M3284443 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

37A0F5AC059CA80C

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	2⁶⁸	18.1476	67.6471%	4000000	150000000	1.8206	8.7825%	19.9682	70.4885%	2.8414%
PrimeNet	2⁶⁰	0.0468	63.3333%	14000	260000	0.0042	2.7761%	0.0509	64.3512%	1.0179%
GPU72	2⁶⁴	1.0837	65.6250%	17000	280000	0.0048	1.6877%	1.0885	66.2052%	0.5802%
Difference	+4	+17.0639	+2.0221%	+3983000	+149720000	+1.8158	+7.0948%	+18.8797	+4.2833%	+4.2833%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

18.1476

67.6471%

4000000

150000000

1.8206

8.7825%

19.9682

70.4885%

2.8414%

PrimeNet

2⁶⁰

0.0468

63.3333%

14000

260000

0.0042

2.7761%

0.0509

64.3512%

1.0179%

GPU72

2⁶⁴

1.0837

65.6250%

17000

280000

0.0048

1.6877%

1.0885

66.2052%

0.5802%

Difference

+17.0639

+2.0221%

+3983000

+149720000

+1.8158

+7.0948%

+18.8797

+4.2833%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3284443	40486443430768175787599	23	75.100	6163365208464293 1609 × 2609 × 1468208653	2021-03-12	2609	1468208653	4,262.7	12.182	22.753

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3284443

40486443430768175787599

75.100

6163365208464293
1609 × 2609 × 1468208653

2021-03-12

2609

1468208653

4,262.7

12.182

22.753

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-09T19:16:00	Carsten Kossendey	durandal	15000	191250		-		-	-	0.004	-	-	0.787%
2011-09-22T16:42:00	harlee	P4_2600	60000	1065000		-		-	-	0.017	-	-	1.939%
2014-06-26T21:22:00	ANONYMOUS	Manual testing	79542	79542		-		-	-	0.012	-	-	0.754%
2014-10-10T20:28:00	Jocelyn Larouche	Manual testing	99084	99084		-		-	-	0.015	-	-	0.861%
2016-01-25T11:49:46	Jocelyn Larouche	Manual testing	383400	3834000	6	-		-	-	0.087	-	-	3.600%
2021-03-16T13:38:18	mikr	MSI	4000000	150000000	12	-		-	-	1.821	-	-	8.782%
2022-04-02T19:48:43	Jocelyn Larouche	Manual testing	1000000	134316000		-		-	-	1.258	-	-	7.651%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-06-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.047	-	-
2009-04-01T15:39:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.047	-	-
2011-09-30T01:54:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.094	-	-
2012-12-30T00:06:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.299	-	-
2015-02-07T18:05:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.598	-	-
2015-02-07T18:05:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.138	-	-
2015-06-29T20:47:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.275	-	-
2017-04-06T14:00:09	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.550	-	-
2018-11-26T14:19:35	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.101	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.932 GHz-days
Estimated T-Level:	1.350

Digits	B1	Curves	Complete	FacMiss
20	11000	27 / 100	0.270	76.234%
25	50000	27 / 280	0.096	90.792%

New Calculation Method

Total ECM effort:	3.932 GHz-days
Estimated T-Level:	1.350

Digits	B1	Complete	FacMiss
20	11000	0.871	41.855%
25	50000	0.079	92.430%
30	250000	0.005	99.516%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		22	3.204
50000	5000000	40486443430768175787599	5	0.728

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-25T22:27:00	TeamResslerTUB	1062319	50000	5000000						3	0.437
2011-10-04T04:31:00	sannerud.com	Jens2010	50000	5000000						3	0.437
2014-07-21T22:51:00	fireredd	ont111	50000	5000000						3	0.437
2016-09-13T12:55:49	Dennis Schreiber	z400	50000	5000000						3	0.437
2019-02-12T17:59:04	Idgo	Pentium_Desktop	50000	5000000						3	0.437
2021-02-20T19:43:14	Corwin McKnight	Desktop	50000	5000000						7	1.019
2021-03-12T16:08:46	mnd9	75202	50000	5000000	40486443430768175787599	75.100	5	2	7119738956120591	5	0.728

date	userid	compid	res64	spent (GHz-days)
1999-06-15T00:00:00	ANONYMOUS	v4_computers	E3C577516326D1__	0.345

date

userid

compid

res64

spent (GHz-days)

1999-06-15T00:00:00

ANONYMOUS

v4_computers

E3C577516326D1__

0.345

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 = 4000000, B2 = 150000000 (P-1 stage 2)

B1 = 1000000, B2 = 134316000 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 383400, B2 = 3834000 (P-1 stage 2)

B1 = 383400 (P-1 stage 1)

B1 = 60000, B2 = 1065000 (P-1 stage 2)

B1 = 99084 (P-1 stage 1)

B1 = 79542 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 15000, B2 = 191250 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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