New Factor leaves a C168 Mersenne Composite

wblipp · 2012-11-09, 04:46

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.

rcv · 2012-11-09, 07:07

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.

debrouxl · 2012-11-09, 07:38

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.

aketilander · 2012-11-09, 13:02

Quote:

Originally Posted by wblipp

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!!!

debrouxl · 2012-11-14, 09:14

Shall NFS@Home's 14e factor this composite ?

rcv · 2012-11-14, 11:31

Quote:

Originally Posted by debrouxl

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.

debrouxl · 2012-11-21, 14:43

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

wblipp · 2013-01-17, 02:54

After sieving, Mathew post processed this to P78 * P91, posting in the BOINC NFS thread

2012-11-09, 04:46	#1
wblipp "William" May 2003 New Haven 2³·5·59 Posts	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

2012-11-09, 07:07	#2
rcv Dec 2011 11×13 Posts	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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2012-11-09, 07:38	#3
debrouxl Sep 2009 3D1₁₆ Posts	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.

2012-11-14, 09:14	#5
debrouxl Sep 2009 977 Posts	Shall NFS@Home's 14e factor this composite ?

2013-01-17, 02:54	#8
wblipp "William" May 2003 New Haven 100100111000₂ Posts	After sieving, Mathew post processed this to P78 * P91, posting in the BOINC NFS thread