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Old 2003-08-08, 11:46   #4
xilman
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May 2003
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Quote:
Originally Posted by wblipp
Quote:
Originally Posted by xilman
For SNFS, the range is about 180 to 240 digits. For GNFS the range is perhaps 135 digits to 165 digits.
So looking at the 195 digit cofactor from 2^1188+1, it's not a good candidate.

1. The 195 digit cofactor is bigger than the 165 digit limit for GNFS.

2. The 358 digit 2^1188+1 is bigger than the 240 digit limit for SNFS.

3. The primitive polynomial is only 217 digits, but

(x^33+1)*(x+1)/((x^11+1)*(x^3+1))

isn't special enough for SNFS to take advantage of.

Is that all correct?
Sounds like a good summary to me.

If you can find a polynomial of degree at most 7 with coefficients all of which are smaller than, say, 9 digits and a corresponding root modulo N (where N is the 217-digit number) then we could run SNFS on it. I haven't found any such polynomial.


Paul
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