M3454469 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

5F09A107E9610ECF

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	2⁶⁹	34.5601	68.1159%	1000000	126668850	1.1950	6.9956%	35.7551	70.3464%	2.2305%
PrimeNet	2⁶⁰	0.0445	63.3333%	15000	280000	0.0045	2.9021%	0.0489	64.3974%	1.0641%
GPU72	2⁶⁴	1.0304	65.6250%	19000	340000	0.0056	1.8552%	1.0359	66.2627%	0.6377%
Difference	+5	+33.5297	+2.4909%	+981000	+126328850	+1.1894	+5.1404%	+34.7192	+4.0837%	+4.0837%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

34.5601

68.1159%

1000000

126668850

1.1950

6.9956%

35.7551

70.3464%

2.2305%

PrimeNet

2⁶⁰

0.0445

63.3333%

15000

280000

0.0045

2.9021%

0.0489

64.3974%

1.0641%

GPU72

2⁶⁴

1.0304

65.6250%

19000

340000

0.0056

1.8552%

1.0359

66.2627%

0.6377%

Difference

+33.5297

+2.4909%

+981000

+126328850

+1.1894

+5.1404%

+34.7192

+4.0837%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3454469	15220221974473313369191	23	73.688	2202975620055255 3 × 5 × 37 × 59 × 73 × 921598663	2021-05-20	73	921598663	836.02	7.6467	14.282

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3454469

15220221974473313369191

73.688

2202975620055255
3 × 5 × 37 × 59 × 73 × 921598663

2021-05-20

921598663

836.02

7.6467

14.282

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-08-16T02:22:00	Carsten Kossendey	durandal	20000	235000		-		-	-	0.005	-	-	0.806%
2011-11-06T04:32:00	harlee	P4_2600	60000	990000		-		-	-	0.017	-	-	1.687%
2014-08-21T21:46:00	Jocelyn Larouche	Manual testing	78580	78580		-		-	-	0.012	-	-	0.653%
2014-09-21T05:57:00	HBendtz	HAL9007	500000	10000000		-		-	-	0.155	-	-	4.163%
2022-04-10T23:56:34	Jocelyn Larouche	Manual testing	1000000	126668850		-		-	-	1.195	-	-	6.996%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-03-22T09:53:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.044	-	-
2011-07-31T08:42:00	markr	Manual testing	2¹	2⁶²		-	-	0.178	-	-
2012-08-18T15:34:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.462	-	-
2016-02-23T16:29:30	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.284	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.568	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.082	-	-
2015-04-17T12:32:00	Gordon Spence	Manual testing	2⁶⁵	2⁶⁶		-	-	2.163	-	-
2017-02-09T04:36:22	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.326	-	-
2019-02-11T13:34:47	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.653	-	-
2021-01-05T14:21:13	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	17.31	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.529 GHz-days
Estimated T-Level:	1.200

Digits	B1	Curves	Complete	FacMiss
20	11000	24 / 100	0.240	78.568%
25	50000	24 / 280	0.086	91.772%

New Calculation Method

Total ECM effort:	3.529 GHz-days
Estimated T-Level:	1.200

Digits	B1	Complete	FacMiss
20	11000	0.774	46.108%
25	50000	0.070	93.242%
30	250000	0.004	99.570%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		22	3.235
50000	5000000	15220221974473313369191	2	0.294

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-21T21:33:00	Aca Arsov	backo6400	50000	5000000						3	0.441
2012-02-07T05:22:00	CuBr	H0E2035EE	50000	5000000						3	0.441
2015-02-17T10:42:00	joe b.	Pandora	50000	5000000						3	0.441
2016-12-19T05:26:18	ANONYMOUS	q9550	50000	5000000						3	0.441
2019-06-09T11:57:16	IanGlencross	glenx24	50000	5000000						3	0.441
2021-03-28T08:47:47	Zenzoma	AMD3970X	50000	5000000						7	1.029
2021-05-20T13:42:16	daveward2005	d12436	50000	5000000	15220221974473313369191	73.688	2	2	932725704876777	2	0.294

date	userid	compid	res64	spent (GHz-days)
1999-08-31T00:00:00	ANONYMOUS	v4_computers	8D8999BDABF095__	0.363
2000-03-22T00:00:00	ANONYMOUS	v4_computers	751BDA6289C68A__	0.363

date

userid

compid

res64

spent (GHz-days)

1999-08-31T00:00:00

ANONYMOUS

v4_computers

8D8999BDABF095__

0.363

2000-03-22T00:00:00

ANONYMOUS

v4_computers

751BDA6289C68A__

0.363

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, B2 = 126668850 (P-1 stage 2)

B1 = 500000, B2 = 10000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 60000, B2 = 990000 (P-1 stage 2)

B1 = 78580 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 20000, B2 = 235000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

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