M1268713 Mersenne number exponent details

Residue

Status

L-L

608EA569FF9A0CD0

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	23.4205	68.6567%	4178000	4178000	0.1920	4.0675%	23.6125	69.9316%	1.2749%
PrimeNet	2⁵⁶	0.0076	62.5000%	5500	90000	0.0005	2.4437%	0.0080	63.4164%	0.9164%
GPU72	2⁶⁰	0.1211	65.0000%	5500	36000	0.0003	0.9297%	0.1214	65.3254%	0.3254%
Difference	+7	+23.2995	+3.6567%	+4172500	+4142000	+0.1917	+3.1378%	+23.4911	+4.6062%	+4.6062%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

23.4205

68.6567%

4178000

0.1920

4.0675%

23.6125

69.9316%

1.2749%

PrimeNet

2⁵⁶

0.0076

62.5000%

5500

90000

0.0005

2.4437%

0.0080

63.4164%

0.9164%

GPU72

2⁶⁰

0.1211

65.0000%

5500

36000

0.0003

0.9297%

0.1214

65.3254%

0.3254%

Difference

+23.2995

+3.6567%

+4172500

+4142000

+0.1917

+3.1378%

+23.4911

+4.6062%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1268713	65221148669116950932820161	26	85.754	25703665316394232160 2⁵ × 5 × 7² × 17 × 1171 × 380713 × 432589	2015-02-16	380713	432589	11,416,481	0.0176	0.0356

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1268713

65221148669116950932820161

85.754

25703665316394232160
2⁵ × 5 × 7² × 17 × 1171 × 380713 × 432589

2015-02-16

380713

432589

11,416,481

0.0176

0.0356

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-24T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.239%
2003-12-31T00:00:00	eteo	v4_computers	200000	5000000		-		-	-	0.021	-	-	3.421%
2014-09-30T23:23:00	Jocelyn Larouche	Manual testing	250590	250590		-		-	-	0.012	-	-	1.373%
2015-02-16T05:20:00	mikr	MSI	4178000	4178000			65221148669116950932820161	26	85.754	0.192	0.080	0.384	4.068%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-10T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.015	-	-
2003-06-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.030	-	-
2022-03-07T17:32:04	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.091	-	-
2009-02-16T02:30:00	Sturle Sunde	gouache.ifi	2⁶⁰	2⁶¹		-	-	0.121	-	-
2012-09-14T18:00:00	Axelsson	Manual testing	2⁶¹	2⁶²		-	-	0.242	-	-
2012-10-13T12:00:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.774	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.256 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	301 / 100	3.010	4.855%
25	50000	301 / 280	1.075	34.064%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	19.256 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.263	0.000%
25	50000	1.334	26.337%
30	250000	0.110	89.576%
35	1000000	0.007	99.255%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		251	9.65
250000	25000000		50	9.61

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-11-25T04:13:00	Andi47	Core2Duo	50000	5000000						1	0.038
2007-11-25T16:40:00	Andi47	Core2Duo	50000	5000000						1	0.038
2007-11-28T18:57:00	Andi47	Core2Duo	50000	5000000						1	0.038
2009-01-05T18:42:00	Sturle Sunde	v23	50000	5000000						3	0.115
2009-05-30T22:40:00	Lukasz Wrobel	WORKER-1	50000	5000000						3	0.115
2009-09-18T18:53:00	Lupo	yorick	50000	5000000						3	0.115
2010-01-28T21:29:00	James Hintz	paden	50000	5000000						3	0.115
2010-10-22T16:21:00	Charles A. Morris	magnetar	50000	5000000						3	0.115
2011-04-28T13:56:00	unconnected	can-01	50000	5000000						3	0.115
2012-04-05T17:34:00	Scott Kurowski	DM6400	50000	5000000						3	0.115
2012-09-25T19:07:00	OS1	Tina	50000	5000000						3	0.115
2013-07-13T04:38:00	zampel	dufay	50000	5000000						3	0.115
2014-01-15T02:28:00	jim f in mn	asus	50000	5000000						3	0.115
2014-03-08T12:25:00	Bruce	snowflake	50000	5000000						3	0.115
2014-08-05T22:02:00	OS1	Tina	50000	5000000						3	0.115
2018-01-05T12:42:19	TJAOI	Manual testing	50000	5000000						212	8.148
2021-03-05T18:06:39	TJAOI	Manual testing	250000	25000000						50	9.61

date	userid	compid	res64	spent (GHz-days)
2002-08-31T00:00:00	ANONYMOUS	v4_computers	608EA569FF9A0CD0	0.040

date

userid

compid

res64

spent (GHz-days)

2002-08-31T00:00:00

ANONYMOUS

v4_computers

608EA569FF9A0CD0

0.040

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 = 4178000 (P-1 stage 1)

B1 = 200000, B2 = 5000000 (P-1 stage 2)

B1 = 250590 (P-1 stage 1)

B1 = 200000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

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