M3501041 Mersenne number exponent details

Residue

Status

L-L

2EDF2268ADE8D389

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	2⁷²	273.1569	69.4444%	4000000	150000000	1.8206	6.4108%	274.9775	71.4033%	1.9588%
PrimeNet	2⁶⁰	0.0439	63.3333%	15000	300000	0.0046	2.9606%	0.0485	64.4189%	1.0856%
GPU72	2⁶⁴	1.0166	65.6250%	20000	360000	0.0059	1.9155%	1.0225	66.2835%	0.6585%
Difference	+8	+272.1403	+3.8194%	+3980000	+149640000	+1.8147	+4.4953%	+273.9550	+5.1198%	+5.1198%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷²

273.1569

69.4444%

4000000

150000000

1.8206

6.4108%

274.9775

71.4033%

1.9588%

PrimeNet

2⁶⁰

0.0439

63.3333%

15000

300000

0.0046

2.9606%

0.0485

64.4189%

1.0856%

GPU72

2⁶⁴

1.0166

65.6250%

20000

360000

0.0059

1.9155%

1.0225

66.2835%

0.6585%

Difference

+272.1403

+3.8194%

+3980000

+149640000

+1.8147

+4.4953%

+273.9550

+5.1198%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-03T21:43:00	Carsten Kossendey	leela	20000	240000		-		-	-	0.005	-	-	0.510%
2011-11-03T12:10:00	markr	tiny	235000	5875000		-		-	-	0.083	-	-	2.424%
2021-08-20T01:00:51	mikr	MSI	4000000	150000000	12	-		-	-	1.821	-	-	6.411%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2021-08-24T18:02:36	ArtyomP	axioo	50000	2500000	2	7			-	-	0.032
2021-08-24T18:21:21	ArtyomP	axioo	50000	2500000	6	5			-	-	0.032

date

userid

compid

start

factor

Smooth

digits

bits*

ghz-days

2021-08-24T18:02:36

ArtyomP

axioo

50000

2500000

0.032

2021-08-24T18:21:21

ArtyomP

axioo

50000

2500000

0.032

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:31	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.044	-	-
2009-02-19T05:52:00	Jayson King	atlas	2⁶⁰	2⁶¹		-	-	0.044	-	-
2011-07-19T04:01:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.088	-	-
2012-06-20T01:18:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.456	-	-
2016-02-23T16:29:31	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.280	-	-
2015-01-25T20:43:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.561	-	-
2015-01-25T20:43:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.067	-	-
2016-03-04T00:01:28	omylist	Manual testing	2⁶⁵	2⁶⁶		-	-	2.134	-	-
2017-01-07T17:26:11	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.269	-	-
2018-12-17T13:21:51	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.538	-	-
2021-01-14T15:38:14	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	17.08	-	-
2021-03-17T11:32:49	-Anonymous-	Manual testing	2⁶⁹	2⁷⁰		-	-	34.15	-	-
2021-03-17T11:32:49	-Anonymous-	Manual testing	2⁷⁰	2⁷¹		-	-	68.30	-	-
2021-03-19T11:33:30	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	136.6	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.731 GHz-days
Estimated T-Level:	2.850

Digits	B1	Curves	Complete	FacMiss
20	11000	57 / 100	0.570	56.391%
25	50000	57 / 280	0.204	81.551%

New Calculation Method

Total ECM effort:	8.731 GHz-days
Estimated T-Level:	2.850

Digits	B1	Complete	FacMiss
20	11000	2.237	10.676%
25	50000	0.207	81.312%
30	250000	0.013	98.701%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	43	6.339
50000	6692405	7	1.191
50000	6800000	7	1.201

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-08T00:03:00	Smurgs	Praca	50000	5000000						3	0.442
2012-03-13T07:49:00	Smurgs	Praca	50000	5000000						3	0.442
2015-05-21T22:49:00	WileECoyote	Beaker	50000	5000000						3	0.442
2017-02-03T08:44:43	Lelikoid	QH	50000	5000000						3	0.442
2019-07-23T05:51:14	furkell	furkell1	50000	5000000						3	0.442
2021-04-25T16:13:22	daveward2005	Dave2	50000	5000000						7	1.032
2021-06-15T16:05:44	daveward2005	d12436	50000	5000000						7	1.032
2021-07-26T06:13:36	kutens	arcturus	50000	6800000						7	1.201
2021-10-15T11:22:28	Kamil Mudrunka	LinuxServer	50000	5000000						7	1.032
2022-01-19T14:00:52	GAN	KL-SCH09	50000	5000000						7	1.032
2022-05-05T18:49:47	Stef42	AMD-DESKTOP	50000	6692405						7	1.191

date	userid	compid	res64	spent (GHz-days)
1999-10-15T00:00:00	ANONYMOUS	v4_computers	2EDF2268ADE8D389	0.368

date

userid

compid

res64

spent (GHz-days)

1999-10-15T00:00:00

ANONYMOUS

v4_computers

2EDF2268ADE8D389

0.368

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 = 4000000, B2 = 150000000 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 235000, B2 = 5875000 (P-1 stage 2)

B1 = 235000 (P-1 stage 1)

B1 = 20000, B2 = 240000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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