M3425893 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

F36F52D843E08701

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	34.8484	68.1159%	1000000	126668850	1.1950	6.9893%	36.0434	70.3444%	2.2285%
PrimeNet	2⁶⁰	0.0448	63.3333%	14000	280000	0.0043	2.8511%	0.0492	64.3787%	1.0454%
GPU72	2⁶⁴	1.0389	65.6250%	19000	320000	0.0054	1.8218%	1.0443	66.2512%	0.6262%
Difference	+5	+33.8094	+2.4909%	+981000	+126348850	+1.1896	+5.1676%	+34.9990	+4.0932%	+4.0932%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

34.8484

68.1159%

1000000

126668850

1.1950

6.9893%

36.0434

70.3444%

2.2285%

PrimeNet

2⁶⁰

0.0448

63.3333%

14000

280000

0.0043

2.8511%

0.0492

64.3787%

1.0454%

GPU72

2⁶⁴

1.0389

65.6250%

19000

320000

0.0054

1.8218%

1.0443

66.2512%

0.6262%

Difference

+33.8094

+2.4909%

+981000

+126348850

+1.1896

+5.1676%

+34.9990

+4.0932%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3425893	59495743909568552919647	23	75.655	8683246077675011 73 × 118948576406507	2021-03-20	73	118948576406507	2,790.0	986,939	1,843,328

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3425893

59495743909568552919647

75.655

8683246077675011
73 × 118948576406507

2021-03-20

118948576406507

2,790.0

986,939

1,843,328

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-06T10:50:00	Carsten Kossendey	leela	15000	210000		-		-	-	0.004	-	-	0.698%
2011-10-30T07:53:00	harlee	P4_2600	60000	945000		-		-	-	0.016	-	-	1.663%
2014-07-18T01:20:00	Jocelyn Larouche	Manual testing	78735	78735		-		-	-	0.012	-	-	0.652%
2014-09-13T14:08:00	HBendtz	HAL9007	500000	10000000		-		-	-	0.155	-	-	4.159%
2022-04-09T09:24:21	Jocelyn Larouche	Manual testing	1000000	1000000		-		-	-	0.152	-	-	2.308%
2022-04-10T15:21:25	Jocelyn Larouche	Manual testing	1000000	126668850		-		-	-	1.195	-	-	6.989%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:29	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.045	-	-
2009-03-24T06:24:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.045	-	-
2011-07-24T20:25:00	Carsten Kossendey	Manual testing	2⁶¹	2⁶²		-	-	0.090	-	-
2012-08-18T15:31:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.466	-	-
2016-02-23T16:29:29	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.287	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.573	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.091	-	-
2015-04-11T09:16:00	Gordon Spence	Manual testing	2⁶⁵	2⁶⁶		-	-	2.181	-	-
2017-02-05T22:59:56	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.363	-	-
2018-11-12T14:47:32	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.725	-	-
2020-12-30T17:06:32	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	17.45	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	5.285 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:	5.285 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		15	2.202
50000	5000000	59495743909568552919647	21	3.083

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-06-28T21:50:00	willreid	jing	50000	5000000						3	0.440
2012-01-12T00:41:00	Lukasz Wrobel	i-5	50000	5000000						3	0.440
2014-12-31T08:16:00	jdcs	desktop	50000	5000000						3	0.440
2014-12-31T09:12:00	jdcs	desktop	50000	5000000						3	0.440
2019-05-17T00:38:39	furkell	furkell1	50000	5000000						3	0.440
2021-03-20T14:57:24	MarkS	desktop-i7	50000	5000000	59495743909568552919647	75.655	21	2	2661521102574594	21	3.083

date	userid	compid	res64	spent (GHz-days)
1999-12-08T00:00:00	Klaas de Jong	v4_computers	862051820CFF55__	0.360

date

userid

compid

res64

spent (GHz-days)

1999-12-08T00:00:00

Klaas de Jong

v4_computers

862051820CFF55__

0.360

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 = 945000 (P-1 stage 2)

B1 = 78735 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 15000, B2 = 210000 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

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