M2557201 Mersenne number exponent details

Residue

Status

L-L

4317E88E007CA2F6

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	11.6197	67.1642%	2000000	60000000	0.5190	7.6649%	12.1387	69.6810%	2.5168%
PrimeNet	2⁵⁹	0.0300	62.7119%	11000	200000	0.0021	2.6867%	0.0322	63.7137%	1.0018%
GPU72	2⁶³	0.6241	65.0794%	12000	180000	0.0021	1.4789%	0.6263	65.5958%	0.5164%
Difference	+4	+10.9956	+2.0848%	+1988000	+59820000	+0.5168	+6.1861%	+11.5124	+4.0852%	+4.0852%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

11.6197

67.1642%

2000000

60000000

0.5190

7.6649%

12.1387

69.6810%

2.5168%

PrimeNet

2⁵⁹

0.0300

62.7119%

11000

200000

0.0021

2.6867%

0.0322

63.7137%

1.0018%

GPU72

2⁶³

0.6241

65.0794%

12000

180000

0.0021

1.4789%

0.6263

65.5958%

0.5164%

Difference

+10.9956

+2.0848%

+1988000

+59820000

+0.5168

+6.1861%

+11.5124

+4.0852%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2557201	8036689788175280968447	22	72.767	1571384061748623 3 × 479 × 8017 × 136399787	2009-02-15	8017	136399787	714.26	0.7482	1.3959
2557201	108485317997166505207616833	27	86.488	21211730715959853216 2⁵ × 3 × 7 × 17 × 193 × 922309 × 10430957	2018-12-29	922309	10430957	12,145,313	0.1449	0.1888

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2557201

8036689788175280968447

72.767

1571384061748623
3 × 479 × 8017 × 136399787

2009-02-15

8017

136399787

714.26

0.7482

1.3959

2557201

108485317997166505207616833

86.488

21211730715959853216
2⁵ × 3 × 7 × 17 × 193 × 922309 × 10430957

2018-12-29

922309

10430957

12,145,313

0.1449

0.1888

exponent	prime factors	composite factor	digits	bits*
2557201	8036689788175280968447 108485317997166505207616833	871862847314776076938527125022702951289139068351	48	159.255

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-23T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.293%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	198750		-		-	-	0.003	-	-	0.885%
2018-12-29T19:54:30	alpertron	laptop2	2000000	60000000	12		108485317997166505207616833	27	86.488	0.519	0.355	1.038	7.665%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.030	-	-
2022-03-11T02:05:00	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.060	-	-
2009-02-01T17:10:00	Sturle Sunde	korsmo.ifi	2⁶⁰	2⁶¹		-	-	0.060	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.277 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:	0.277 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
		8036689788175280968447	1	0.00000e+0
50000	5000000		3	0.277

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-15T23:51:00	SubPrime	dijkstra			8036689788175280968447	72.767		1		1	-
2018-11-15T02:00:16	rucio		50000	5000000						3	0.277

date	userid	compid	res64	spent (GHz-days)
1999-03-26T00:00:00	ANONYMOUS	v4_computers	4317E88E007CA2F6	0.177

date

userid

compid

res64

spent (GHz-days)

1999-03-26T00:00:00

ANONYMOUS

v4_computers

4317E88E007CA2F6

0.177

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-14T23:01:16

Oliver Kruse

GTX-3

15890FB915377E__

2017-12-01T15:17:44

kkmrkkblmbrbk

c4.xlarge

8036689788175280968447

15890FB915377E__

2018-12-30T03:08:18

Oliver Kruse

GTX-5

8036689788175280968447

108485317997166505207616833

15890FB915377EEF

2018-12-30T14:59:18

Daniil Tsarkov

tsar1

8036689788175280968447

108485317997166505207616833

15890FB915377EEF

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 = 2000000, B2 = 60000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 15000, B2 = 198750 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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