M1752827 Mersenne number exponent details

Residue

Status

L-L

9A8AE775341BAD47

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	16.9520	68.6567%	3642200	123456789	0.8000	8.6369%	17.7520	71.3638%	2.7071%
PrimeNet	2⁵⁷	0.0110	63.1579%	8000	140000	0.0012	2.8033%	0.0121	64.1907%	1.0328%
GPU72	2⁶¹	0.1752	65.5738%	8000	110000	0.0011	1.4131%	0.1763	66.0603%	0.4865%
Difference	+6	+16.7767	+3.0829%	+3634200	+123346789	+0.7989	+7.2237%	+17.5757	+5.3035%	+5.3035%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.9520

68.6567%

3642200

123456789

0.8000

8.6369%

17.7520

71.3638%

2.7071%

PrimeNet

2⁵⁷

0.0110

63.1579%

8000

140000

0.0012

2.8033%

0.0121

64.1907%

1.0328%

GPU72

2⁶¹

0.1752

65.5738%

8000

110000

0.0011

1.4131%

0.1763

66.0603%

0.4865%

Difference

+16.7767

+3.0829%

+3634200

+123346789

+0.7989

+7.2237%

+17.5757

+5.3035%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1752827	274812659905629876143	21	67.897	78391267337173 7 × 11198752476739	2015-12-28	7	11198752476739	32.946	47,995	89,641

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1752827

274812659905629876143

67.897

78391267337173
7 × 11198752476739

2015-12-28

11198752476739

32.946

47,995

89,641

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-08T16:01:00	Carsten Kossendey	leela	95000	1567500		-		-	-	0.014	-	-	2.411%
2014-04-08T23:00:00	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.008	-	-	0.888%
2014-05-06T21:04:00	Jocelyn Larouche	Manual testing	136618	136618		-		-	-	0.011	-	-	1.059%
2014-09-16T20:52:00	ANONYMOUS	Manual testing	173236	173236		-		-	-	0.014	-	-	1.202%
2015-04-24T23:12:00	Squeeky_Squirrel	P4_2600	130000	3640000		-		-	-	0.025	-	-	3.107%
2015-06-30T22:30:00	mikr	MSI	3642200	123456789		-		-	-	0.800	-	-	8.637%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.022	-	-
2016-02-23T16:28:50	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.066	-	-
2010-04-20T15:50:00	Architects Cubed	i4l_1	2⁶⁰	2⁶¹		-	-	0.088	-	-
2016-02-23T16:28:50	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.175	-	-
2010-12-13T03:32:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.911	-	-
2016-02-23T16:28:50	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.560	-	-
2015-05-13T21:10:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.120	-	-
2015-05-13T21:10:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.132	-	-
2015-09-05T13:49:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.263	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.460 GHz-days
Estimated T-Level:	24.536

Digits	B1	Curves	Complete	FacMiss
20	11000	254 / 100	2.540	7.786%
25	50000	254 / 280	0.907	40.302%

New Calculation Method

Total ECM effort:	17.460 GHz-days
Estimated T-Level:	24.536

Digits	B1	Complete	FacMiss
20	11000	8.194	0.028%
25	50000	0.741	47.686%
30	250000	0.046	95.542%
35	1000000	0.002	99.791%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		252	17.32
50000	5000000	274812659905629876143	2	0.137

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-27T00:41:00	paulie	iMac3.4	50000	5000000						3	0.206
2009-06-26T10:28:00	Lupo	yorick	50000	5000000						3	0.206
2010-08-23T21:38:00	James Classen	towerofart	50000	5000000						3	0.206
2012-01-11T11:08:00	OS1	L3	50000	5000000						3	0.206
2013-05-21T23:40:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2014-02-14T21:58:00	Bruce	snowflake	50000	5000000						3	0.206
2014-12-27T16:16:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2015-08-15T20:29:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2015-12-28T21:20:29	Chang Chia-Tche	exbpc13	50000	5000000	274812659905629876143	67.897	2	2		2	0.137
2020-08-07T11:07:14	TJAOI	Manual testing	50000	5000000						225	15.47
2020-08-07T19:08:53	debrouxl	athlon2	50000	5000000						3	0.206

date	userid	compid	res64	spent (GHz-days)
1999-05-09T00:00:00	ANONYMOUS	v4_computers	9A8AE775341BAD47	0.095
2015-07-06T20:15:00	MadPoo	Manual testing	9A8AE775341BAD47	0.095

date

userid

compid

res64

spent (GHz-days)

1999-05-09T00:00:00

ANONYMOUS

v4_computers

9A8AE775341BAD47

0.095

2015-07-06T20:15:00

MadPoo

Manual testing

9A8AE775341BAD47

0.095

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 = 3642200, B2 = 123456789 (P-1 stage 2)

B1 = 3642200 (P-1 stage 1)

B1 = 130000, B2 = 3640000 (P-1 stage 2)

B1 = 95000, B2 = 1567500 (P-1 stage 2)

B1 = 173236 (P-1 stage 1)

B1 = 136618 (P-1 stage 1)

B1 = 130000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 95000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

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