M1550663 Mersenne number exponent details

Residue

Status

L-L

5EB8351823737694

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	19.1621	68.6567%	10000000	200000000	1.3181	9.7242%	20.4802	71.7046%	3.0479%
PrimeNet	2⁵⁷	0.0124	63.1579%	6500	110000	0.0008	2.4207%	0.0132	64.0497%	0.8918%
GPU72	2⁶¹	0.1981	65.5738%	6500	60000	0.0006	1.0490%	0.1987	65.9349%	0.3611%
Difference	+6	+18.9640	+3.0829%	+9993500	+199940000	+1.3175	+8.6752%	+20.2815	+5.7697%	+5.7697%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

19.1621

68.6567%

10000000

200000000

1.3181

9.7242%

20.4802

71.7046%

3.0479%

PrimeNet

2⁵⁷

0.0124

63.1579%

6500

110000

0.0008

2.4207%

0.0132

64.0497%

0.8918%

GPU72

2⁶¹

0.1981

65.5738%

6500

60000

0.0006

1.0490%

0.1987

65.9349%

0.3611%

Difference

+18.9640

+3.0829%

+9993500

+199940000

+1.3175

+8.6752%

+20.2815

+5.7697%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1550663	9123147198859133967017	22	72.950	2941692424098316 2² × 7 × 401 × 261996118997	2016-03-02	401	261996118997	642.89	924.50	1,726.7

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1550663

9123147198859133967017

72.950

2941692424098316
2² × 7 × 401 × 261996118997

2016-03-02

401

261996118997

642.89

924.50

1,726.7

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-29T00:00:00	Team Prime Rib	v4_computers	20000	290000		-		-	-	0.002	-	-	0.994%
2011-02-04T15:52:00	James Heinrich	WHS	80000	1360000		-		-	-	0.010	-	-	2.206%
2013-12-08T16:21:00	David Campeau	i5-2500k	945000	27405000		-		-	-	0.155	-	-	5.948%
2015-03-25T10:09:00	VictordeHollander	Manual testing	10000000	200000000		-		-	-	1.318	-	-	9.724%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-10-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.012	-	-
2003-08-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.025	-	-
2016-02-23T16:28:38	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.074	-	-
2010-04-29T06:30:00	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.099	-	-
2016-02-23T16:28:38	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.198	-	-
2010-06-10T15:34:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	1.029	-	-
2016-02-23T16:28:38	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.633	-	-
2015-02-16T03:59:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.266	-	-
2015-02-16T03:59:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.410	-	-
2015-10-11T16:52:55	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.819	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.029 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	14.029 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.097	0.030%
25	50000	0.732	48.105%
30	250000	0.045	95.594%
35	1000000	0.002	99.794%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		248	13.86
50000	5000000	9123147198859133967017	3	0.168

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-02-29T07:47:00	Sturle Sunde	lara	50000	5000000						3	0.168
2009-04-20T17:45:00	Lupo	yorick	50000	5000000						3	0.168
2010-02-23T07:09:00	SubPrime	stor	50000	5000000						3	0.168
2011-05-28T19:34:00	Brian V.	sydt4300	50000	5000000						3	0.168
2012-11-21T16:44:00	Donna Noble	PH2x6	50000	5000000						3	0.168
2013-09-23T01:01:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.168
2014-03-27T18:52:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.168
2015-01-25T02:09:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.168
2015-07-26T10:11:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.168
2015-12-12T12:40:42	Bruce	Desk7	50000	5000000						3	0.168
2016-03-02T12:43:57	Bruce	DESK3	50000	5000000	9123147198859133967017	72.950	3	2		3	0.168
2019-07-12T08:38:06	TJAOI	Manual testing	50000	5000000						218	12.18

date	userid	compid	res64	spent (GHz-days)
1998-11-07T00:00:00	ANONYMOUS	v4_computers	5EB8351823737694	0.069
2015-07-20T22:07:00	MadPoo	Manual testing	5EB8351823737694	0.069

date

userid

compid

res64

spent (GHz-days)

1998-11-07T00:00:00

ANONYMOUS

v4_computers

5EB8351823737694

0.069

2015-07-20T22:07:00

MadPoo

Manual testing

5EB8351823737694

0.069

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 = 10000000, B2 = 200000000 (P-1 stage 2)

B1 = 10000000 (P-1 stage 1)

B1 = 945000, B2 = 27405000 (P-1 stage 2)

B1 = 945000 (P-1 stage 1)

B1 = 80000, B2 = 1360000 (P-1 stage 2)

B1 = 80000 (P-1 stage 1)

B1 = 20000, B2 = 290000 (P-1 stage 2)

B1 = 20000 (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