M3052591 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

7055D313E6CC2576

verified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	19.5260	67.6471%	3000000	100000000	1.0224	8.0357%	20.5484	70.2468%	2.5998%
PrimeNet	2⁶⁰	0.0503	63.3333%	12000	220000	0.0029	2.5232%	0.0532	64.2585%	0.9252%
GPU72	2⁶⁴	1.1660	65.6250%	14000	220000	0.0031	1.4652%	1.1691	66.1287%	0.5037%
Difference	+4	+18.3600	+2.0221%	+2986000	+99780000	+1.0193	+6.5705%	+19.3793	+4.1182%	+4.1182%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

19.5260

67.6471%

3000000

100000000

1.0224

8.0357%

20.5484

70.2468%

2.5998%

PrimeNet

2⁶⁰

0.0503

63.3333%

12000

220000

0.0029

2.5232%

0.0532

64.2585%

0.9252%

GPU72

2⁶⁴

1.1660

65.6250%

14000

220000

0.0031

1.4652%

1.1691

66.1287%

0.5037%

Difference

+18.3600

+2.0221%

+2986000

+99780000

+1.0193

+6.5705%

+19.3793

+4.1182%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3052591	4098519672935698192087	22	71.796	671318180675973 3² × 607 × 122884528771	2020-12-20	607	122884528771	200.46	826.25	1,543.2

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3052591

4098519672935698192087

71.796

671318180675973
3² × 607 × 122884528771

2020-12-20

607

122884528771

200.46

826.25

1,543.2

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-02-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.249%
2010-10-05T09:11:00	markr	tiny	110000	2447500		-		-	-	0.029	-	-	2.665%
2016-03-17T20:53:18	Squeeky_Squirrel	P4_2600	205000	5688750	12	-		-	-	0.062	-	-	3.572%
2017-10-06T07:40:19	mikr	MSI	3000000	100000000	12	-		-	-	1.022	-	-	8.036%
2021-01-14T13:16:35	Jocelyn Larouche	Manual testing	305259	305259		-		-	-	0.038	-	-	1.535%
2021-01-16T17:21:45	Jocelyn Larouche	Manual testing	305259	3052591	6	-		-	-	0.056	-	-	3.288%
2022-01-23T08:35:02	Jocelyn Larouche	Manual testing	1055258	119912100		-		-	-	0.929	-	-	7.513%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-06-03T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.050	-	-
2009-02-13T20:04:00	Sturle Sunde	gouffy.ifi	2⁶⁰	2⁶¹		-	-	0.050	-	-
2011-03-22T01:52:00	Sid & Andy	Buzz	2⁶¹	2⁶²		-	-	0.101	-	-
2013-01-07T13:54:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.322	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.643	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.224	-	-
2015-06-06T19:31:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.448	-	-
2017-05-07T02:13:05	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.896	-	-
2018-07-28T13:20:23	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	9.79	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.193 GHz-days
Estimated T-Level:	1.800

Digits	B1	Curves	Complete	FacMiss
20	11000	36 / 100	0.360	69.641%
25	50000	36 / 280	0.129	87.915%

New Calculation Method

Total ECM effort:	4.193 GHz-days
Estimated T-Level:	1.800

Digits	B1	Complete	FacMiss
20	11000	1.161	31.308%
25	50000	0.105	90.036%
30	250000	0.006	99.356%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		29	3.378
50000	5000000	4098519672935698192087	7	0.815

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-02T03:04:00	borkencode	CFF2DC1CD	50000	5000000						3	0.349
2011-06-17T06:37:00	sannerud.com	JimEmcLW7	50000	5000000						3	0.349
2013-10-17T13:18:00	timc995	ec2_win	50000	5000000						3	0.349
2016-01-31T20:01:17	Bruce	Desk7	50000	5000000						3	0.349
2017-09-07T19:28:08	driveByUpgrades	AMD8	50000	5000000						3	0.349
2020-10-14T21:43:37	daveward2005	Dave2	50000	5000000						7	0.815
2020-11-12T17:05:06	Zenzoma	i7-6820HQ	50000	5000000						7	0.815
2020-12-20T09:14:10	daveward2005	Dave2	50000	5000000	4098519672935698192087	71.796	7	2	3213731800308833	7	0.815

date	userid	compid	res64	spent (GHz-days)
1999-05-16T00:00:00	ANONYMOUS	v4_computers	3ED7A11CE84B99__	0.260

date

userid

compid

res64

spent (GHz-days)

1999-05-16T00:00:00

ANONYMOUS

v4_computers

3ED7A11CE84B99__

0.260

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 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 1055258, B2 = 119912100 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 1055258 (P-1 stage 1)

B1 = 205000, B2 = 5688750 (P-1 stage 2)

B1 = 305259, B2 = 3052591 (P-1 stage 2)

B1 = 305259 (P-1 stage 1)

B1 = 110000, B2 = 2447500 (P-1 stage 2)

B1 = 205000 (P-1 stage 1)

B1 = 110000 (P-1 stage 1)

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

B1 = 2048 (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