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Old 2010-03-09, 19:40   #1
rogue
 
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Default Factoring EM47

Quote:
Originally Posted by frmky View Post
EM43 is factored by NFS@Home:

Code:
68-digit prime factor:
87991098722552272708281251793312351581099392851768893748012603709343
112-digit prime factor:
3164988789995660286920661075702707824540509995347150710802440021290930042981317991635632012608684057669131233917
EM44 - EM46 all have a small factor. The next roadblock is EM47, a 256-digit number with no factor smaller than 20 digits.
Many people have been waiting for this for a while. One would have needed some luck to find that factor with GMP-ECM.
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Old 2010-03-09, 19:52   #2
sean
 
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Quote:
Originally Posted by frmky View Post
EM43 is factored by NFS@Home:

Code:
68-digit prime factor:
87991098722552272708281251793312351581099392851768893748012603709343
112-digit prime factor:
3164988789995660286920661075702707824540509995347150710802440021290930042981317991635632012608684057669131233917
EM44 - EM46 all have a small factor. The next roadblock is EM47, a 256-digit number with no factor smaller than 20 digits.
Awesome! Have you notified Crandall and Pomerance, this particular number is mentioned in their book.
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Old 2010-03-09, 19:58   #3
henryzz
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Quote:
Originally Posted by frmky View Post
The next roadblock is EM47, a 256-digit number with no factor smaller than 20 digits.
And where can we get hold of that number?
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Old 2010-03-09, 20:03   #4
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Just to clarify:

EM44 has factor 107
EM45 has factor 127
EM46 has factor 3313
EM47 is this number:
Code:
1103211021556224950320857474629136274403207171149379589714114723150386622499653804938278785515108572580176773848180740319473132010224746780126854078078147700083327285484886146503985210746878713815121432016326226877964286156464913770459306370172713035675031
Can someone email this to Neil Sloane for inclusion in A000945?

Last fiddled with by 10metreh on 2010-03-09 at 20:07
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Old 2010-03-09, 21:39   #5
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I'm searching for factors of the c256 up to 45 digits (~9700 curves at 11M, simultaneous with 4700 at 3M).

Last fiddled with by CRGreathouse on 2010-03-09 at 21:46
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Old 2010-03-09, 22:04   #6
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Quote:
Originally Posted by R. Gerbicz View Post
Here is the few easy numbers. I think the title is wrong because by factoring a[1]*..*a[43]+1 we got actually the 44th term of the sequence and not the 43rd.
The convention seems to be that the number generated by the n'th term is EMn, and factoring EMn gives the (n+1)th term of the sequence. That is, the first 43 terms were known. Their product plus one is referred to as EM43. The smallest prime factor of EM43 is the 44'th term of the sequence.
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Old 2010-03-10, 05:44   #7
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Quote:
Originally Posted by frmky View Post
The next roadblock is EM47, a 256-digit number with no factor smaller than 20 digits.
Using Dario's applet, I ran curves 1-383, so no factor smaller than 25 digits.
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Old 2010-03-10, 19:03   #8
sean
 
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Not that it is needed, but one more factor for the 46th stage:

Code:
46 127.6069700067.56020785082237742556947.c215
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Old 2010-03-10, 19:06   #9
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Quote:
Originally Posted by Uncwilly View Post
Using Dario's applet, I ran curves 1-383, so no factor smaller than 25 digits.
I already have it to 35 digits (work in progress on 45 digits across 10 cores).
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Old 2010-03-10, 19:20   #10
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intersting sequence, and a quick summary here!
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Old 2010-03-10, 19:46   #11
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Quote:
Originally Posted by frmky View Post
Interesting credit for the large term.
ok, was a quick shot!

perhaps 'NFS@Home' better?

PS: edited!

Last fiddled with by kar_bon on 2010-03-10 at 19:50
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