M3052099 Mersenne number exponent details

Residue

Status

L-L

9FF0DD7F93AFA8AA

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	2⁶⁹	39.1163	68.1159%	1055209	119912100	0.9294	6.8898%	40.0457	70.3127%	2.1967%
PrimeNet	2⁶⁰	0.0503	63.3333%	12000	220000	0.0029	2.5231%	0.0532	64.2585%	0.9251%
GPU72	2⁶⁴	1.1662	65.6250%	14000	220000	0.0031	1.4651%	1.1693	66.1286%	0.5036%
Difference	+5	+37.9501	+2.4909%	+1041209	+119692100	+0.9263	+5.4246%	+38.8764	+4.1840%	+4.1840%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

39.1163

68.1159%

1055209

119912100

0.9294

6.8898%

40.0457

70.3127%

2.1967%

PrimeNet

2⁶⁰

0.0503

63.3333%

12000

220000

0.0029

2.5231%

0.0532

64.2585%

0.9251%

GPU72

2⁶⁴

1.1662

65.6250%

14000

220000

0.0031

1.4651%

1.1693

66.1286%

0.5036%

Difference

+37.9501

+2.4909%

+1041209

+119692100

+0.9263

+5.4246%

+38.8764

+4.1840%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3052099	15921087982182287926159	23	73.753	2608219455231021 3 × 2693 × 322839392899	2013-10-15	2693	322839392899	890.06	2,170.7	4,054.3

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3052099

15921087982182287926159

73.753

2608219455231021
3 × 2693 × 322839392899

2013-10-15

2693

322839392899

890.06

2,170.7

4,054.3

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	-	-	0.201%
2010-10-05T05:52:00	markr	tiny	110000	2447500		-		-	-	0.029	-	-	2.369%
2021-01-17T03:41:52	Jocelyn Larouche	Manual testing	305209	3052099	6	-		-	-	0.056	-	-	2.954%
2022-01-23T08:35:02	Jocelyn Larouche	Manual testing	1055209	119912100		-		-	-	0.929	-	-	6.890%

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	-	-
2009-02-13T17:20:00	Sturle Sunde	gouffy.ifi	2⁶⁰	2⁶¹		-	-	0.050	-	-
2011-03-21T11:28:00	Sid & Andy	Buzz	2⁶¹	2⁶²		-	-	0.101	-	-
2013-01-07T13:54:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.322	-	-
2022-03-12T10:02:53	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	0.643	-	-
2022-03-12T10:02:53	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	1.224	-	-
2022-03-12T10:02:53	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	2.448	-	-
2022-03-12T10:02:53	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	4.897	-	-
2021-05-17T16:57:23	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.79	-	-
2021-12-15T11:27:46	Jocelyn Larouche	Manual testing	2⁶⁸	2⁶⁹		-	-	19.59	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.699 GHz-days
Estimated T-Level:	0.300

Digits	B1	Curves	Complete	FacMiss
20	11000	6 / 100	0.060	94.148%
25	50000	6 / 280	0.021	97.876%

New Calculation Method

Total ECM effort:	0.699 GHz-days
Estimated T-Level:	0.300

Digits	B1	Complete	FacMiss
20	11000	0.194	82.403%
25	50000	0.017	98.266%
30	250000	0.001	99.892%

ECM Summary

B1	B2	factor	curves	GHz-days
		15921087982182287926159	1	0.00000e+0
50000	5000000		6	0.699

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-13T23:46:00	Adel El-Atawy	SRVRARC	50000	5000000						3	0.349
2011-06-13T13:13:00	iwray	lappy	50000	5000000						3	0.349
2013-10-15T20:21:00	Bruce	fx6840-21			15921087982182287926159	73.753		1		1	-

date	userid	compid	res64	spent (GHz-days)
1999-07-12T00:00:00	ANONYMOUS	v4_computers	9FF0DD7F93AFA8AA	0.260

date

userid

compid

res64

spent (GHz-days)

1999-07-12T00:00:00

ANONYMOUS

v4_computers

9FF0DD7F93AFA8AA

0.260

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-28T11:04:10

Oliver Kruse

GTX-0

15921087982182287926159

78ACFCA620AB88__

2017-12-11T00:57:48

kkmrkkblmbrbk

c4.xlarge

15921087982182287926159

78ACFCA620AB88__

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 = 1055209, B2 = 119912100 (P-1 stage 2)

B1 = 1055209 (P-1 stage 1)

B1 = 305209, B2 = 3052099 (P-1 stage 2)

B1 = 305209 (P-1 stage 1)

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

B1 = 110000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

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