M2108941 Mersenne number exponent details

Residue

Status

L-L

62F39F389148A3C6

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	14.0895	67.1642%	500000	15000000	0.1230	5.1558%	14.2125	68.8571%	1.6930%
PrimeNet	2⁵⁸	0.0182	62.0690%	9000	160000	0.0016	2.6799%	0.0198	63.0855%	1.0165%
GPU72	2⁶²	0.2913	64.5161%	10000	140000	0.0016	1.4526%	0.2929	65.0316%	0.5154%
Difference	+5	+13.7982	+2.6481%	+490000	+14860000	+0.1214	+3.7033%	+13.9195	+3.8256%	+3.8256%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.0895

67.1642%

500000

15000000

0.1230

5.1558%

14.2125

68.8571%

1.6930%

PrimeNet

2⁵⁸

0.0182

62.0690%

9000

160000

0.0016

2.6799%

0.0198

63.0855%

1.0165%

GPU72

2⁶²

0.2913

64.5161%

10000

140000

0.0016

1.4526%

0.2929

65.0316%

0.5154%

Difference

+13.7982

+2.6481%

+490000

+14860000

+0.1214

+3.7033%

+13.9195

+3.8256%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2108941	62735783322089173993	20	65.766	14873764444356 2² × 3 × 683 × 1814758961	2008-12-13	683	1814758961	4.9136	9.4264	17.606

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2108941

62735783322089173993

65.766

14873764444356
2² × 3 × 683 × 1814758961

2008-12-13

683

1814758961

4.9136

9.4264

17.606

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.277%
2016-03-17T11:24:15	alpertron	Manual testing	500000	15000000	12	-		-	-	0.123	-	-	5.156%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-17T00:00:00	Ethan O'Connor	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.217 GHz-days
Estimated T-Level:	1.200

Digits	B1	Curves	Complete	FacMiss
20	11000	24 / 100	0.240	78.568%
25	50000	24 / 280	0.086	91.772%

New Calculation Method

Total ECM effort:	2.217 GHz-days
Estimated T-Level:	1.200

Digits	B1	Complete	FacMiss
20	11000	0.968	37.986%
25	50000	0.090	91.435%
30	250000	0.006	99.434%

ECM Summary

B1	B2	factor	curves	GHz-days
		62735783322089173993	1	0.00000e+0
50000	5000000		10	0.851
50000	6750000		7	0.681
50000	6823189		7	0.685

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-13T13:01:00	alan145	Bear4			62735783322089173993	65.766		1		1	-
2019-09-12T06:38:28	Ivan M	LAB	50000	5000000						3	0.255
2021-10-29T18:27:06	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.596
2022-03-17T06:12:25	Dylan Delgado	colab	50000	6750000						7	0.681
2022-06-15T23:49:06	debrouxl	dl380g9-1	50000	6823189						7	0.685

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-11-21T00:00:00	DL	v4_computers	62F39F389148A3C6	0.139
1999-02-07T00:00:00	Ethan O'Connor	v4_computers	62F39F389148A3C6	0.139

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-07T03:18:45

Oliver Kruse

GTX-2

62735783322089173993

0F595078646760__

2017-11-17T06:43:01

ATH

ec2-1xf

62735783322089173993

0F595078646760__

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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