M2175577 Mersenne number exponent details

Residue

Status

L-L

6A0CC54F7D73D8B8

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	13.6579	67.1642%	500000	15000000	0.1230	5.1751%	13.7809	68.8635%	1.6993%
PrimeNet	2⁵⁸	0.0176	62.0690%	10000	180000	0.0018	2.8572%	0.0195	63.1527%	1.0838%
GPU72	2⁶²	0.2824	64.5161%	11000	160000	0.0018	1.5681%	0.2842	65.0726%	0.5564%
Difference	+5	+13.3756	+2.6481%	+489000	+14840000	+0.1212	+3.6070%	+13.4967	+3.7909%	+3.7909%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.6579

67.1642%

500000

15000000

0.1230

5.1751%

13.7809

68.8635%

1.6993%

PrimeNet

2⁵⁸

0.0176

62.0690%

10000

180000

0.0018

2.8572%

0.0195

63.1527%

1.0838%

GPU72

2⁶²

0.2824

64.5161%

11000

160000

0.0018

1.5681%

0.2842

65.0726%

0.5564%

Difference

+13.3756

+2.6481%

+489000

+14840000

+0.1212

+3.6070%

+13.4967

+3.7909%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2175577	9459987647797467232919	22	73.002	2174133034086467 157 × 13847981108831	2009-12-05	157	13847981108831	1,390.6	71,930	134,345

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2175577

9459987647797467232919

73.002

2174133034086467
157 × 13847981108831

2009-12-05

157

13847981108831

1,390.6

71,930

134,345

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.280%
2016-03-16T13:46:03	alpertron	Manual testing	500000	15000000	12	-		-	-	0.123	-	-	5.175%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2000-04-05T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2002-09-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2022-03-09T16:35:57	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.071	-	-
2009-01-04T17:49:00	Sturle Sunde	antonov.ifi	2⁶⁰	2⁶¹		-	-	0.071	-	-
2009-01-06T20:56:00	Sturle Sunde	gonsha.ifi	2⁶¹	2⁶²		-	-	0.141	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.516 GHz-days
Estimated T-Level:	0.850

Digits	B1	Curves	Complete	FacMiss
20	11000	17 / 100	0.170	84.294%
25	50000	17 / 280	0.061	94.099%

New Calculation Method

Total ECM effort:	1.516 GHz-days
Estimated T-Level:	0.850

Digits	B1	Complete	FacMiss
20	11000	0.665	51.447%
25	50000	0.062	93.988%
30	250000	0.004	99.609%

ECM Summary

B1	B2	factor	curves	GHz-days
		9459987647797467232919	1	0.00000e+0
50000	5000000		10	0.855
50000	6276980		7	0.661

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-03T23:22:00	bayanne	MacBook	50000	5000000						3	0.256
2009-12-05T02:18:00	James Hintz	ryan			9459987647797467232919	73.002		1		1	-
2022-03-20T22:04:07	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.598
2022-06-13T01:38:18	debrouxl	dl380g9-1	50000	6276980						7	0.661

date	userid	compid	res64	spent (GHz-days)
1999-02-07T00:00:00	Dry Creek Photo	v4_computers	6A0CC54F7D73D8B8	0.143

date

userid

compid

res64

spent (GHz-days)

1999-02-07T00:00:00

Dry Creek Photo

v4_computers

6A0CC54F7D73D8B8

0.143

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-09T16:42:47

kkmrkkblmbrbk

old

9459987647797467232919

0EA83B92C45328__

2017-10-23T02:49:40

Oliver Kruse

GTX-3

9459987647797467232919

0EA83B92C45328__

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

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

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