M1080901 Mersenne number exponent details

Residue

Status

L-L

E13921E3903D741D

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	27.4900	68.6567%	300000	10000000	0.0356	4.1055%	27.5256	69.9435%	1.2868%
PrimeNet	2⁵⁶	0.0089	62.5000%	4500	65000	0.0003	2.0201%	0.0092	63.2575%	0.7575%
GPU72	2⁶⁰	0.1421	65.0000%	4500	20000	0.0002	0.6528%	0.1423	65.2285%	0.2285%
Difference	+7	+27.3479	+3.6567%	+295500	+9980000	+0.0354	+3.4527%	+27.3832	+4.7150%	+4.7150%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

27.4900

68.6567%

300000

10000000

0.0356

4.1055%

27.5256

69.9435%

1.2868%

PrimeNet

2⁵⁶

0.0089

62.5000%

4500

65000

0.0003

2.0201%

0.0092

63.2575%

0.7575%

GPU72

2⁶⁰

0.1421

65.0000%

4500

20000

0.0002

0.6528%

0.1423

65.2285%

0.2285%

Difference

+27.3479

+3.6567%

+295500

+9980000

+0.0354

+3.4527%

+27.3832

+4.7150%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1080901	4126069392637281017	19	61.839	1908625023308 2² × 477156255827	2008-03-17	4	477156255827	0.4028	1,117.2	2,086.7

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1080901

4126069392637281017

61.839

1908625023308
2² × 477156255827

2008-03-17

477156255827

0.4028

1,117.2

2,086.7

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-03-03T00:00:00	Jocelyn Larouche	v4_computers	15000	172500		-		-	-	0.001	-	-	0.707%
unknown			300000	10000000		-		-	-	0.036	-	-	4.105%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2001-11-24T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.018	-	-

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2001-11-24T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁷

0.018

-

-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.488 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	322 / 100	3.220	3.931%
25	50000	322 / 280	1.150	31.599%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	17.488 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	14.692	0.000%
25	50000	1.609	20.008%
30	250000	0.131	87.737%
35	1000000	0.009	99.133%

ECM Summary

B1	B2	factor	curves	GHz-days
		4126069392637281017	1	0.00000e+0
50000	5000000		278	9.76
250000	25000000		44	7.726

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-09-27T20:02:00	ANONYMOUS	banger	50000	5000000						1	0.035
2008-03-17T12:47:00	Team_Bundu	bundu3			4126069392637281017	61.839		1		1	-
2017-03-24T17:19:29	TJAOI	Manual testing	50000	5000000						136	4.776
2018-01-19T13:25:04	TJAOI	Manual testing	50000	5000000						141	4.951
2021-04-09T16:08:57	TJAOI	Manual testing	250000	25000000						44	7.726

date	userid	compid	res64	spent (GHz-days)
2002-03-16T00:00:00	ANONYMOUS	v4_computers	E13921E3903D741D	0.032

date

userid

compid

res64

spent (GHz-days)

2002-03-16T00:00:00

ANONYMOUS

v4_computers

E13921E3903D741D

0.032

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T23:40:31

Oliver Kruse

GTX-1

4126069392637281017

603F3F7A717E74__

2017-10-16T07:56:32

Oliver Kruse

Threadripper

4126069392637281017

603F3F7A717E74__

2018-01-02T09:18:15

ATH

ec2-1xf

4126069392637281017

603F3F7A717E74__

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 = 300000, B2 = 10000000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 15000, B2 = 172500 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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