M1984013 Mersenne number exponent details

Residue

Status

L-L

A56412E01B233B76

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	2⁶⁷	14.9767	68.6567%	1984013	198401300	1.2094	8.9238%	16.1861	71.4537%	2.7970%
PrimeNet	2⁵⁸	0.0194	63.7931%	8000	140000	0.0014	2.4750%	0.0208	64.6892%	0.8961%
GPU72	2⁶²	0.3097	66.1290%	8000	100000	0.0012	1.1977%	0.3109	66.5347%	0.4057%
Difference	+5	+14.6670	+2.5277%	+1976013	+198301300	+1.2082	+7.7261%	+15.8752	+4.9190%	+4.9190%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.9767

68.6567%

1984013

198401300

1.2094

8.9238%

16.1861

71.4537%

2.7970%

PrimeNet

2⁵⁸

0.0194

63.7931%

8000

140000

0.0014

2.4750%

0.0208

64.6892%

0.8961%

GPU72

2⁶²

0.3097

66.1290%

8000

100000

0.0012

1.1977%

0.3109

66.5347%

0.4057%

Difference

+14.6670

+2.5277%

+1976013

+198301300

+1.2082

+7.7261%

+15.8752

+4.9190%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1984013	9102890693988441891689	22	72.947	2294060244057988 2² × 7 × 29 × 59 × 47884700761	2018-07-15	59	47884700761	572.60	248.73	464.55

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1984013

9102890693988441891689

72.947

2294060244057988
2² × 7 × 29 × 59 × 47884700761

2018-07-15

47884700761

572.60

248.73

464.55

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-01-21T22:41:00	kurly	hex	1000000	30000000		-		-	-	0.246	-	-	6.248%
2018-01-21T01:09:51	Jocelyn Larouche	low 4M	1205760	1205760		-		-	-	0.115	-	-	2.851%
2018-01-27T10:55:56	Jocelyn Larouche	low 4M	1984013	30000000	12	-		-	-	0.335	-	-	6.622%
2018-02-15T13:14:27	Jocelyn Larouche	low 4M	1984013	60000000	12	-		-	-	0.491	-	-	7.463%
2018-03-11T02:36:11	Jocelyn Larouche	low 4M	1984013	120000000	12	-		-	-	0.802	-	-	8.308%
2018-05-21T11:06:49	Jocelyn Larouche	low 4M	1984013	198401300	12	-		-	-	1.209	-	-	8.924%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-12-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-
2016-02-23T16:29:02	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.058	-	-
2009-12-17T03:53:00	S485122	USB-W	2⁶⁰	2⁶¹		-	-	0.077	-	-
2016-02-23T16:29:02	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.155	-	-
2011-07-01T19:06:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.804	-	-
2016-02-23T16:29:02	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.495	-	-
2015-03-13T07:58:00	lycorn	Manual testing	2⁶³	2⁶⁴		-	-	0.990	-	-
2015-03-13T07:59:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	1.883	-	-
2015-09-11T08:33:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.766	-	-
2018-01-08T13:22:29	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	7.533	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.380 GHz-days
Estimated T-Level:	2.000

Digits	B1	Curves	Complete	FacMiss
20	11000	40 / 100	0.400	66.897%
25	50000	40 / 280	0.143	86.666%

New Calculation Method

Total ECM effort:	3.380 GHz-days
Estimated T-Level:	2.000

Digits	B1	Complete	FacMiss
20	11000	1.290	27.518%
25	50000	0.117	88.993%
30	250000	0.007	99.284%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		39	3.296
50000	5000000	9102890693988441891689	1	0.085

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-11-26T02:13:00	Chang Chia-Tche	euler06	50000	5000000						3	0.254
2009-08-28T11:33:00	SubPrime	pitr	50000	5000000						3	0.254
2011-01-31T05:51:00	arnaud	Arnaud-PC	50000	5000000						3	0.254
2012-12-09T19:13:00	Donna Noble	q8200v2	50000	5000000						3	0.254
2014-02-12T18:46:00	OS1	L3	50000	5000000						3	0.254
2015-06-24T15:02:00	Jayder	HPJared	50000	5000000						3	0.254
2016-02-15T02:38:52	Sintax	cloud	50000	5000000						3	0.254
2016-04-02T01:29:49	Bruce	Desk6	50000	5000000						3	0.254
2016-07-09T22:50:14	Bruce	test	50000	5000000						3	0.254
2016-11-12T22:00:18	Bruce	Desk6	50000	5000000						3	0.254
2017-06-13T16:30:29	Bruce	Desk6	50000	5000000						3	0.254
2017-10-17T07:33:53	Bruce	Desk6	50000	5000000						3	0.254
2018-04-11T14:28:04	Bruce	eleven	50000	5000000						3	0.254
2018-07-16T00:21:49	Bruce	Desk6	50000	5000000	9102890693988441891689	72.947	1	2		1	0.085

date	userid	compid	res64	spent (GHz-days)
1999-04-02T00:00:00	ANONYMOUS	v4_computers	A56412E01B233B76	0.130
2015-07-12T18:10:00	MadPoo	Manual testing	A56412E01B233B76	0.130

date

userid

compid

res64

spent (GHz-days)

1999-04-02T00:00:00

ANONYMOUS

v4_computers

A56412E01B233B76

0.130

2015-07-12T18:10:00

MadPoo

Manual testing

A56412E01B233B76

0.130

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 = 1984013, B2 = 198401300 (P-1 stage 2)

B1 = 1984013, B2 = 120000000 (P-1 stage 2)

B1 = 1984013, B2 = 60000000 (P-1 stage 2)

B1 = 1984013, B2 = 30000000 (P-1 stage 2)

B1 = 1000000, B2 = 30000000 (P-1 stage 2)

B1 = 1984013 (P-1 stage 1)

B1 = 1205760 (P-1 stage 1)

B1 = 1000000 (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