M3474619 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

EADE7B93F7FB5A22

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	34.3597	68.1159%	1000000	126668850	1.1950	7.0000%	35.5547	70.3478%	2.2319%
PrimeNet	2⁶⁰	0.0442	63.3333%	15000	300000	0.0046	2.9567%	0.0489	64.4174%	1.0841%
GPU72	2⁶⁴	1.0244	65.6250%	19000	360000	0.0057	1.8862%	1.0301	66.2734%	0.6484%
Difference	+5	+33.3353	+2.4909%	+981000	+126308850	+1.1893	+5.1137%	+34.5246	+4.0744%	+4.0744%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

34.3597

68.1159%

1000000

126668850

1.1950

7.0000%

35.5547

70.3478%

2.2319%

PrimeNet

2⁶⁰

0.0442

63.3333%

15000

300000

0.0046

2.9567%

0.0489

64.4174%

1.0841%

GPU72

2⁶⁴

1.0244

65.6250%

19000

360000

0.0057

1.8862%

1.0301

66.2734%

0.6484%

Difference

+33.3353

+2.4909%

+981000

+126308850

+1.1893

+5.1137%

+34.5246

+4.0744%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3474619	4325573680639228324946929	25	81.839	622452948170609256 2³ × 3 × 10488187 × 2472833437	2021-04-05	10488187	2472833437	244,550	22.028	38.321

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3474619

4325573680639228324946929

81.839

622452948170609256
2³ × 3 × 10488187 × 2472833437

2021-04-05

10488187

2472833437

244,550

22.028

38.321

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-07T04:42:00	Carsten Kossendey	leela	20000	240000		-		-	-	0.005	-	-	0.812%
2011-11-12T00:08:00	harlee	P4_2600	60000	990000		-		-	-	0.017	-	-	1.688%
2014-08-21T21:46:00	Jocelyn Larouche	Manual testing	78472	78472		-		-	-	0.012	-	-	0.653%
2014-09-26T18:07:00	HBendtz	HAL9007	500000	10000000		-		-	-	0.155	-	-	4.166%
2022-04-10T23:56:43	Jocelyn Larouche	Manual testing	1000000	126668850		-		-	-	1.195	-	-	7.000%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:31	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.044	-	-
2009-03-20T18:24:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.044	-	-
2011-07-21T08:54:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.088	-	-
2012-08-18T15:36:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.459	-	-
2016-02-23T16:29:30	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.283	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.565	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.075	-	-
2016-01-05T09:38:56	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.151	-	-
2017-02-16T15:33:25	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.301	-	-
2018-12-10T15:07:49	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.603	-	-
2021-01-09T15:34:21	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	17.21	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.502 GHz-days
Estimated T-Level:	0.850

Digits	B1	Curves	Complete	FacMiss
20	11000	17 / 100	0.170	84.294%
25	50000	17 / 280	0.061	94.099%

New Calculation Method

Total ECM effort:	2.502 GHz-days
Estimated T-Level:	0.850

Digits	B1	Complete	FacMiss
20	11000	0.548	57.788%
25	50000	0.050	95.165%
30	250000	0.003	99.695%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	2.208
50000	5000000	4325573680639228324946929	2	0.294

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-18T16:33:00	Martti Järvi	Cassady	50000	5000000						3	0.442
2012-02-22T20:23:00	Lukasz Wrobel	u-w	50000	5000000						3	0.442
2015-03-22T04:14:00	joe b.	Pandora	50000	5000000						3	0.442
2017-01-14T14:07:55	Lelikoid	QH	50000	5000000						3	0.442
2019-06-26T21:14:09	furkell	furkell1	50000	5000000						3	0.442
2021-04-05T01:14:49	daveward2005	Dave2	50000	5000000	4325573680639228324946929	81.839	2	2	5348464674608205	2	0.294

date	userid	compid	res64	spent (GHz-days)
1999-08-07T00:00:00	ANONYMOUS	v4_computers	3D368C630DE3AF__	0.365

date

userid

compid

res64

spent (GHz-days)

1999-08-07T00:00:00

ANONYMOUS

v4_computers

3D368C630DE3AF__

0.365

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 = 78472 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 20000, B2 = 240000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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