M1306589 Mersenne number exponent details

Residue

Status

L-L

A28F28E10A5BF66A

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	22.7416	68.6567%	500000	15000000	0.0593	4.8663%	22.8009	70.1820%	1.5253%
PrimeNet	2⁵⁶	0.0073	62.5000%	6000	100000	0.0005	2.5962%	0.0079	63.4736%	0.9736%
GPU72	2⁶⁰	0.1176	65.0000%	5500	36000	0.0003	0.9360%	0.1179	65.3276%	0.3276%
Difference	+7	+22.6240	+3.6567%	+494500	+14964000	+0.0590	+3.9303%	+22.6830	+4.8544%	+4.8544%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

22.7416

68.6567%

500000

15000000

0.0593

4.8663%

22.8009

70.1820%

1.5253%

PrimeNet

2⁵⁶

0.0073

62.5000%

6000

100000

0.0005

2.5962%

0.0079

63.4736%

0.9736%

GPU72

2⁶⁰

0.1176

65.0000%

5500

36000

0.0003

0.9360%

0.1179

65.3276%

0.3276%

Difference

+22.6240

+3.6567%

+494500

+14964000

+0.0590

+3.9303%

+22.6830

+4.8544%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1306589	4886581083507817319	19	62.084	1869976359631 43 × 43487822317	2009-07-19	43	43487822317	1.0704	108.89	203.37

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1306589

4886581083507817319

62.084

1869976359631
43 × 43487822317

2009-07-19

43487822317

1.0704

108.89

203.37

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-21T00:00:00	ANONYMOUS	v4_computers	10000	1000000		-		-	-	0.003	-	-	1.010%
2016-03-17T19:04:44	alpertron	Manual testing	500000	15000000	12	-		-	-	0.059	-	-	4.866%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-03T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.015	-	-
2003-06-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.029	-	-
2022-03-07T17:32:09	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.088	-	-
2009-02-17T20:52:00	Sturle Sunde	goldiek.ifi	2⁶⁰	2⁶¹		-	-	0.118	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.688 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	298 / 100	2.980	5.004%
25	50000	298 / 280	1.064	34.432%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	20.688 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	14.538	0.000%
25	50000	1.640	19.395%
30	250000	0.140	86.925%
35	1000000	0.010	99.024%

ECM Summary

B1	B2	factor	curves	GHz-days
		4886581083507817319	1	0.00000e+0
50000	5000000		248	9.58
250000	35000000		50	11.11

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-12-10T20:25:00	Steve Scott	Epox	50000	5000000						1	0.039
2008-09-04T19:58:00	Sturle Sunde	v21	50000	5000000						3	0.116
2009-02-18T00:45:00	Sturle Sunde	v21	50000	5000000						3	0.116
2009-07-19T18:48:00	SubPrime	c2d0			4886581083507817319	62.084		1		1	-
2018-04-06T10:52:51	TJAOI	Manual testing	50000	5000000						241	9.306
2021-05-21T15:30:15	TJAOI	Manual testing	250000	35000000						50	11.11

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T01:28:37

Oliver Kruse

GTX-3

4886581083507817319

5E1F27C5A66EF9__

2017-10-23T00:21:27

kkmrkkblmbrbk

c4.xlarge

4886581083507817319

5E1F27C5A66EF9__

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 10000, B2 = 1000000 (P-1 stage 2)

B1 = 10000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

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