M5032427 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	5.9045	65.6716%	-	-	-	-	5.9045	65.6716%	0.0000%
PrimeNet	2⁶¹	0.0610	62.2951%	22000	450000	0.0091	3.3168%	0.0701	63.5457%	1.2506%
GPU72	2⁶⁵	1.4497	64.6154%	34000	700000	0.0141	2.4186%	1.4639	65.4712%	0.8558%
Difference	+2	+4.4548	+1.0563%	-34000	-700000	-0.0141	-2.4186%	+4.4406	+0.2004%	+0.2004%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

5.9045

65.6716%

5.9045

65.6716%

0.0000%

PrimeNet

2⁶¹

0.0610

62.2951%

22000

450000

0.0091

3.3168%

0.0701

63.5457%

1.2506%

GPU72

2⁶⁵

1.4497

64.6154%

34000

700000

0.0141

2.4186%

1.4639

65.4712%

0.8558%

Difference

+4.4548

+1.0563%

-34000

-700000

-0.0141

-2.4186%

+4.4406

+0.2004%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5032427	885707153	9	29.722	88 2³ × 11	-	8	11	1.448e-11	1.641e-6	3.272e-6
5032427	35881204511	11	35.063	3565 5 × 23 × 31	2008-09-08	23	31	1.611e-9	4.710e-6	9.408e-6
5032427	6077833593012161	16	52.432	603867040 2⁵ × 5 × 7 × 539167	2014-08-09	32	539167	0.0001	0.0059	0.0110
5032427	1172846182366220966951	22	69.991	116528881826425 5² × 41 × 113686713977	2019-09-28	41	113686713977	24.469	1,244.9	2,325.1

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5032427

885707153

29.722

88
2³ × 11

1.448e-11

1.641e-6

3.272e-6

5032427

35881204511

35.063

3565
5 × 23 × 31

2008-09-08

1.611e-9

4.710e-6

9.408e-6

5032427

6077833593012161

52.432

603867040
2⁵ × 5 × 7 × 539167

2014-08-09

539167

0.0001

0.0059

0.0110

5032427

1172846182366220966951

69.991

116528881826425
5² × 41 × 113686713977

2019-09-28

113686713977

24.469

1,244.9

2,325.1

exponent	prime factors	composite factor	digits	bits*
5032427	885707153 35881204511	31780239493648567183	20	64.785
5032427	885707153 6077833593012161	5383180688074561813687633	25	82.155
5032427	35881204511 6077833593012161	218079990134695289351058271	27	87.495
5032427	885707153 1172846182366220966951	1038798253090504376007077300503	31	99.713
5032427	35881204511 1172846182366220966951	42083133729427976413385003115961	32	105.053
5032427	885707153 35881204511 6077833593012161	193155007188469051253637038744512463	36	117.217
5032427	6077833593012161 1172846182366220966951	7128363926621485003819486198122091111	37	122.423
5032427	885707153 35881204511 1172846182366220966951	37273332564809925307650382202733946169033	41	134.775
5032427	885707153 6077833593012161 1172846182366220966951	6313642918995816391365151246461511264330416983	46	152.145
5032427	35881204511 6077833593012161 1172846182366220966951	255774283879940500708566600401760615300766201721	48	157.485
5032427	885707153 35881204511 6077833593012161 1172846182366220966951	22654111278591589469197900635273205076556987124493 0610313	57	187.208

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2014-08-09T10:23:00	ANONYMOUS	Manual testing	?	?	6077833593012161	52.432	16	1.80635e-5	1.480	3.83162e-5
2008-09-08T00:22:00	Will Edgington	Manual testing	?	?	35881204511	35.063	11	7.01865e-10	1.480	1.48903e-9

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	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	1172846182366220966951	3	0.632

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2019-09-28T11:16:18	ATH	ec2-ECMCF	50000	5000000	1172846182366220966951	69.991	3	2	2113142836148344	3	0.632

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-23T01:52:28

Oliver Kruse

GTX-0

885707153

35881204511

6077833593012161

0D042F4BC539C5__

2018-01-16T08:03:18

kkmrkkblmbrbk

c4.xlarge

885707153

35881204511

6077833593012161

0D042F4BC539C5__

2019-10-03T13:17:55

roemer2201

ws-rebentrost-o

885707153

35881204511

6077833593012161

1172846182366220966951

0D042F4BC539C51C

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

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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