M1745693 Mersenne number exponent details

Residue

Status

L-L

AE38E8A667B28EED

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	17.0213	68.6567%	2475400	86660000	0.5555	7.9493%	17.5768	71.1483%	2.4916%
PrimeNet	2⁵⁷	0.0110	63.1579%	8000	140000	0.0012	2.8012%	0.0122	64.1899%	1.0320%
GPU72	2⁶¹	0.1760	65.5738%	8000	110000	0.0011	1.4119%	0.1770	66.0598%	0.4861%
Difference	+6	+16.8453	+3.0829%	+2467400	+86550000	+0.5544	+6.5373%	+17.3998	+5.0884%	+5.0884%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.0213

68.6567%

2475400

86660000

0.5555

7.9493%

17.5768

71.1483%

2.4916%

PrimeNet

2⁵⁷

0.0110

63.1579%

8000

140000

0.0012

2.8012%

0.0122

64.1899%

1.0320%

GPU72

2⁶¹

0.1760

65.5738%

8000

110000

0.0011

1.4119%

0.1770

66.0598%

0.4861%

Difference

+16.8453

+3.0829%

+2467400

+86550000

+0.5544

+6.5373%

+17.3998

+5.0884%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1745693	4493774300176519823273	22	71.928	1287103259329252 2² × 631 × 509945823823	2016-03-13	631	509945823823	437.05	2,185.5	4,081.9

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1745693

4493774300176519823273

71.928

1287103259329252
2² × 631 × 509945823823

2016-03-13

631

509945823823

437.05

2,185.5

4,081.9

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-10T16:23:00	Carsten Kossendey	leela	95000	1543750		-		-	-	0.014	-	-	2.401%
2014-04-05T13:21:00	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.008	-	-	0.887%
2014-05-06T10:53:00	Jocelyn Larouche	Manual testing	136767	136767		-		-	-	0.011	-	-	1.059%
2014-09-15T22:12:00	ANONYMOUS	Manual testing	173534	173534		-		-	-	0.014	-	-	1.203%
2015-04-19T17:08:00	mikr	MSI	2475400	86660000		-		-	-	0.556	-	-	7.949%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.011	-	-
2003-02-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.022	-	-
2016-02-23T16:28:49	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.066	-	-
2010-04-18T22:56:00	Architects Cubed	m1_fw	2⁶⁰	2⁶¹		-	-	0.088	-	-
2016-02-23T16:28:49	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.176	-	-
2011-01-21T16:10:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.914	-	-
2016-02-23T16:28:49	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.562	-	-
2015-05-12T21:20:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.125	-	-
2015-05-12T21:20:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.140	-	-
2015-09-04T17:59:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.281	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.453 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:	17.453 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		253	17.38
50000	5000000	4493774300176519823273	1	0.069

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-21T22:11:00	Scott Kurowski	UW1	50000	5000000						3	0.206
2009-06-26T12:35:00	Piepen	T41-2000	50000	5000000						3	0.206
2010-11-27T02:08:00	JudgeGabranth	Midgardsormr	50000	5000000						3	0.206
2011-12-26T06:03:00	S36049	Wolle5	50000	5000000						3	0.206
2013-05-15T22:12:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2014-02-13T03:52:00	Bruce	snowflake	50000	5000000						3	0.206
2014-12-16T22:27:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2015-08-04T10:08:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2015-12-21T18:37:52	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2016-03-13T03:30:12	Chang Chia-Tche	exbpc13	50000	5000000	4493774300176519823273	71.928	1	2		1	0.069
2020-07-25T04:06:44	Ahmed Azhad	c5.4xlarge.azf	50000	5000000						3	0.206
2020-07-27T11:05:31	TJAOI	Manual testing	50000	5000000						223	15.32

date	userid	compid	res64	spent (GHz-days)
1998-11-28T00:00:00	ANONYMOUS	v4_computers	AE38E8A667B28EED	0.095
2015-06-27T00:56:00	MadPoo	Manual testing	AE38E8A667B28EED	0.095

date

userid

compid

res64

spent (GHz-days)

1998-11-28T00:00:00

ANONYMOUS

v4_computers

AE38E8A667B28EED

0.095

2015-06-27T00:56:00

MadPoo

Manual testing

AE38E8A667B28EED

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 = 2475400, B2 = 86660000 (P-1 stage 2)

B1 = 2475400 (P-1 stage 1)

B1 = 95000, B2 = 1543750 (P-1 stage 2)

B1 = 173534 (P-1 stage 1)

B1 = 136767 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 95000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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