M7144201 Mersenne number exponent details

Residue

Status

L-L

D794B4DB9850AAA8

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	4.1592	65.6716%	135000	2902500	0.0904	3.6337%	4.2495	66.9190%	1.2474%
PrimeNet	2⁶³	0.2234	63.4921%	30000	800000	0.0227	3.3245%	0.2462	64.7058%	1.2137%
GPU72	2⁶⁷	4.1592	65.6716%	45000	1000000	0.0307	2.3075%	4.1898	66.4638%	0.7921%
Difference	-	-	-	+90000	+1902500	+0.0597	+1.3262%	+0.0597	+0.4553%	+0.4553%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

4.1592

65.6716%

135000

2902500

0.0904

3.6337%

4.2495

66.9190%

1.2474%

PrimeNet

2⁶³

0.2234

63.4921%

30000

800000

0.0227

3.3245%

0.2462

64.7058%

1.2137%

GPU72

2⁶⁷

4.1592

65.6716%

45000

1000000

0.0307

2.3075%

4.1898

66.4638%

0.7921%

Difference

+90000

+1902500

+0.0597

+1.3262%

+0.0597

+0.4553%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
7144201	26095556534037047695753	23	74.466	1826345348768676 2² × 3 × 152195445730723	2017-10-11	4	152195445730723	977.87	2,621,778	4,896,751

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

7144201

26095556534037047695753

74.466

1826345348768676
2² × 3 × 152195445730723

2017-10-11

152195445730723

977.87

2,621,778

4,896,751

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-02-10T00:00:00	ANONYMOUS	v4_computers	35000	507500		-		-	-	0.019	-	-	1.824%
2011-12-22T07:19:00	James Heinrich	3930K	135000	2902500		-		-	-	0.090	-	-	3.634%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-06-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.086	-	-
2005-08-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.223	-	-
2014-02-02T23:30:00	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.275	-	-
2014-02-06T22:41:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.523	-	-
2015-06-21T19:54:00	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.046	-	-
2016-10-23T19:16:35	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.092	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.326 GHz-days
Estimated T-Level:	0.200

Digits	B1	Curves	Complete	FacMiss
20	11000	4 / 100	0.040	96.060%
25	50000	4 / 280	0.014	98.579%

New Calculation Method

Total ECM effort:	1.326 GHz-days
Estimated T-Level:	0.200

Digits	B1	Complete	FacMiss
20	11000	0.129	87.895%
25	50000	0.012	98.841%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.995
50000	5000000	26095556534037047695753	1	0.332

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2012-10-25T03:54:00	Donna Noble	i7-2600k	50000	5000000						3	0.995
2017-10-12T02:55:26	Bruce	Desk7	50000	5000000	26095556534037047695753	74.466	1	2		1	0.332

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-16T00:00:00	sssvs	v4_computers	D794B4DB9850AAA8	1.558
2002-02-24T00:00:00	ANONYMOUS	v4_computers	D794B4DB9850AAA8	1.558

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-02-14T21:17:48

Oliver Kruse

GTX-1

26095556534037047695753

2B60343B69E026__

2019-03-25T08:08:03

kkmrkkblmbrbk

c5.large

26095556534037047695753

2B60343B69E0263D

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 = 135000, B2 = 2902500 (P-1 stage 2)

B1 = 135000 (P-1 stage 1)

B1 = 35000, B2 = 507500 (P-1 stage 2)

B1 = 35000 (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

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