M1363027 Mersenne number exponent details

Residue

Status

L-L

FBC0975B9D19E3AE

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	21.7999	68.6567%	500000	15000000	0.0714	4.8914%	21.8714	70.1898%	1.5331%
PrimeNet	2⁵⁶	0.0070	62.5000%	6000	100000	0.0006	2.6180%	0.0077	63.4817%	0.9817%
GPU72	2⁶⁰	0.1127	65.0000%	5500	40000	0.0004	0.9838%	0.1131	65.3443%	0.3443%
Difference	+7	+21.6873	+3.6567%	+494500	+14960000	+0.0710	+3.9076%	+21.7583	+4.8455%	+4.8455%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

21.7999

68.6567%

500000

15000000

0.0714

4.8914%

21.8714

70.1898%

1.5331%

PrimeNet

2⁵⁶

0.0070

62.5000%

6000

100000

0.0006

2.6180%

0.0077

63.4817%

0.9817%

GPU72

2⁶⁰

0.1127

65.0000%

5500

40000

0.0004

0.9838%

0.1131

65.3443%

0.3443%

Difference

+21.6873

+3.6567%

+494500

+14960000

+0.0710

+3.9076%

+21.7583

+4.8455%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1363027	11436311683066894817	20	63.310	4195188973904 2⁴ × 173 × 1515602953	2013-11-05	173	1515602953	1.8207	4.5715	8.5382
1363027	257853853668800338647463	24	77.771	94588681540717953 3² × 19 × 31 × 751207 × 23753179	2018-09-28	751207	23753179	44,781	0.1110	0.1338

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1363027

11436311683066894817

63.310

4195188973904
2⁴ × 173 × 1515602953

2013-11-05

173

1515602953

1.8207

4.5715

8.5382

1363027

257853853668800338647463

77.771

94588681540717953
3² × 19 × 31 × 751207 × 23753179

2018-09-28

751207

23753179

44,781

0.1110

0.1338

exponent	prime factors	composite factor	digits	bits*
1363027	11436311683066894817 257853853668800338647463	2948897039236322811822256702473589064899271	43	141.081

exponent

prime factors

composite factor

digits

bits*

1363027

11436311683066894817
257853853668800338647463

2948897039236322811822256702473589064899271

141.081

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2003-09-21T00:00:00	ANONYMOUS	v4_computers	15000	225000		-		-	-	0.001	-	-	0.808%
unknown			500000	15000000		-		-	-	0.071	-	-	4.891%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2003-09-21T00:00:00

ANONYMOUS

v4_computers

15000

225000

0.001

-

-

0.808%

unknown

500000

15000000

0.071

-

-

4.891%

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		-	-	0.014	-	-
2003-06-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.028	-	-
2022-03-07T17:32:37	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.085	-	-
2009-02-16T03:40:00	Sturle Sunde	hindemith.ifi	2⁶⁰	2⁶¹		-	-	0.113	-	-
2011-05-09T14:43:00	Xyzzy	Manual testing	2⁶¹	2⁶²		-	-	0.225	-	-
2013-01-23T08:20:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.720	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.152 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	299 / 100	2.990	4.954%
25	50000	299 / 280	1.068	34.309%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	25.152 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	14.577	0.000%
25	50000	1.644	19.326%
30	250000	0.140	86.905%
35	1000000	0.010	99.023%

ECM Summary

B1	B2	factor	curves	GHz-days
		11436311683066894817	1	0.00000e+0
50000	5000000		219	10.26
50000	5000000	257853853668800338647463	30	1.405
250000	35000000		50	13.49

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-12-27T06:00:00	Steve Scott	Epox	50000	5000000						1	0.047
2009-02-21T19:57:00	C King	black	50000	5000000						3	0.141
2009-05-26T23:16:00	Lukasz Wrobel	WORKER-1	50000	5000000						3	0.141
2009-08-07T16:22:00	SubPrime	c2d0	50000	5000000						3	0.141
2009-11-29T15:56:00	Lupo	yorick	50000	5000000						3	0.141
2010-06-28T06:19:00	Geoff Wing	GW1	50000	5000000						3	0.141
2011-03-26T16:49:00	OS1	majjaNy	50000	5000000						3	0.141
2012-01-22T09:51:00	Oscar Östlin		50000	5000000						1	0.047
2012-08-30T14:21:00	OS1	Tina	50000	5000000						3	0.141
2013-01-23T08:56:00	OS1	Tina	50000	5000000						3	0.141
2013-11-05T03:35:00	jim f in mn	asus			11436311683066894817	63.310		1		1	-
2018-09-28T10:44:31	TJAOI	Manual testing	50000	5000000	257853853668800338647463	77.771	30	2		30	1.405
2018-09-28T10:44:31	TJAOI	Manual testing	50000	5000000						193	9.040
2021-05-28T18:40:03	TJAOI	Manual testing	250000	35000000						50	13.49

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T09:19:01

Oliver Kruse

GTX-0

11436311683066894817

A9F45B8B1C65F1__

2017-10-25T00:13:15

kkmrkkblmbrbk

c4.xlarge

11436311683066894817

A9F45B8B1C65F1__

2018-09-28T18:31:52

camaju

Lenovo-L470

11436311683066894817

257853853668800338647463

7CF42F831F111B__

2018-09-28T18:44:39

ANONYMOUS

11436311683066894817

257853853668800338647463

7CF42F831F111B__

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 = 225000 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

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