mersenneforum.org Typo in reported factor?
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 2011-02-19, 23:03 #1 R.D. Silverman     Nov 2003 1D2416 Posts Typo in reported factor? Bruce reports finding a factor of 6^391-1 on the ECMNET webpage. But unless my software is really screwing up, the factor does not divide. I am guessing that one or more digits are missing?
 2011-02-19, 23:17 #2 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2×3×1,543 Posts Yep, it is 7,359-. Cofactor c224 is composite. (It must have divided a number from the list because othewise Paul's form wouldn't accept it. This sudoku puzzle was easy.) Last fiddled with by Batalov on 2011-02-19 at 23:18
2011-02-20, 02:20   #3
bdodson

Jun 2005
lehigh.edu

210 Posts

Quote:
 Originally Posted by Batalov Yep, it is 7,359-. Cofactor c224 is composite. (It must have divided a number from the list because othewise Paul's form wouldn't accept it. This sudoku puzzle was easy.)
Yes, sorry; and thanks. Different c27x first five hole. But another
small one; seems likely that there are more to find. Too many new
inputs over the weekend, when many of the labs are closed. Distracted
by exam grading and _three_ new top5000 Proth primes. Plus the wind
knocked out our power for two hours here today.
Regards, Bruce
---

2011-02-21, 02:14   #4
bdodson

Jun 2005
lehigh.edu

210 Posts

Quote:
 Originally Posted by Batalov (It must have divided a number from the list because othewise Paul's form wouldn't accept it. This sudoku puzzle was easy.)
474942339376967475871960321762614254290810243038880418971061342256529

2nd hole. -bd

 2011-02-21, 02:34 #5 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2·3·1,543 Posts A hole in one. Now, this is not a futile factor. :-) Congratulations!
2011-02-21, 14:33   #6
bdodson

Jun 2005
lehigh.edu

210 Posts

Quote:
 Originally Posted by Batalov A hole in one. Now, this is not a futile factor. :-) Congratulations!
Here's the group order:

Code:
Magma V2.16-4     Mon Feb 21 2011 09:16:48 on altair1  [Seed =3370645033]

[ <2, 2>, <3, 2>, <7, 2>, <11, 2>, <53, 1>, <353, 1>, <467, 1>, <779591,1>,
<1057367, 1>, <15751453, 1>, <40771103, 1>, <43303219, 1>, <356236847,1>,
<31186368729239, 1> ]
So that's p = 356236847 < 400M = B1 for the step1 prime,
q = 31186368729239 > 1.59e13 = B2 for the step2. Ooops. If it matters,
this ran with k = 20. Sounds like this really used some GMP-ECM features;
and I was more than just lucky with the parameters!

Bruce (This is the new p69 by ecm, from 2,1822L C197.)

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