M2890637 Mersenne number exponent details

Residue

Status

L-L

71872F5E4B4EB176

double-checked

PRP

8DAEFBD5F936B56F

verified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	20.6200	67.6471%	5000000	200000000	1.7498	9.1853%	22.3698	70.6188%	2.9717%
PrimeNet	2⁵⁹	0.0266	62.7119%	13000	240000	0.0028	3.0004%	0.0294	63.8307%	1.1188%
GPU72	2⁶³	0.5521	65.0794%	16000	300000	0.0035	1.9078%	0.5557	65.7456%	0.6662%
Difference	+5	+20.0678	+2.5677%	+4984000	+199700000	+1.7463	+7.2775%	+21.8141	+4.8732%	+4.8732%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

20.6200

67.6471%

5000000

200000000

1.7498

9.1853%

22.3698

70.6188%

2.9717%

PrimeNet

2⁵⁹

0.0266

62.7119%

13000

240000

0.0028

3.0004%

0.0294

63.8307%

1.1188%

GPU72

2⁶³

0.5521

65.0794%

16000

300000

0.0035

1.9078%

0.5557

65.7456%

0.6662%

Difference

+20.0678

+2.5677%

+4984000

+199700000

+1.7463

+7.2775%

+21.8141

+4.8732%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2890637	10813965297545245969631	23	73.195	1870515961973995 5 × 7 × 3203 × 16685392819	2020-08-21	3203	16685392819	1,228.3	101.81	190.15

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2890637

10813965297545245969631

73.195

1870515961973995
5 × 7 × 3203 × 16685392819

2020-08-21

3203

16685392819

1,228.3

101.81

190.15

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-12-02T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.245%
2016-10-27T15:25:31	Jocelyn Larouche	low 4M	172800	172800		-		-	-	0.019	-	-	1.146%
2016-12-14T18:29:38	Jocelyn Larouche	low 4M	248832	248832		-		-	-	0.028	-	-	1.379%
2017-03-03T01:10:45	Jocelyn Larouche	low 4M	298598	2985980	6	-		-	-	0.050	-	-	3.238%
2017-10-18T00:38:01	Jocelyn Larouche	low 4M	597196	5971960	6	-		-	-	0.100	-	-	4.107%
2019-10-23T17:07:28	masser	Manual testing	2900000	29000000	12	-		-	-	0.484	-	-	6.443%
2020-02-11T03:26:37	masser	Manual testing	5000000	200000000	12	-		-	-	1.750	-	-	9.185%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:24	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.053	-	-
2009-02-14T07:22:00	Sturle Sunde	korsmo.ifi	2⁶⁰	2⁶¹		-	-	0.053	-	-
2012-01-16T17:29:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.106	-	-
2013-01-07T13:47:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.340	-	-
2015-04-21T09:21:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.679	-	-
2015-04-21T09:21:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.293	-	-
2015-11-28T11:39:31	omylist	Manual testing	2⁶⁵	2⁶⁶		-	-	2.585	-	-
2017-11-16T23:14:59	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.170	-	-
2019-01-12T08:34:57	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.34	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.932 GHz-days
Estimated T-Level:	1.400

Digits	B1	Curves	Complete	FacMiss
20	11000	28 / 100	0.280	75.472%
25	50000	28 / 280	0.100	90.468%

New Calculation Method

Total ECM effort:	2.932 GHz-days
Estimated T-Level:	1.400

Digits	B1	Complete	FacMiss
20	11000	0.903	40.526%
25	50000	0.082	92.161%
30	250000	0.005	99.499%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		21	2.199
50000	5000000	10813965297545245969631	7	0.733

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-29T12:36:00	Lukasz Wrobel	LINUX_01	50000	5000000						3	0.314
2011-02-20T19:08:00	Bdot	eisbaer	50000	5000000						3	0.314
2013-05-11T18:31:00	driveByUpgrades	Build_4	50000	5000000						3	0.314
2015-12-18T10:34:24	Bruce	Desk7	50000	5000000						3	0.314
2016-09-15T05:21:44	Bruce	test	50000	5000000						3	0.314
2019-06-21T00:25:08	Idgo	Pentium_Desktop	50000	5000000						3	0.314
2020-08-09T07:31:24	GAN	LMS-02	50000	5000000						3	0.314
2020-08-21T00:53:27	GAN	KL-10	50000	5000000	10813965297545245969631	73.195	7	2		7	0.733

date	userid	compid	res64	spent (GHz-days)
1999-10-21T00:00:00	ANONYMOUS	v4_computers	71872F5E4B4EB176	0.223
2018-09-27T14:22:57	kkmrkkblmbrbk	old	71872F5E4B4EB176	0.223

date

userid

compid

res64

spent (GHz-days)

1999-10-21T00:00:00

ANONYMOUS

v4_computers

71872F5E4B4EB176

0.223

2018-09-27T14:22:57

kkmrkkblmbrbk

old

71872F5E4B4EB176

0.223

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 5000000, B2 = 200000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 2900000, B2 = 29000000 (P-1 stage 2)

B1 = 2900000 (P-1 stage 1)

B1 = 597196, B2 = 5971960 (P-1 stage 2)

B1 = 597196 (P-1 stage 1)

B1 = 298598, B2 = 2985980 (P-1 stage 2)

B1 = 298598 (P-1 stage 1)

B1 = 248832 (P-1 stage 1)

B1 = 172800 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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