Factoring EM47

rogue · 2010-03-09, 19:40

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.

sean · 2010-03-09, 19:52

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.

henryzz · 2010-03-09, 19:58

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?

10metreh · 2010-03-09, 20:03

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?

CRGreathouse · 2010-03-09, 21:39

I'm searching for factors of the c256 up to 45 digits (~9700 curves at 11M, simultaneous with 4700 at 3M).

frmky · 2010-03-09, 22:04

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.

Uncwilly · 2010-03-10, 05:44

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.

sean · 2010-03-10, 19:03

Not that it is needed, but one more factor for the 46th stage:

Code:

46 127.6069700067.56020785082237742556947.c215

CRGreathouse · 2010-03-10, 19:06

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).

kar_bon · 2010-03-10, 19:20

intersting sequence, and a quick summary here!

kar_bon · 2010-03-10, 19:46

Quote:

Originally Posted by frmky

Interesting credit for the large term.

ok, was a quick shot!

perhaps 'NFS@Home' better?

PS: edited!

2010-03-09, 20:03	#4
10metreh Nov 2008 100100010010₂ 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 3·1,987 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

2010-03-10, 19:03	#8
sean Aug 2004 New Zealand 13·17 Posts	Not that it is needed, but one more factor for the 46th stage: Code: 46 127.6069700067.56020785082237742556947.c215

2010-03-10, 19:20	#10
kar_bon Mar 2006 Germany B32₁₆ Posts	intersting sequence, and a quick summary here!