M9758857 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

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	3.0448	64.1791%	7000000	27210573390	629.7761	18.4068%	632.8209	70.7726%	6.5935%
PrimeNet	2⁶⁴	0.3647	62.5000%	40000	1100000	0.0413	3.5152%	0.4061	63.8182%	1.3182%
GPU72	2⁶⁸	6.1078	64.7059%	65000	1500000	0.0606	2.5580%	6.1683	65.6087%	0.9028%
Difference	-1	-3.0630	-0.5268%	+6935000	+27209073390	+629.7155	+15.8487%	+626.6526	+5.1638%	+5.1638%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

3.0448

64.1791%

7000000

27210573390

629.7761

18.4068%

632.8209

70.7726%

6.5935%

PrimeNet

2⁶⁴

0.3647

62.5000%

40000

1100000

0.0413

3.5152%

0.4061

63.8182%

1.3182%

GPU72

2⁶⁸

6.1078

64.7059%

65000

1500000

0.0606

2.5580%

6.1683

65.6087%

0.9028%

Difference

-1

-3.0630

-0.5268%

+6935000

+27209073390

+629.7155

+15.8487%

+626.6526

+5.1638%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
9758857	12074904587263441241	20	63.389	618663875660 2² × 5 × 107 × 289095269	1999-06-06	107	289095269	0.3238	6.6613	12.441
9758857	751591240766356025327959	24	79.314	38508159345216147 3² × 29 × 601 × 245492246927	2022-05-03	601	245492246927	18,322	5,656.6	10,565

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

9758857

12074904587263441241

63.389

618663875660
2² × 5 × 107 × 289095269

1999-06-06

107

289095269

0.3238

6.6613

12.441

9758857

751591240766356025327959

79.314

38508159345216147
3² × 29 × 601 × 245492246927

2022-05-03

601

245492246927

18,322

5,656.6

10,565

exponent	prime factors	composite factor	digits	bits*
9758857	12074904587263441241 751591240766356025327959	9075392520876693894699878930808157950957119	43	142.703

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-05-14T06:09:20	riccardo uberti	Xeon20C	7000000	27210573390		-	skipped known factor: 12074904587263441241	-	-	629.8	-	-	18.407%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2022-04-27T17:37:04	riccardo uberti	Colab_noGPU15	2000000	50000000	2	7			-	-	2.370
2022-05-03T17:09:22	riccardo uberti	Colab_noGPU15	2300000	60000000	6	5	751591240766356025327959	P+1	24	79.314	2.781

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-06-06T00:00:00	ANONYMOUS	v4_computers	?	?	12074904587263441241	63.389	20	0.160	5.789	0.326

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.584 GHz-days
Estimated T-Level:	0.500

Digits	B1	Curves	Complete	FacMiss
20	11000	10 / 100	0.100	90.438%
25	50000	10 / 280	0.036	96.485%

New Calculation Method

Total ECM effort:	8.584 GHz-days
Estimated T-Level:	0.500

Digits	B1	Complete	FacMiss
20	11000	0.435	64.741%
25	50000	0.040	96.125%
30	250000	0.003	99.748%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	14400000		10	8.584

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2021-01-01T15:48:51	riccardo uberti	Colab_noGPU7	50000	14400000						10	8.584

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-10-22T20:20:22

mnd9

f3b

12074904587263441241

B3D8D3D92B380C__

2020-12-29T18:17:19

kutens

hadar

12074904587263441241

B3D8D3D92B380C1B

2022-05-04T03:34:16

riccardo uberti

Nomad2C

12074904587263441241

751591240766356025327959

B3D8D3D92B380C1B

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 = 7000000, B2 = 27210573390 (P-1 stage 2)

B1 = 7000000 (P-1 stage 1)

B1 = 2300000, B2 = 60000000 (P+1 stage 2)

B1 = 2300000 (P+1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

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