M5012981 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

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	5.9274	65.6716%	-	-	-	-	5.9274	65.6716%	0.0000%
PrimeNet	2⁶¹	0.0613	62.2951%	22000	450000	0.0091	3.3147%	0.0704	63.5449%	1.2498%
GPU72	2⁶⁵	1.4554	64.6154%	34000	700000	0.0141	2.4171%	1.4695	65.4707%	0.8553%
Difference	+2	+4.4720	+1.0563%	-34000	-700000	-0.0141	-2.4171%	+4.4579	+0.2010%	+0.2010%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

5.9274

65.6716%

5.9274

65.6716%

0.0000%

PrimeNet

2⁶¹

0.0613

62.2951%

22000

450000

0.0091

3.3147%

0.0704

63.5449%

1.2498%

GPU72

2⁶⁵

1.4554

64.6154%

34000

700000

0.0141

2.4171%

1.4695

65.4707%

0.8553%

Difference

+4.4720

+1.0563%

-34000

-700000

-0.0141

-2.4171%

+4.4579

+0.2010%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5012981	2569403411551	13	41.225	256275 3² × 5² × 17 × 67	-	25	67	8.595e-8	5.485e-6	1.023e-5
5012981	5037893222111140577	19	62.128	502484771248 2⁴ × 41 × 443 × 1303 × 1327	2016-06-30	1303	1327	0.2204	0.0003	0.0005
5012981	17198569203941220654509129	26	83.830	1715403390112711444 2² × 95351023 × 4497600907	2019-09-16	95351023	4497600907	578,884	67.370	91.985

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5012981

2569403411551

41.225

256275
3² × 5² × 17 × 67

8.595e-8

5.485e-6

1.023e-5

5012981

5037893222111140577

62.128

502484771248
2⁴ × 41 × 443 × 1303 × 1327

2016-06-30

1303

1327

0.2204

0.0003

0.0005

5012981

17198569203941220654509129

83.830

1715403390112711444
2² × 95351023 × 4497600907

2019-09-16

95351023

4497600907

578,884

67.370

91.985

exponent	prime factors	composite factor	digits	bits*
5012981	2569403411551 5037893222111140577	12944380031922024385027546604927	32	103.352
5012981	2569403411551 17198569203941220654509129	44190062386402538624571021163873549079	38	125.055
5012981	5037893222111140577 17198569203941220654509129	86644555222544870126658402663850100248827433	44	145.958
5012981	2569403411551 5037893222111140577 17198569203941220654509129	22262481578112580333161032527609671383981056033767 7878583	57	187.183

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-06-30T15:38:36	TJAOI	Manual testing	2⁶²	2⁶³*	5037893222111140577	62.128	19	0.098	1.413	0.199

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.632 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	0.632 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.097	90.776%
25	50000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	17198569203941220654509129	3	0.632

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2019-09-16T09:34:31	mnd9	mnd2	50000	5000000	17198569203941220654509129	83.830	3	2	4542131139503502	3	0.632

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T06:41:19

kkmrkkblmbrbk

Manual testing

2569403411551

5037893222111140577

3BE2A3E514ADE8__

2018-04-26T12:01:54

Oliver Kruse

GTX-4

2569403411551

5037893222111140577

3BE2A3E514ADE8__

2019-09-17T04:11:25

mnd9

office2

2569403411551

5037893222111140577

17198569203941220654509129

B2952E5748356069

2019-09-18T07:03:16

marssystems

SYSTEM01

2569403411551

5037893222111140577

17198569203941220654509129

B2952E5748356069

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

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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