M3452809 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

C49637DD724EC3__

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	34.5767	68.1159%	5000000	200000000	2.3794	8.6492%	36.9561	70.8737%	2.7577%
PrimeNet	2⁶⁰	0.0445	63.3333%	15000	280000	0.0045	2.9018%	0.0490	64.3973%	1.0640%
GPU72	2⁶⁴	1.0309	65.6250%	19000	340000	0.0056	1.8550%	1.0364	66.2627%	0.6377%
Difference	+5	+33.5459	+2.4909%	+4981000	+199660000	+2.3738	+6.7942%	+35.9197	+4.6110%	+4.6110%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

34.5767

68.1159%

5000000

200000000

2.3794

8.6492%

36.9561

70.8737%

2.7577%

PrimeNet

2⁶⁰

0.0445

63.3333%

15000

280000

0.0045

2.9018%

0.0490

64.3973%

1.0640%

GPU72

2⁶⁴

1.0309

65.6250%

19000

340000

0.0056

1.8550%

1.0364

66.2627%

0.6377%

Difference

+33.5459

+2.4909%

+4981000

+199660000

+2.3738

+6.7942%

+35.9197

+4.6110%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3452809	93997843296326395029896658521	29	96.247	13611793078668179304140 2² × 5 × 7 × 11 × 567257 × 2039491 × 7639993	2021-09-07	2039491	7639993	7.746e+9	0.3571	0.6321

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3452809

93997843296326395029896658521

96.247

13611793078668179304140
2² × 5 × 7 × 11 × 567257 × 2039491 × 7639993

2021-09-07

2039491

7639993

7.746e+9

0.3571

0.6321

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-08-15T23:39:00	Carsten Kossendey	durandal	20000	235000		-		-	-	0.005	-	-	0.806%
2011-11-05T19:14:00	harlee	P4_2600	60000	945000		-		-	-	0.016	-	-	1.666%
2014-08-21T21:46:00	Jocelyn Larouche	Manual testing	78589	78589		-		-	-	0.012	-	-	0.653%
2014-09-20T21:34:00	HBendtz	HAL9007	500000	10000000		-		-	-	0.155	-	-	4.163%
2021-09-07T15:01:42	mikr	MSI	5000000	200000000	12		93997843296326395029896658521	29	96.247	2.379	0.725	4.759	8.649%
2022-04-10T23:56:41	Jocelyn Larouche	Manual testing	1000000	126668850		-		-	-	1.195	-	-	6.995%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-06-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.044	-	-
2009-03-21T17:09:00	S485122	USB-Z	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		-	-	0.569	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.082	-	-
2015-04-17T10:12:00	Gordon Spence	Manual testing	2⁶⁵	2⁶⁶		-	-	2.164	-	-
2017-02-20T16:19:37	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.328	-	-
2019-02-18T10:31:21	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.657	-	-
2021-01-05T05:53:58	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	17.31	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.322 GHz-days
Estimated T-Level:	2.150

Digits	B1	Curves	Complete	FacMiss
20	11000	43 / 100	0.430	64.910%
25	50000	43 / 280	0.154	85.740%

New Calculation Method

Total ECM effort:	6.322 GHz-days
Estimated T-Level:	2.150

Digits	B1	Complete	FacMiss
20	11000	1.387	24.980%
25	50000	0.125	88.218%
30	250000	0.008	99.231%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		43	6.322

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-02T07:38:00	James Hintz	4115	50000	5000000						3	0.441
2012-02-04T20:54:00	Smurgs	Praca	50000	5000000						3	0.441
2015-02-12T08:16:00	Sid & Andy	Emperor_Zurg	50000	5000000						3	0.441
2017-02-17T21:51:55	f0rteOC	Fortissimo	50000	5000000						3	0.441
2019-06-07T16:57:41	IanGlencross	glenx24	50000	5000000						3	0.441
2021-03-28T20:22:38	C.D.B.	i7-6850K	50000	5000000						7	1.029
2021-06-29T04:31:29	C.D.B.	i7-6850K	50000	5000000						7	1.029
2021-08-10T07:19:23	daveward2005	d12436	50000	5000000						7	1.029
2021-09-02T13:47:56	mnd9	75211backdoor	50000	5000000						7	1.029

date	userid	compid	res64	spent (GHz-days)
1999-07-27T00:00:00	ANONYMOUS	v4_computers	95850458C64358__	0.363

date

userid

compid

res64

spent (GHz-days)

1999-07-27T00:00:00

ANONYMOUS

v4_computers

95850458C64358__

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 = 5000000, B2 = 200000000 (P-1 stage 2)

B1 = 1000000, B2 = 126668850 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

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

B1 = 1000000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 60000, B2 = 945000 (P-1 stage 2)

B1 = 78589 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 20000, B2 = 235000 (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