M41 681 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

-unknown-

-unknown-

Cofactor is a certified prime

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	712.8888	76.1194%	-	-	-	-	712.8888	76.1194%
Target	2⁴⁴	0.0001	63.6364%	500	50000	0.0000	1.9357%	0.0001	64.3402%
Difference	+23	+712.8887	+12.4830%	-500	-50000	0.0000	-1.9357%	+712.8887	+11.7792%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

2⁶⁷

712.8888

76.1194%

712.8888

76.1194%

Target

2⁴⁴

0.0001

63.6364%

500

50000

0.0000

1.9357%

0.0001

64.3402%

Difference

+23

+712.8887

+12.4830%

-500

-50000

0.0000

-1.9357%

+712.8887

+11.7792%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
41681	1052945423	10	29.972	12631 17 × 743	-	17	743	2.975e-9	5.854e-8	7.812e-8
41681	16647332713153	14	43.920	199699296 2⁵ × 3 × 2080201	2008-08-26	32	2080201	5.499e-5	0.0001	0.0002
41681	2853686272534246492102086015457	31	101.171	34232459304410240782395888 2⁴ × 3² × 349 × 681161638499089477523	2015-04-26	349	681161638499089477523	3.496e+12	3.842e+10	7.175e+10
41681	hide decimal representation P12495 click to show decimal representation	12,495	41,505.937		2015-04-26

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

41681

1052945423

29.972

12631
17 × 743

743

2.975e-9

5.854e-8

7.812e-8

41681

16647332713153

43.920

199699296
2⁵ × 3 × 2080201

2008-08-26

2080201

5.499e-5

0.0001

0.0002

41681

2853686272534246492102086015457

101.171

34232459304410240782395888
2⁴ × 3² × 349 × 681161638499089477523

2015-04-26

349

681161638499089477523

3.496e+12

3.842e+10

7.175e+10

41681

P12495

click to show decimal representation

12,495

41,505.937

2015-04-26

exponent	prime factors	composite factor	digits	bits*
41681	1052945423 16647332713153	17528732785472623248719	23	73.892
41681	1052945423 2853686272534246492102086015457	3004775899342865454612697118727755403311	40	131.142
41681	16647332713153 2853686272534246492102086015457	47506264837835009040474292373948758905205921	44	145.091
41681	1052945423 16647332713153 2853686272534246492102086015457	50021504124824209998331027904313150125767065389449 583	53	175.063

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-08-26	ANONYMOUS	Manual testing	?	?	16647332713153	43.920	14	2.68722e-5	6.05645e-5	5.46956e-5

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-08-26

ANONYMOUS

Manual testing

16647332713153

43.920

2.68722e-5

6.05645e-5

5.46956e-5

ECM factoring results:

Total ECM effort:	0.304 GHz-days
Estimated T-Level:	25.512

Digits	B1	Complete	FacMiss
20	11000	13.157	0.000%
25	50000	1.359	25.686%
30	250000	0.102	90.266%
35	1000000	0.006	99.376%

ECM Summary

B1	B2	factor	curves	GHz-days
		2853686272534246492102086015457	1	0.00000e+0
50000	5000000		283	0.211
250000	25000000		25	0.093

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-22	Matthias Wurtinger	WUR_E6600	50000	5000000						30	0.022
2010-04-27	James Hintz	09_122109	50000	5000000						11	0.008
2010-04-28	James Hintz	09_122109	50000	5000000						11	0.008
2010-04-28	James Hintz	09_122109	50000	5000000						11	0.008
2010-04-29	James Hintz	09_122109	50000	5000000						11	0.008
2010-04-29	James Hintz	09_122109	50000	5000000						11	0.008
2010-04-29	James Hintz	09_122109	50000	5000000						11	0.008
2010-04-30	James Hintz	09_122109	50000	5000000						11	0.008
2010-04-30	James Hintz	09_122109	50000	5000000						11	0.008
2010-04-30	James Hintz	09_122109	50000	5000000						11	0.008
2010-04-30	James Hintz	09_122109	50000	5000000						11	0.008
2010-05-01	James Hintz	09_122109	50000	5000000						11	0.008
2010-05-01	James Hintz	09_122109	50000	5000000						11	0.008
2010-05-01	James Hintz	09_122109	50000	5000000						11	0.008
2010-05-01	James Hintz	09_122109	50000	5000000						11	0.008
2010-05-02	James Hintz	09_122109	50000	5000000						11	0.008
2010-05-02	James Hintz	09_122109	50000	5000000						11	0.008
2010-05-02	James Hintz	09_122109	50000	5000000						11	0.008
2010-05-02	James Hintz	09_122109	50000	5000000						11	0.008
2010-05-03	James Hintz	09_122109	50000	5000000						11	0.008
2010-05-03	James Hintz	09_122109	50000	5000000						11	0.008
2010-05-03	James Hintz	09_122109	50000	5000000						11	0.008
2010-05-03	James Hintz	09_122109	50000	5000000						11	0.008
2010-05-04	James Hintz	09_122109	50000	5000000						11	0.008
2011-01-23	James Hintz	NEW_OMFG	250000	25000000						3	0.011
2011-02-19	James Hintz	17_051310	250000	25000000						11	0.041
2011-03-02	James Hintz	13_052010	250000	25000000						11	0.041
2015-04-26	Serge Batalov	Manual testing			2853686272534246492102086015457	101.171		1		1	-