New factor for F17

Buckle · 2011-03-15, 00:58

Found a new factor for F17

using prime95

[Mon Mar 14 15:03:04 2011]
ECM found a factor in curve #3, stage #2
Sigma=10717701036773, B1=44000000, B2=4400000000.
UID: Buckle/G826, F17 has a factor: 7751061099802522589358967058392886922693580423169, AID: ECC0BE7A98422FA33606BA70798F5D21

whats the best way to check co-factor status?

ixfd64 · 2011-03-15, 01:14

Congratulations. :D

The fastest method for checking the cofactor is probably a Fermat PRP test. If it does turn out to be a probable prime, then we'll need a (slower) deterministic in order to know that it's actually prime. The fastest known deterministic algorithm is ECPP; unfortunately, at around 39,000 digits, such a number would be currently beyond what ECPP can do in a reasonable amount of time.

On the other hand, maybe you'll be the lucky discoverer of a Mersenne prime soon!

ATH · 2011-03-15, 01:20

Congratulations on another Fermat factor!

You can do a Fermat PRP test with Prime95. Add this to worktodo.txt:

PRP=1,2,131072,1,"31065037602817,7751061099802522589358967058392886922693580423169"

This means it checks 1*2^131073+1 = 2^(2^17)+1 and divides by the known factor 31065037602817 from here: http://www.prothsearch.net/fermat.html and your new factor.

R.D. Silverman · 2011-03-15, 01:22

Quote:

Originally Posted by Buckle

Found a new factor for F17

using prime95

[Mon Mar 14 15:03:04 2011]
ECM found a factor in curve #3, stage #2
Sigma=10717701036773, B1=44000000, B2=4400000000.
UID: Buckle/G826, F17 has a factor: 7751061099802522589358967058392886922693580423169, AID: ECC0BE7A98422FA33606BA70798F5D21

whats the best way to check co-factor status?

It is only ~39K digits. Just do M-R.

warut · 2011-03-15, 01:35

Congratulations!

I've added the factor to FactorDB. Can't wait to see if the cofactor is composite or not.

ixfd64 · 2011-03-15, 01:41

Assuming I did this correctly:

Quote:

[Mon Mar 14 18:41:12 2011]
UID: ixfd64/dannchia-ws, F17/known_factors is not prime. RES64: 6EF4AD31682CD751. We4: 5530F24D,00000000
Known factors used for PRP test were: 31065037602817,7751061099802522589358967058392886922693580423169

ATH · 2011-03-15, 01:42

Group order is:

[ <2, 2>, <3, 1>, <541, 1>, <2713, 1>, <5153, 1>, <23773, 1>, <152363, 1>,
<239387, 1>, <19359383, 1>, <22095751, 1>, <230254627, 1> ]

calculation stolen from here: http://www.mersenneforum.org/showpos...0&postcount=69

Factor would have been found with a much smaller B2.

ATH · 2011-03-15, 01:58

p-1 = 2^19 * 229 * 9920257 * 49765687 * 860444447189 * 151977745250209
p+1 = 2 * 3^2 * 5 * 7 * 43003 * 286102634397324165621481818300343273307753

P-1 would have required B1=10¹² and B2=2*10¹⁴ to find the factor. Not *totally* unrealistic but would have taken a very long time on a 39444 digit number.

TimSorbet · 2011-03-15, 02:13

Quote:

Originally Posted by ixfd64

Assuming I did this correctly:

Confirmed with PFGW:

Code:

PFGW Version 3.4.4.32BIT.20101104.Win_Dev [GWNUM 26.4]

Generic modular reduction using generic reduction Core2 type-1 FFT length 16K, Pass1=64, Pass2=256 on A 130865-bit number
(2^(2^17)+1)/31065037602817/7751061099802522589358967058392886922693580423169 is composite: RES64: [6EF4AD31682CD751] (95.3671s+0.0139s)

Done.

Prime95 · 2011-03-15, 02:33

Congratulations! Your hard work has paid off again.

ATH · 2011-03-15, 02:39

The last 2 years have been very nice for Fermat ECM factors:

Jul 18th 2009: F19: Buckle (David Bessell). GIMPS' 1st: http://www.mersenneforum.org/showthread.php?t=12168
Feb 2nd 2010: F14: Tapio Rajala. GIMPS' 2nd: http://www.mersenneforum.org/showthread.php?t=13051
Mar 26th 2010: F22: Buckle (David Bessell). GIMPS' 3rd: http://www.mersenneforum.org/showthread.php?t=13209
Mar 27th 2010: F12: Xyzzy. GMP-ECM: http://www.mersenneforum.org/showthread.php?t=13215
Mar 14th 2011: F17: Buckle (David Bessell). GIMPS' 4th.

I'm wondering why Buckle only have 2 success listed: http://www.mersenne.org/report_top_5...&B1=Get+Report

2011-03-15, 00:58	#1
Buckle Jul 2009 Hobart, Australia 11 Posts	New factor for F17 Found a new factor for F17 using prime95 [Mon Mar 14 15:03:04 2011] ECM found a factor in curve #3, stage #2 Sigma=10717701036773, B1=44000000, B2=4400000000. UID: Buckle/G826, F17 has a factor: 7751061099802522589358967058392886922693580423169, AID: ECC0BE7A98422FA33606BA70798F5D21 whats the best way to check co-factor status?

2011-03-15, 02:39	#11
ATH Einyen Dec 2003 Denmark 2·17·101 Posts	The last 2 years have been very nice for Fermat ECM factors: Jul 18th 2009: F19: Buckle (David Bessell). GIMPS' 1st: http://www.mersenneforum.org/showthread.php?t=12168 Feb 2nd 2010: F14: Tapio Rajala. GIMPS' 2nd: http://www.mersenneforum.org/showthread.php?t=13051 Mar 26th 2010: F22: Buckle (David Bessell). GIMPS' 3rd: http://www.mersenneforum.org/showthread.php?t=13209 Mar 27th 2010: F12: Xyzzy. GMP-ECM: http://www.mersenneforum.org/showthread.php?t=13215 Mar 14th 2011: F17: Buckle (David Bessell). GIMPS' 4th. I'm wondering why Buckle only have 2 success listed: http://www.mersenne.org/report_top_5...&B1=Get+Report Last fiddled with by ATH on 2011-03-15 at 02:40

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2011-03-15, 01:14	#2
ixfd64 Bemusing Prompter "Danny" Dec 2002 California 2·29·43 Posts	Congratulations. :D The fastest method for checking the cofactor is probably a Fermat PRP test. If it does turn out to be a probable prime, then we'll need a (slower) deterministic in order to know that it's actually prime. The fastest known deterministic algorithm is ECPP; unfortunately, at around 39,000 digits, such a number would be currently beyond what ECPP can do in a reasonable amount of time. On the other hand, maybe you'll be the lucky discoverer of a Mersenne prime soon! Last fiddled with by ixfd64 on 2019-10-18 at 20:46

2011-03-15, 01:20	#3
ATH Einyen Dec 2003 Denmark 6552₈ Posts	Congratulations on another Fermat factor! You can do a Fermat PRP test with Prime95. Add this to worktodo.txt: PRP=1,2,131072,1,"31065037602817,7751061099802522589358967058392886922693580423169" This means it checks 1*2^131073+1 = 2^(2^17)+1 and divides by the known factor 31065037602817 from here: http://www.prothsearch.net/fermat.html and your new factor.

2011-03-15, 01:35	#5
warut Dec 2009 89 Posts	Congratulations! I've added the factor to FactorDB. Can't wait to see if the cofactor is composite or not.

2011-03-15, 01:42	#7
ATH Einyen Dec 2003 Denmark 2×17×101 Posts	Group order is: [ <2, 2>, <3, 1>, <541, 1>, <2713, 1>, <5153, 1>, <23773, 1>, <152363, 1>, <239387, 1>, <19359383, 1>, <22095751, 1>, <230254627, 1> ] calculation stolen from here: http://www.mersenneforum.org/showpos...0&postcount=69 Factor would have been found with a much smaller B2.

2011-03-15, 01:58	#8
ATH Einyen Dec 2003 Denmark D6A₁₆ Posts	p-1 = 2^19 * 229 * 9920257 * 49765687 * 860444447189 * 151977745250209 p+1 = 2 * 3^2 * 5 * 7 * 43003 * 286102634397324165621481818300343273307753 P-1 would have required B1=10¹² and B2=210¹⁴ to find the factor. Not totally* unrealistic but would have taken a very long time on a 39444 digit number.

2011-03-15, 02:33	#10
Prime95 P90 years forever! Aug 2002 Yeehaw, FL 8151₁₀ Posts	Congratulations! Your hard work has paid off again.