M3347887 Mersenne number exponent details

Residue

Status

L-L

9190F9C782964B97

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	2⁶⁸	17.8037	67.6471%	1469576	111642300	1.1379	7.7643%	18.9417	70.1590%	2.5120%
PrimeNet	2⁶⁰	0.0459	63.3333%	14000	260000	0.0042	2.7856%	0.0500	64.3547%	1.0214%
GPU72	2⁶⁴	1.0632	65.6250%	18000	300000	0.0051	1.7552%	1.0682	66.2283%	0.6033%
Difference	+4	+16.7406	+2.0221%	+1451576	+111342300	+1.1328	+6.0091%	+17.8734	+3.9307%	+3.9307%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

17.8037

67.6471%

1469576

111642300

1.1379

7.7643%

18.9417

70.1590%

2.5120%

PrimeNet

2⁶⁰

0.0459

63.3333%

14000

260000

0.0042

2.7856%

0.0500

64.3547%

1.0214%

GPU72

2⁶⁴

1.0632

65.6250%

18000

300000

0.0051

1.7552%

1.0682

66.2283%

0.6033%

Difference

+16.7406

+2.0221%

+1451576

+111342300

+1.1328

+6.0091%

+17.8734

+3.9307%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3347887	10969926027375444359	20	63.250	1638335766317 16903 × 96925739	2014-09-07	16903	96925739	0.6160	0.8066	1.5020
3347887	20949670663636468729	20	64.184	3128789989572 2² × 3 × 13 × 20056346087	2017-08-08	13	20056346087	1.5878	166.41	310.81

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3347887

10969926027375444359

63.250

1638335766317
16903 × 96925739

2014-09-07

16903

96925739

0.6160

0.8066

1.5020

3347887

20949670663636468729

64.184

3128789989572
2² × 3 × 13 × 20056346087

2017-08-08

20056346087

1.5878

166.41

310.81

exponent	prime factors	composite factor	digits	bits*
3347887	10969926027375444359 20949670663636468729	229816337477969496450198808293982949711	39	127.434

exponent

prime factors

composite factor

digits

bits*

3347887

10969926027375444359
20949670663636468729

229816337477969496450198808293982949711

127.434

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-05T05:41:00	Carsten Kossendey	durandal	15000	206250		-		-	-	0.004	-	-	0.809%
2011-10-10T12:18:00	harlee	P4_2600	55000	907500		-		-	-	0.015	-	-	1.828%
2012-12-15T04:08:00	Squeeky_Squirrel	P4_2600	230000	6670000		-		-	-	0.088	-	-	3.804%
2021-03-10T11:45:15	Jocelyn Larouche	Manual testing	334788	3682675	6	-		-	-	0.079	-	-	3.519%
2021-03-10T15:34:12	Jocelyn Larouche	Manual testing	334788	7030562	6	-		-	-	0.107	-	-	4.055%
2022-01-06T11:34:16	Jocelyn Larouche	Manual testing	1469576	111642300		-	skipped known factor: 10969926027375444359	-	-	1.138	-	-	7.764%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-03-27T18:50:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.046	-	-
2011-08-23T13:42:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.092	-	-
2022-04-22T15:56:51	LordJulius	Manual testing	2¹	2⁶²		-	-	0.184	-	-
2012-11-15T00:20:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.477	-	-
2022-04-22T15:56:52	LordJulius	Manual testing	2⁶²	2⁶³		-	-	0.293	-	-
2022-04-22T15:56:52	LordJulius	Manual testing	2⁶³	2⁶⁴	10969926027375444359	63.250	20	0.139	0.714	0.283
2017-08-08T11:29:01	TJAOI	Manual testing	2⁶⁴	2⁶⁵*	20949670663636468729	64.184	20	0.525	0.714	1.066
2022-04-22T15:56:52	LordJulius	Manual testing	2⁶⁴	2⁶⁵	20949670663636468729	64.184	20	0.525	0.714	1.066
2022-04-22T15:56:52	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	2.232	-	-
2022-04-22T15:56:52	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	4.464	-	-
2021-10-20T10:52:34	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	8.928	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.315 GHz-days
Estimated T-Level:	0.450

Digits	B1	Curves	Complete	FacMiss
20	11000	9 / 100	0.090	91.352%
25	50000	9 / 280	0.032	96.831%

New Calculation Method

Total ECM effort:	1.315 GHz-days
Estimated T-Level:	0.450

Digits	B1	Complete	FacMiss
20	11000	0.346	70.740%
25	50000	0.032	96.848%
30	250000	0.002	99.798%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	0.877
50000	5000000	10969926027375444359	3	0.438

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-06-03T15:18:00	TeamResslerTUB	1062323	50000	5000000						3	0.438
2011-11-25T08:30:00	S00030	op9020-usff	50000	5000000						3	0.438
2014-09-07T11:27:00	swildner	collider	50000	5000000	10969926027375444359	63.250	3	2		3	0.438

date	userid	compid	res64	spent (GHz-days)
1999-07-04T00:00:00	ANONYMOUS	v4_computers	9190F9C782964B97	0.352

date

userid

compid

res64

spent (GHz-days)

1999-07-04T00:00:00

ANONYMOUS

v4_computers

9190F9C782964B97

0.352

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T13:09:58

alpertron

Manual testing

10969926027375444359

20949670663636468729

3F1C66E3AC75CC__

2017-11-20T10:54:47

Oliver Kruse

GTX-3

10969926027375444359

20949670663636468729

3F1C66E3AC75CC__

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 = 1469576, B2 = 111642300 (P-1 stage 2)

B1 = 1469576 (P-1 stage 1)

B1 = 334788, B2 = 7030562 (P-1 stage 2)

B1 = 230000, B2 = 6670000 (P-1 stage 2)

B1 = 334788, B2 = 3682675 (P-1 stage 2)

B1 = 334788 (P-1 stage 1)

B1 = 230000 (P-1 stage 1)

B1 = 55000, B2 = 907500 (P-1 stage 2)

B1 = 55000 (P-1 stage 1)

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

B1 = 15000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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