my concern is that c0=2^299-10^91-1 looks very big. The question is:

Is there significant performance drop if SNFS polynomial is "dirty" like this case?
If so, how the people who SNFSed 150^149+149^150 or other numbers solved this issue?
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Old 2018-09-29, 17:48   #2
didgogns
 
Mar 2014
South Korea

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So the SNFS polynomials of XYYXF numbers are of the these form.
Quote:
Originally Posted by XYYXF View Post
SNFS is faster but is restricted to numbers of special form, e.g. sextic a*b6+c*d6 or quintic a*b5+c*d5 for Leyland numbers.
How can I create a .poly file of these form? Is there any online guide?
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Old 2018-09-29, 18:22   #3
R. Gerbicz
 
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"Robert Gerbicz"
Oct 2005
Hungary

26258 Posts
Default

Quote:
Originally Posted by didgogns View Post
The number is very close to 2^300*10^91 and a reasonable SNFS polynomial will be something like 10*x^5+2^299-10^91-1, where x=2^60*10^18.
Now my concern is that c0=2^299-10^91-1 looks very big. The question is:

Is there significant performance drop if SNFS polynomial is "dirty" like this case?
I'd call it uninteresting, digit related, totally boring numbers. But there is a better polynom, most likely this is still gnfs job. Hint: 2 | 10.
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