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Old 2012-11-09, 04:46   #1
wblipp
 
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Default New Factor leaves a C168 Mersenne Composite

yoyo@home user Shawn Reimerdes found a P54 that reduced the unfactored primitive of 21584+1 from C222 to C168. This is the fourth known factor of this primitive. A P33 was previously found by ElevenSmooth. The remaining composite has had sufficient ECM to justify GNFS factoring. It is the smallest unfactored Mersenne composite Elevensmooth composite and is believed to be the sixth smallest unfactored Mersenne composite.

Last fiddled with by wblipp on 2012-11-09 at 23:57 Reason: Not Smallest Composite
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Old 2012-11-09, 07:07   #2
rcv
 
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Congrats to Shawn!!

Based on your posted progress data, a rough calculation suggests finding the next factor via ECM has an expected time of about 20000 core-days on an i7 2600K. Now that the number has been "cracked" down to 168 digits, a very rough estimate of GNFS difficulty is about 500 core-days on the same CPU. (I'm sure someone with more experience will correct my estimates.)

And while the other thread acknowledges it isn't the smallest 2+ Table composite cofactor, it is clearly the smallest unfactored ElevenSmooth composite cofactor.

I'm afraid it is much bigger than anything I've ever attempted, but I bet you will find a set of users/projects who have the capability of handling a 168-digit GNFS and the interest in finding the last factor of a future Cunningham Table entry. I would be happy to contribute some cycles if there is a distributed effort.

Last fiddled with by rcv on 2012-11-09 at 07:21
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Old 2012-11-09, 07:38   #3
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Although here on MF, people usually switch to 15e above GNFS difficulty 162-163, 14e can cope with difficulty 168. When the activity on RSALS burst by nearly an order of magnitude after I announced we were shutting down, I had the clients work on near-repdigit 77771_259, GNFS difficulty 172. The polynomial used 31-bit LPs, 2LP.
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Old 2012-11-09, 13:02   #4
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Quote:
Originally Posted by wblipp View Post
yoyo@home user Shawn Reimerdes found a P54 that reduced the unfactored primitive of 21584+1 from C222 to C168. This is the fourth known factor of this primitive. A P33 was previously found by ElevenSmooth. The remaining composite has had sufficient ECM to justify GNFS factoring. It is the smallest unfactored Mersenne composite.
Congratulations!!!

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Old 2012-11-14, 09:14   #5
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Shall NFS@Home's 14e factor this composite ?
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Old 2012-11-14, 11:31   #6
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Quote:
Originally Posted by debrouxl View Post
Shall NFS@Home's 14e factor this composite ?
I vote "Yes", please. As already noted, this number is definitely ready for GNFS.

BTW, I added four other future 2-table entries to the "sixth-smallest" thread referenced by wblipp. However, I don't know how much ECM has been performed on these numbers.
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Old 2012-11-21, 14:43   #7
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In the next few days, I'll queue the composite cofactor of 2^1584+1 to NFS@Home's 14e, using the following polynomial provided by Greg Childers:
Code:
# norm 2.550152e-16 alpha -6.342621 e 4.936e-13 rroots 5
skew: 8702992.93
c0: -1114440592287328527195245530261195706821
c1: 420303723002969758765944488602445
c2: 1192641766822455254646269947
c3: 155159242787910119869
c4: -15269072427156
c5: 112056
Y0: -375237357010895436011270610824532
Y1: 4114903083139799
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Old 2013-01-17, 02:54   #8
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After sieving, Mathew post processed this to P78 * P91, posting in the BOINC NFS thread
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