M1441049 Mersenne number exponent details

Residue

Status

L-L

98A0DA7F2E3A1A95

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	20.6196	68.6567%	500000	15000000	0.0714	4.9244%	20.6911	70.2002%	1.5435%
PrimeNet	2⁵⁶	0.0067	62.5000%	6500	110000	0.0007	2.7777%	0.0073	63.5416%	1.0416%
GPU72	2⁶⁰	0.1066	65.0000%	6000	90000	0.0006	1.3553%	0.1072	65.4744%	0.4744%
Difference	+7	+20.5131	+3.6567%	+494000	+14910000	+0.0708	+3.5691%	+20.5839	+4.7258%	+4.7258%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

20.6196

68.6567%

500000

15000000

0.0714

4.9244%

20.6911

70.2002%

1.5435%

PrimeNet

2⁵⁶

0.0067

62.5000%

6500

110000

0.0007

2.7777%

0.0073

63.5416%

1.0416%

GPU72

2⁶⁰

0.1066

65.0000%

6000

90000

0.0006

1.3553%

0.1072

65.4744%

0.4744%

Difference

+20.5131

+3.6567%

+494000

+14910000

+0.0708

+3.5691%

+20.5839

+4.7258%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1441049	399871867197596904559	21	68.438	138743327672271 3² × 7 × 2202275042417	2008-12-18	9	2202275042417	69.836	6,642.6	12,407

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1441049

399871867197596904559

68.438

138743327672271
3² × 7 × 2202275042417

2008-12-18

2202275042417

69.836

6,642.6

12,407

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-29T00:00:00	Team Prime Rib	v4_computers	15000	243750		-		-	-	0.002	-	-	0.838%
2016-03-17T19:14:22	alpertron	Manual testing	500000	15000000	12	-		-	-	0.071	-	-	4.924%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-10-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.013	-	-
2003-07-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.027	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.360 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:	25.360 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
		399871867197596904559	1	0.00000e+0
50000	5000000		248	11.73
250000	35000000		50	13.63

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-01-06T16:31:00	Team_Bundu	bundu3	50000	5000000						1	0.047
2008-12-18T09:36:00	James Heinrich	WHS			399871867197596904559	68.438		1		1	-
2018-11-24T19:35:31	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2019-02-22T12:22:42	TJAOI	Manual testing	50000	5000000						244	11.54
2021-12-28T11:11:51	TJAOI	Manual testing	250000	35000000						50	13.63

date	userid	compid	res64	spent (GHz-days)
1998-12-27T00:00:00	ANONYMOUS	v4_computers	98A0DA7F2E3A1A95	0.055

date

userid

compid

res64

spent (GHz-days)

1998-12-27T00:00:00

ANONYMOUS

v4_computers

98A0DA7F2E3A1A95

0.055

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-01T00:01:23

Oliver Kruse

GTX-1

399871867197596904559

1591E41AE4CC9D__

2017-10-27T06:02:24

kkmrkkblmbrbk

c4.xlarge

399871867197596904559

1591E41AE4CC9D__

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 = 15000, B2 = 243750 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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