M2176171 Mersenne number exponent details

Residue

Status

L-L

9903D3C651CFCD60

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	13.6542	67.1642%	500000	15000000	0.1230	5.1753%	13.7772	68.8635%	1.6993%
PrimeNet	2⁵⁸	0.0176	62.0690%	10000	180000	0.0018	2.8573%	0.0195	63.1528%	1.0838%
GPU72	2⁶²	0.2823	64.5161%	11000	160000	0.0018	1.5682%	0.2841	65.0726%	0.5565%
Difference	+5	+13.3719	+2.6481%	+489000	+14840000	+0.1212	+3.6071%	+13.4931	+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

13.6542

67.1642%

500000

15000000

0.1230

5.1753%

13.7772

68.8635%

1.6993%

PrimeNet

2⁵⁸

0.0176

62.0690%

10000

180000

0.0018

2.8573%

0.0195

63.1528%

1.0838%

GPU72

2⁶²

0.2823

64.5161%

11000

160000

0.0018

1.5682%

0.2841

65.0726%

0.5565%

Difference

+13.3719

+2.6481%

+489000

+14840000

+0.1212

+3.6071%

+13.4931

+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
2176171	1675053184430659249	19	60.539	384862491144 2³ × 3² × 5345312377	2009-01-05	9	5345312377	0.1067	27.765	51.857
2176171	25561685545690607187359	23	74.436	5873087534410349 11 × 67 × 7968911172877	2009-01-04	67	7968911172877	2,088.8	41,393	77,310

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2176171

1675053184430659249

60.539

384862491144
2³ × 3² × 5345312377

2009-01-05

5345312377

0.1067

27.765

51.857

2176171

25561685545690607187359

74.436

5873087534410349
11 × 67 × 7968911172877

2009-01-04

7968911172877

2,088.8

41,393

77,310

exponent	prime factors	composite factor	digits	bits*
2176171	1675053184430659249 25561685545690607187359	42817182772724205348360249578718029233391	41	134.975

exponent

prime factors

composite factor

digits

bits*

2176171

1675053184430659249
25561685545690607187359

42817182772724205348360249578718029233391

134.975

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%
2016-03-15T11:16:43	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
2009-01-05T00:22:00	Sturle Sunde	antonov.ifi	?	?	1675053184430659249	60.539	19	0.036	0.291	0.073
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.577 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:	1.577 GHz-days
Estimated T-Level:	0.850

Digits	B1	Complete	FacMiss
20	11000	0.687	50.306%
25	50000	0.063	93.860%
30	250000	0.004	99.599%

ECM Summary

B1	B2	factor	curves	GHz-days
		25561685545690607187359	1	0.00000e+0
50000	5000000		3	0.256
50000	5450000		7	0.621
50000	7061368		7	0.700

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-04T01:40:00	SubPrime	c2d0			25561685545690607187359	74.436		1		1	-
2018-08-23T05:34:49	ATH	ec2-ECMCF	50000	5000000						3	0.256
2022-03-22T00:25:39	Eric	miniPCWindows	50000	5450000						7	0.621
2022-06-15T21:03:17	debrouxl	o9020	50000	7061368						7	0.700

date	userid	compid	res64	spent (GHz-days)
1999-03-01T00:00:00	ANONYMOUS	v4_computers	9903D3C651CFCD60	0.143

date

userid

compid

res64

spent (GHz-days)

1999-03-01T00:00:00

ANONYMOUS

v4_computers

9903D3C651CFCD60

0.143

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-10T00:11:15

kkmrkkblmbrbk

Manual testing

1675053184430659249

25561685545690607187359

83E1F160ADA642__

2017-10-23T05:45:39

Oliver Kruse

GTX-3

1675053184430659249

25561685545690607187359

83E1F160ADA642__

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)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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