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-   -   New Factor leaves a C168 Mersenne Composite (https://www.mersenneforum.org/showthread.php?t=17405)

wblipp 2012-11-09 04:46

New Factor leaves a C168 Mersenne Composite
 
yoyo@home user Shawn Reimerdes found a P54 that reduced the unfactored primitive of 2[sup]1584[/sup]+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 [strike]unfactored Mersenne composite[/strike] Elevensmooth composite and is believed to be the [URL="http://www.mersenneforum.org/showthread.php?p=317769#post317769"]sixth smallest[/URL] 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 [URL="http://www.mersenneforum.org/showthread.php?t=4427&page=8"]other thread[/URL] acknowledges it isn't the smallest 2+ Table composite cofactor, it is clearly the smallest [URL="http://www.factordb.com/index.php?id=1100000000217719058"]unfactored ElevenSmooth[/URL] 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=wblipp;317634]yoyo@home user Shawn Reimerdes found a P54 that reduced the unfactored primitive of 2[sup]1584[/sup]+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.[/QUOTE]

Congratulations!!!

:george::george::george::george::george::george::george::george::george::george:

debrouxl 2012-11-14 09:14

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

rcv 2012-11-14 11:31

[QUOTE=debrouxl;318298]Shall NFS@Home's 14e factor this composite ? :smile:[/QUOTE]
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[/code]

wblipp 2013-01-17 02:54

After sieving, Mathew post processed this to P78 * P91, posting in the BOINC NFS [URL="http://www.mersenneforum.org/showthread.php?p=321864#post321864"]thread[/URL]


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