M1705051 Mersenne number exponent details

Residue

Status

L-L

128F42021723F2C8

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	17.4270	68.6567%	500000	15000000	0.0880	5.0255%	17.5150	70.2319%	1.5752%
PrimeNet	2⁵⁷	0.0113	63.1579%	8000	130000	0.0010	2.7328%	0.0123	64.1647%	1.0068%
GPU72	2⁶¹	0.1802	65.5738%	7000	100000	0.0008	1.3021%	0.1810	66.0220%	0.4483%
Difference	+6	+17.2468	+3.0829%	+493000	+14900000	+0.0872	+3.7234%	+17.3340	+4.2098%	+4.2098%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.4270

68.6567%

500000

15000000

0.0880

5.0255%

17.5150

70.2319%

1.5752%

PrimeNet

2⁵⁷

0.0113

63.1579%

8000

130000

0.0010

2.7328%

0.0123

64.1647%

1.0068%

GPU72

2⁶¹

0.1802

65.5738%

7000

100000

0.0008

1.3021%

0.1810

66.0220%

0.4483%

Difference

+17.2468

+3.0829%

+493000

+14900000

+0.0872

+3.7234%

+17.3340

+4.2098%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1705051	899625336683566214119	21	69.608	263811855681609 3 × 37 × 2376683384519	2014-01-08	37	2376683384519	99.298	8,836.4	16,504

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1705051

899625336683566214119

69.608

263811855681609
3 × 37 × 2376683384519

2014-01-08

2376683384519

99.298

8,836.4

16,504

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-01-29T02:00:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.003	-	-	0.571%
2011-02-01T09:15:00	Carsten Kossendey	leela	90000	1507500		-		-	-	0.011	-	-	2.353%
2016-03-16T12:29:45	alpertron	Manual testing	500000	15000000	12	-		-	-	0.088	-	-	5.026%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-28T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.011	-	-
1999-03-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.011	-	-
2003-02-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.023	-	-
2022-03-08T23:06:23	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.068	-	-
2010-04-20T22:46:00	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.090	-	-
2010-10-16T22:16:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.936	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.984 GHz-days
Estimated T-Level:	24.500

Digits	B1	Curves	Complete	FacMiss
20	11000	252 / 100	2.520	7.945%
25	50000	252 / 280	0.900	40.592%

New Calculation Method

Total ECM effort:	14.984 GHz-days
Estimated T-Level:	24.500

Digits	B1	Complete	FacMiss
20	11000	8.129	0.029%
25	50000	0.735	47.965%
30	250000	0.045	95.577%
35	1000000	0.002	99.793%

ECM Summary

B1	B2	factor	curves	GHz-days
		899625336683566214119	1	0.00000e+0
50000	5000000		252	14.98

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-08-26T22:24:00	paulie	iMac3.4	50000	5000000						3	0.178
2009-06-18T15:54:00	James Hintz	08_060209	50000	5000000						3	0.178
2010-10-21T03:48:00	NeoGen	MMC	50000	5000000						3	0.178
2011-11-19T23:26:00	Bud	annan	50000	5000000						3	0.178
2013-04-20T10:47:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2014-01-08T20:36:00	Chang Chia-Tche	exbpc13			899625336683566214119	69.608		1		1	-
2020-02-29T07:31:46	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-03-09T11:17:25	TJAOI	Manual testing	50000	5000000						234	13.91

date	userid	compid	res64	spent (GHz-days)
1999-01-29T00:00:00	ANONYMOUS	v4_computers	128F42021723F2C8	0.080
1999-03-26T00:00:00	ANONYMOUS	v4_computers	128F42021723F2C8	0.080

date

userid

compid

res64

spent (GHz-days)

1999-01-29T00:00:00

ANONYMOUS

v4_computers

128F42021723F2C8

0.080

1999-03-26T00:00:00

ANONYMOUS

v4_computers

128F42021723F2C8

0.080

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 = 90000, B2 = 1507500 (P-1 stage 2)

B1 = 90000 (P-1 stage 1)

B1 = 50000 (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