M3445643 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

6C25947049AB06CC

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	34.6486	68.1159%	5000000	200000000	2.3794	8.6475%	37.0280	70.8731%	2.7572%
PrimeNet	2⁶⁰	0.0446	63.3333%	15000	280000	0.0045	2.9007%	0.0491	64.3969%	1.0636%
GPU72	2⁶⁴	1.0330	65.6250%	19000	340000	0.0056	1.8543%	1.0386	66.2624%	0.6374%
Difference	+5	+33.6156	+2.4909%	+4981000	+199660000	+2.3738	+6.7932%	+35.9895	+4.6107%	+4.6107%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

34.6486

68.1159%

5000000

200000000

2.3794

8.6475%

37.0280

70.8731%

2.7572%

PrimeNet

2⁶⁰

0.0446

63.3333%

15000

280000

0.0045

2.9007%

0.0491

64.3969%

1.0636%

GPU72

2⁶⁴

1.0330

65.6250%

19000

340000

0.0056

1.8543%

1.0386

66.2624%

0.6374%

Difference

+33.6156

+2.4909%

+4981000

+199660000

+2.3738

+6.7932%

+35.9895

+4.6107%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3445643	1890553429784423153435939023	28	90.611	274339713920511085077 3 × 7 × 11 × 19 × 2777 × 469031 × 47989439	2021-07-19	469031	47989439	98,241,105	0.4657	0.7437

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3445643

1890553429784423153435939023

90.611

274339713920511085077
3 × 7 × 11 × 19 × 2777 × 469031 × 47989439

2021-07-19

469031

47989439

98,241,105

0.4657

0.7437

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-06T10:59:00	Carsten Kossendey	leela	15000	210000		-		-	-	0.004	-	-	0.699%
2011-11-04T04:01:00	harlee	P4_2600	60000	945000		-		-	-	0.016	-	-	1.665%
2014-07-18T01:20:00	Jocelyn Larouche	Manual testing	78628	78628		-		-	-	0.012	-	-	0.653%
2014-09-19T04:03:00	HBendtz	HAL9007	500000	10000000		-		-	-	0.155	-	-	4.162%
2021-06-09T21:07:39	mognuts	Manual testing	1000000	30000000		-		-	-	0.393	-	-	5.546%
2021-07-19T19:23:21	mikr	MSI	5000000	200000000	12		1890553429784423153435939023	28	90.611	2.379	0.724	4.759	8.648%
2022-04-10T23:56:40	Jocelyn Larouche	Manual testing	1000000	126668850		-	skipped known factor: 1890553429784423153435939023	-	-	1.195	-	-	6.994%

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-Z	2⁶⁰	2⁶¹		-	-	0.045	-	-
2011-08-05T21:27:00	markr	Manual testing	2¹	2⁶²		-	-	0.178	-	-
2012-08-18T15:34:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.463	-	-
2016-02-23T16:29:30	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.285	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.570	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.084	-	-
2015-04-16T08:55:00	Gordon Spence	Manual testing	2⁶⁵	2⁶⁶		-	-	2.169	-	-
2017-02-06T16:31:38	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.338	-	-
2018-07-23T16:23:38	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.675	-	-
2021-01-04T01:35:42	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	17.35	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	5.291 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:	5.291 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		36	5.291

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-06-28T01:08:00	borkencode	CFF2DC1CD	50000	5000000						3	0.441
2012-01-29T04:40:00	Smurgs	Praca	50000	5000000						3	0.441
2015-02-01T17:00:00	Chris Smith	cloud3-c1large	50000	5000000						3	0.441
2016-12-16T03:31:28	ANONYMOUS	q9550	50000	5000000						3	0.441
2019-06-01T07:02:57	Idgo	Pentium_Desktop	50000	5000000						3	0.441
2021-03-25T20:09:53	Zenzoma	AMD3970X	50000	5000000						7	1.029
2021-05-16T11:46:46	Sergey Nosov	TS140-02	50000	5000000						7	1.029
2021-06-24T03:45:22	RIHATEC	i7-3770K	50000	5000000						7	1.029

date	userid	compid	res64	spent (GHz-days)
1999-07-12T00:00:00	TobyLL	v4_computers	445EC75AB93FF3__	0.362

date

userid

compid

res64

spent (GHz-days)

1999-07-12T00:00:00

TobyLL

v4_computers

445EC75AB93FF3__

0.362

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 = 1000000, B2 = 30000000 (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 = 78628 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

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

B1 = 15000 (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