M3403021 Mersenne number exponent details

Residue

Status

L-L

A7AD28A0B1A54EBD

double-checked

PRP

633F13AE4F0BC628

double-checked

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁹	35.0826	68.1159%	15000000	750000000	8.3828	11.0347%	43.4654	79.1507%	15.8174%
PrimeNet	2⁶⁰	0.0451	63.3333%	14000	280000	0.0043	2.8477%	0.0495	66.1810%	2.8477%
GPU72	2⁶⁴	1.0459	65.6250%	19000	320000	0.0054	1.8195%	1.0513	67.4445%	1.8195%
Difference	+5	+34.0367	+2.4909%	+14981000	+749680000	+8.3774	+9.2152%	+42.4141	+11.7062%	+11.7062%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

35.0826

68.1159%

15000000

750000000

8.3828

11.0347%

43.4654

79.1507%

15.8174%

PrimeNet

2⁶⁰

0.0451

63.3333%

14000

280000

0.0043

2.8477%

0.0495

66.1810%

2.8477%

GPU72

2⁶⁴

1.0459

65.6250%

19000

320000

0.0054

1.8195%

1.0513

67.4445%

1.8195%

Difference

+34.0367

+2.4909%

+14981000

+749680000

+8.3774

+9.2152%

+42.4141

+11.7062%

	GHz-days
exponent	factor	digits	bits*	k	min B1	min B2	date found	min. TF	min. P-1	normal P-1
3403021	6440511285502027751889751835491770679	37	122.277	946293203230604182561575705159 3 × 97 × 233 × 30089 × 920233 × 14791859 × 34075991	14791859	34075991	2021-03-30	5.234e+10	2.4127	4.5845

GHz-days

exponent

factor

digits

bits*

min B1

min B2

date found

min. TF

min. P-1

normal P-1

3403021

6440511285502027751889751835491770679

122.277

946293203230604182561575705159
3 × 97 × 233 × 30089 × 920233 × 14791859 × 34075991

14791859

34075991

2021-03-30

5.234e+10

2.4127

4.5845

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-03T21:44:00	Carsten Kossendey	leela	15000	206250		-		-	-	0.004	-	-	0.693%
2011-10-27T14:12:00	markr	tiny	225000	5737500		-		-	-	0.080	-	-	3.311%
2020-02-08T17:38:49	BigBrother	Winston	3000000	90000000	12	-		-	-	1.179	-	-	7.363%
2021-03-30T11:36:30	axn	Manual testing	15000000	750000000			6440511285502027751889751835491770679	37	122.277	8.383	0.715	16.77	11.035%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-09-06T00:00:00	ANONYMOUS	v4_computers	?	2⁶⁰		-	-	0.023	-	-
2009-03-26T05:53:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.045	-	-
2011-08-12T19:54:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.090	-	-
2012-08-18T15:30:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.469	-	-
2016-02-23T16:29:28	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.288	-	-
2015-01-30T19:15:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.577	-	-
2015-01-30T19:15:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.098	-	-
2015-04-06T18:28:00	Gordon Spence	Manual testing	2⁶⁵	2⁶⁶		-	-	2.196	-	-
2017-01-26T16:57:42	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.392	-	-
2019-02-18T10:31:23	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.784	-	-
2020-12-25T16:36:23	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	17.57	-	-

ECM factoring results:

Total ECM effort:	3.226 GHz-days
Estimated T-Level:	1.100

Digits	B1	Curves	Complete	FacMiss
20	11000	22 / 100	0.220	80.163%
25	50000	22 / 280	0.079	92.431%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		22	3.226

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-06-29T05:45:00	Net_Force	Vista64	50000	5000000						3	0.440
2012-01-01T22:13:00	sannerud.com	Jens2010	50000	5000000						3	0.440
2014-11-29T16:42:00	S36049	Wolle6	50000	5000000						3	0.440
2016-11-25T10:20:56	bdani	X58_TUF	50000	5000000						3	0.440
2019-04-27T14:50:26	furkell	furkell1	50000	5000000						3	0.440
2021-03-05T13:51:42	tottenhoff	Garage-Band-003	50000	5000000						7	1.026

date	userid	compid	res64	spent (GHz-days)
1999-12-08T00:00:00	ANONYMOUS	v4_computers	A7AD28A0B1A54EBD	0.357

date

userid

compid

res64

spent (GHz-days)

1999-12-08T00:00:00

ANONYMOUS

v4_computers

A7AD28A0B1A54EBD

0.357

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 = 15000000, B2 = 750000000 (stage 2)

B1 = 15000000 (stage 1)

B1 = 3000000, B2 = 90000000 (stage 2)

B1 = 3000000 (stage 1)

B1 = 225000, B2 = 5737500 (stage 2)

B1 = 225000 (stage 1)

B1 = 15000, B2 = 206250 (stage 2)

B1 = 15000 (stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

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