mersenneforum.org Factoring EM47
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2010-03-09, 19:40   #1
rogue

"Mark"
Apr 2003
Between here and the

3·5·419 Posts
Factoring EM47

Quote:
 Originally Posted by frmky 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.

2010-03-09, 19:52   #2
sean

Aug 2004
New Zealand

2×3×37 Posts

Quote:
 Originally Posted by frmky 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.

2010-03-09, 19:58   #3
henryzz
Just call me Henry

"David"
Sep 2007
Cambridge (GMT/BST)

5,857 Posts

Quote:
 Originally Posted by frmky 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?

 2010-03-09, 20:03 #4 10metreh     Nov 2008 2·33·43 Posts 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
 2010-03-09, 21:39 #5 CRGreathouse     Aug 2006 32×5×7×19 Posts 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
2010-03-09, 22:04   #6
frmky

Jul 2003
So Cal

2·3·347 Posts

Quote:
 Originally Posted by R. Gerbicz 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.

2010-03-10, 05:44   #7
Uncwilly
6809 > 6502

"""""""""""""""""""
Aug 2003
101×103 Posts

948910 Posts

Quote:
 Originally Posted by frmky 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.

 2010-03-10, 19:03 #8 sean     Aug 2004 New Zealand 2·3·37 Posts Not that it is needed, but one more factor for the 46th stage: Code: 46 127.6069700067.56020785082237742556947.c215
2010-03-10, 19:06   #9
CRGreathouse

Aug 2006

32·5·7·19 Posts

Quote:
 Originally Posted by Uncwilly 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).

 2010-03-10, 19:20 #10 kar_bon     Mar 2006 Germany 288110 Posts intersting sequence, and a quick summary here!
2010-03-10, 19:46   #11
kar_bon

Mar 2006
Germany

43×67 Posts

Quote:
 Originally Posted by frmky 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