M3401329 Mersenne number exponent details

Residue

Status

L-L

9ADA2F83275C4273

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁷⁰	70.2521	68.5714%	15000000	750000000	8.3828	10.3015%	78.6349	71.8091%	3.2376%
PrimeNet	2⁶⁰	0.0452	63.3333%	14000	280000	0.0043	2.8474%	0.0495	64.3774%	1.0440%
GPU72	2⁶⁴	1.0465	65.6250%	19000	320000	0.0054	1.8193%	1.0518	66.2504%	0.6254%
Difference	+6	+69.2057	+2.9464%	+14981000	+749680000	+8.3774	+8.4822%	+77.5831	+5.5587%	+5.5587%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷⁰

70.2521

68.5714%

15000000

750000000

8.3828

10.3015%

78.6349

71.8091%

3.2376%

PrimeNet

2⁶⁰

0.0452

63.3333%

14000

280000

0.0043

2.8474%

0.0495

64.3774%

1.0440%

GPU72

2⁶⁴

1.0465

65.6250%

19000

320000

0.0054

1.8193%

1.0518

66.2504%

0.6254%

Difference

+69.2057

+2.9464%

+14981000

+749680000

+8.3774

+8.4822%

+77.5831

+5.5587%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3401329	869589521126046973568153	24	79.525	127830845108786444 2² × 61 × 2017 × 259740657503	2021-11-11	2017	259740657503	69,062	2,155.1	4,025.2

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3401329

869589521126046973568153

79.525

127830845108786444
2² × 61 × 2017 × 259740657503

2021-11-11

2017

259740657503

69,062

2,155.1

4,025.2

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-03T21:42:00	Carsten Kossendey	leela	15000	206250		-		-	-	0.004	-	-	0.591%
2011-10-25T20:18:00	markr	tiny	225000	5737500		-		-	-	0.080	-	-	2.971%
2020-02-02T14:57:03	BigBrother	Winston	3000000	90000000	12	-		-	-	1.179	-	-	6.777%
2021-03-28T09:29:49	axn	Manual testing	15000000	750000000		-		-	-	8.383	-	-	10.302%
2022-04-08T06:41:05	Jocelyn Larouche	Manual testing	1000000	145126800		-		-	-	1.348	-	-	6.528%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-05-23T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.045	-	-
2009-03-25T05:53:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.045	-	-
2011-08-10T10:32:00	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		-	-	0.289	-	-
2015-01-30T19:15:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.577	-	-
2015-01-30T19:15:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.099	-	-
2015-04-05T18:06:00	Gordon Spence	Manual testing	2⁶⁵	2⁶⁶		-	-	2.197	-	-
2017-01-26T04:57:42	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.394	-	-
2019-02-18T10:31:24	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.788	-	-
2020-12-25T06:38:52	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	17.58	-	-
2021-09-09T02:09:17	MadPoo	Manual testing	2⁶⁹	2⁷⁰		-	-	35.15	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.210 GHz-days
Estimated T-Level:	2.800

Digits	B1	Curves	Complete	FacMiss
20	11000	56 / 100	0.560	56.960%
25	50000	56 / 280	0.200	81.844%

New Calculation Method

Total ECM effort:	8.210 GHz-days
Estimated T-Level:	2.800

Digits	B1	Complete	FacMiss
20	11000	1.806	16.424%
25	50000	0.163	84.937%
30	250000	0.010	99.000%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		50	7.330
50000	5000000	869589521126046973568153	6	0.880

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-06-17T04:47:00	Net_Force	Vista64	50000	5000000						3	0.440
2011-12-25T12:48:00	sannerud.com	Jens2010	50000	5000000						3	0.440
2014-11-24T10:23:00	arnaud	Chamot18	50000	5000000						3	0.440
2016-11-25T00:41:22	Dennis Schreiber	z400	50000	5000000						3	0.440
2019-04-26T03:26:57	Alvin Bunk	i7-Core	50000	5000000						3	0.440
2021-03-03T21:34:28	Zenzoma	AMD3970X	50000	5000000						7	1.026
2021-04-09T00:29:45	Zenzoma	AMD3970X	50000	5000000						7	1.026
2021-06-02T06:16:40	daveward2005	d12436	50000	5000000						7	1.026
2021-07-10T01:23:44	daveward2005	d12436	50000	5000000						7	1.026
2021-08-29T04:54:24	EthanD	Diophantus_Linux	50000	5000000						7	1.026
2021-11-11T15:01:43	daveward2005	d12436	50000	5000000	869589521126046973568153	79.525	6	2	28739597563846	6	0.880

date	userid	compid	res64	spent (GHz-days)
1998-06-07T00:00:00	ANONYMOUS	v4_computers	9ADA2F83275C4273	0.357
1999-07-12T00:00:00	ANONYMOUS	v4_computers	9ADA2F83275C4273	0.357

date

userid

compid

res64

spent (GHz-days)

1998-06-07T00:00:00

ANONYMOUS

v4_computers

9ADA2F83275C4273

0.357

1999-07-12T00:00:00

ANONYMOUS

v4_computers

9ADA2F83275C4273

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 (P-1 stage 2)

B1 = 15000000 (P-1 stage 1)

B1 = 1000000, B2 = 145126800 (P-1 stage 2)

B1 = 3000000, B2 = 90000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 225000, B2 = 5737500 (P-1 stage 2)

B1 = 225000 (P-1 stage 1)

B1 = 15000, B2 = 206250 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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