M20004713 Mersenne number exponent details

Residue

Status

L-L

C28A4188D43771DC

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	2⁷³	95.6197	65.7534%	350000	6500000	0.6429	3.0235%	96.2626	66.7889%	1.0354%
PrimeNet	2⁶⁵	0.3647	61.5385%	90000	3200000	0.2435	4.9971%	0.6082	63.4604%	1.9220%
GPU72	2⁶⁹	5.9679	63.7681%	140000	4000000	0.3288	3.6276%	6.2967	65.0825%	1.3144%
Difference	+4	+89.6518	+1.9853%	+210000	+2500000	+0.3142	-0.6041%	+89.9659	+1.7064%	+1.7064%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷³

95.6197

65.7534%

350000

6500000

0.6429

3.0235%

96.2626

66.7889%

1.0354%

PrimeNet

2⁶⁵

0.3647

61.5385%

90000

3200000

0.2435

4.9971%

0.6082

63.4604%

1.9220%

GPU72

2⁶⁹

5.9679

63.7681%

140000

4000000

0.3288

3.6276%

6.2967

65.0825%

1.3144%

Difference

+89.6518

+1.9853%

+210000

+2500000

+0.3142

-0.6041%

+89.9659

+1.7064%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
20004713	34179547974603656038886273	26	84.821	854287386542452672 2⁶ × 13348240414725823	2022-01-14	64	13348240414725823	315,051	682,502,948	1.275e+9

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

20004713

34179547974603656038886273

84.821

854287386542452672
2⁶ × 13348240414725823

2022-01-14

13348240414725823

315,051

682,502,948

1.275e+9

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-12-31T00:00:00	ANONYMOUS	v4_computers	300000	300000		-		-	-	0.282	-	-	1.103%
2019-06-16T13:02:43	mognuts	Strand	190000	3372500	6	-		-	-	0.341	-	-	2.359%
2019-06-30T05:33:44	ixfd64	dchia-mobl	350000	6500000	12	-		-	-	0.643	-	-	3.023%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2022-01-14T17:44:58	ATH	ec2-P_1	1000000	1000000	2	7	34179547974603656038886273	P+1	26	84.821	1.427

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-12-31T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁶		-	-	0.738	-	-
2011-07-13T06:48:00	Xyzzy	Manual testing	2⁶⁶	2⁶⁷		-	-	0.747	-	-
2016-01-13T17:55:10	mikr	Manual testing	2⁶⁷	2⁶⁸		-	-	1.494	-	-
2016-01-13T17:55:10	mikr	Manual testing	2⁶⁸	2⁶⁹		-	-	2.988	-	-
2017-03-13T22:59:49	ramgeis	Manual testing	2⁶⁹	2⁷⁰		-	-	5.977	-	-
2019-01-14T07:09:04	slaur	Manual testing	2⁷⁰	2⁷¹		-	-	11.95	-	-
2021-05-24T11:02:57	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	23.91	-	-
2021-05-24T11:02:57	-Anonymous-	Manual testing	2⁷²	2⁷³		-	-	47.81	-	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2004-06-12T00:00:00	stephenson	v4_computers	C28A4188D43771DC	12.95
2007-10-29T00:00:00	ANONYMOUS	v4_computers	C28A4188D43771DC	12.95

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 = 1000000 (P+1 stage 1)

B1 = 350000, B2 = 6500000 (P-1 stage 2)

B1 = 190000, B2 = 3372500 (P-1 stage 2)

B1 = 350000 (P-1 stage 1)

B1 = 300000 (P-1 stage 1)

B1 = 190000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

TF factor-bounds graph:

2⁷³

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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