M5078081 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

0613FADB994331C8

verified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁷²	188.3258	68.0556%	305000	9531250	0.1623	2.9670%	188.4881	69.0033%	0.9478%
PrimeNet	2⁶¹	0.0605	62.2951%	22000	500000	0.0097	3.4071%	0.0701	63.5797%	1.2846%
GPU72	2⁶⁵	1.4367	64.6154%	34000	700000	0.0141	2.4223%	1.4508	65.4725%	0.8571%
Difference	+7	+186.8891	+3.4402%	+271000	+8831250	+0.1482	+0.5446%	+187.0373	+3.5308%	+3.5308%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷²

188.3258

68.0556%

305000

9531250

0.1623

2.9670%

188.4881

69.0033%

0.9478%

PrimeNet

2⁶¹

0.0605

62.2951%

22000

500000

0.0097

3.4071%

0.0701

63.5797%

1.2846%

GPU72

2⁶⁵

1.4367

64.6154%

34000

700000

0.0141

2.4223%

1.4508

65.4725%

0.8571%

Difference

+186.8891

+3.4402%

+271000

+8831250

+0.1482

+0.5446%

+187.0373

+3.5308%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5078081	7832025287710898434882394510881	31	102.627	771159940901976399636240 2⁴ × 3⁴ × 5 × 7 × 19 × 48871 × 1438663 × 12726457	2021-11-06	1438663	12726457	2.758e+10	0.4128	0.5885

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5078081

7832025287710898434882394510881

102.627

771159940901976399636240
2⁴ × 3⁴ × 5 × 7 × 19 × 48871 × 1438663 × 12726457

2021-11-06

1438663

12726457

2.758e+10

0.4128

0.5885

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-08-17T03:39:00	harlee	P4_2600	55000	907500		-		-	-	0.020	-	-	1.155%
2017-03-09T14:22:46	Squeeky_Squirrel	i5-5250U_1600	305000	9531250	12	-		-	-	0.162	-	-	2.967%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2021-11-06T04:31:43	ATH	5960X	2500000	92500000	2	7	7832025287710898434882394510881	P-1	31	102.627	1.730

date

userid

compid

start

factor

Smooth

digits

bits*

ghz-days

2021-11-06T04:31:43

ATH

5960X

2500000

92500000

7832025287710898434882394510881

P-1

102.627

1.730

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:39:08	Mark Rose	Manual testing	2¹	2⁶¹		-	-	0.060	-	-
2008-12-29T03:08:00	Sturle Sunde	bruch.ifi	2⁶¹	2⁶²		-	-	0.060	-	-
2009-08-08T04:06:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.314	-	-
2016-02-23T16:39:08	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.193	-	-
2014-09-01T13:55:00	kracker	Manual testing	2⁶³	2⁶⁴		-	-	0.387	-	-
2014-09-15T01:26:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	0.736	-	-
2015-08-02T21:34:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.472	-	-
2016-05-23T19:05:19	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.943	-	-
2018-06-11T12:29:33	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	5.886	-	-
2021-01-11T11:09:10	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	11.77	-	-
2021-03-31T18:48:14	-Anonymous-	Manual testing	2⁶⁹	2⁷⁰		-	-	23.55	-	-
2021-03-31T18:48:14	-Anonymous-	Manual testing	2⁷⁰	2⁷¹		-	-	47.09	-	-
2021-04-02T10:14:40	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	94.18	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.897 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:	1.897 GHz-days
Estimated T-Level:	0.450

Digits	B1	Complete	FacMiss
20	11000	0.290	74.802%
25	50000	0.026	97.410%
30	250000	0.002	99.839%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	1.897

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-07-17T16:18:00	Lukasz Wrobel	4_x_4	50000	5000000						3	0.632
2014-06-26T11:17:00	fireredd	ont1	50000	5000000						3	0.632
2017-07-26T05:02:10	driveByUpgrades	AMD8	50000	5000000						3	0.632

date	userid	compid	res64	spent (GHz-days)
2000-08-01T00:00:00	ANONYMOUS	v4_computers	8676EC08FC3E5A__	0.704

date

userid

compid

res64

spent (GHz-days)

2000-08-01T00:00:00

ANONYMOUS

v4_computers

8676EC08FC3E5A__

0.704

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 = 2500000, B2 = 92500000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 305000, B2 = 9531250 (P-1 stage 2)

B1 = 305000 (P-1 stage 1)

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

B1 = 55000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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