M1928207 Mersenne number exponent details

Residue

Status

L-L

5C712485B8EC2407

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	15.4101	68.6567%	500000	15000000	0.1015	5.1006%	15.5116	70.2554%	1.5987%
PrimeNet	2⁵⁷	0.0100	63.1579%	9000	170000	0.0014	3.0953%	0.0114	64.2983%	1.1404%
GPU72	2⁶¹	0.1593	65.5738%	11000	170000	0.0015	1.8145%	0.1609	66.1984%	0.6247%
Difference	+6	+15.2508	+3.0829%	+489000	+14830000	+0.0999	+3.2861%	+15.3507	+4.0570%	+4.0570%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.4101

68.6567%

500000

15000000

0.1015

5.1006%

15.5116

70.2554%

1.5987%

PrimeNet

2⁵⁷

0.0100

63.1579%

9000

170000

0.0014

3.0953%

0.0114

64.2983%

1.1404%

GPU72

2⁶¹

0.1593

65.5738%

11000

170000

0.0015

1.8145%

0.1609

66.1984%

0.6247%

Difference

+15.2508

+3.0829%

+489000

+14830000

+0.0999

+3.2861%

+15.3507

+4.0570%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1928207	152596530979779280317151	24	77.014	39569540765016225 3 × 5² × 13327 × 39588345229	2022-02-17	13327	39588345229	22,626	169.67	316.89
1928207	2511680180800080268926719	25	81.055	651299414637557137 651299414637557137	2016-03-10	1	651299414637557137	384,659	2.791e+9	5.213e+9

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1928207

152596530979779280317151

77.014

39569540765016225
3 × 5² × 13327 × 39588345229

2022-02-17

13327

39588345229

22,626

169.67

316.89

1928207

2511680180800080268926719

81.055

651299414637557137
651299414637557137

2016-03-10

651299414637557137

384,659

2.791e+9

5.213e+9

exponent	prime factors	composite factor	digits	bits*
1928207	152596530979779280317151 2511680180800080268926719	383273682520757072690838494537223371952697857569	48	158.069

exponent

prime factors

composite factor

digits

bits*

1928207

152596530979779280317151
2511680180800080268926719

383273682520757072690838494537223371952697857569

158.069

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2004-05-11T00:00:00	ANONYMOUS	v4_computers	300000	9000000		-		-	-	0.061	-	-	4.332%
2015-10-08T07:30:07	Bruno Victal	5820K-linux	500000	15000000	12	-		-	-	0.101	-	-	5.101%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2004-05-11T00:00:00

ANONYMOUS

v4_computers

300000

9000000

0.061

-

-

4.332%

2015-10-08T07:30:07

Bruno Victal

5820K-linux

500000

15000000

0.101

-

-

5.101%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2002-12-09T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.020	-	-
2016-02-23T16:28:58	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.060	-	-
2010-02-09T00:19:00	S485122	USB-W	2⁶⁰	2⁶¹		-	-	0.080	-	-
2016-02-23T16:28:58	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.159	-	-
2011-08-27T22:21:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.828	-	-
2016-02-23T16:28:58	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.509	-	-
2015-05-17T23:04:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.018	-	-
2015-05-17T23:04:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	1.938	-	-
2015-09-03T11:06:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.875	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.900 GHz-days
Estimated T-Level:	24.589

Digits	B1	Curves	Complete	FacMiss
20	11000	257 / 100	2.570	7.555%
25	50000	257 / 280	0.918	39.872%

New Calculation Method

Total ECM effort:	19.900 GHz-days
Estimated T-Level:	24.589

Digits	B1	Complete	FacMiss
20	11000	8.804	0.015%
25	50000	0.797	45.050%
30	250000	0.049	95.186%
35	1000000	0.002	99.773%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		28	1.946
50000	5000000	2511680180800080268926719	2	0.139
50000	6600000		168	13.17
50000	6600000	152596530979779280317151	45	3.529
50000	6750000		7	0.555
50000	6856613		7	0.559

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-11-12T15:45:00	dachshund	Ann	50000	5000000						3	0.208
2009-08-14T17:01:00	Conductor	home	50000	5000000						3	0.208
2010-12-13T02:56:00	Lupo	yorick	50000	5000000						3	0.208
2012-11-15T10:51:00	Lukasz Wrobel	i-1	50000	5000000						3	0.208
2013-12-07T15:28:00	arnaud	srv-630	50000	5000000						3	0.208
2015-04-02T15:16:00	Sara	Sara	50000	5000000						3	0.208
2015-09-25T21:47:21	Chris Smith	starcraft2	50000	5000000						3	0.208
2016-03-10T19:55:02	Bruce	Desk6	50000	5000000	2511680180800080268926719	81.055	2	2		2	0.139
2021-07-09T21:58:10	rushyn	linux	50000	5000000						7	0.486
2021-09-22T10:45:05	Dylan Delgado	colab	50000	6750000						7	0.555
2022-02-04T12:14:45	carlos56	febrero2022	50000	6856613						7	0.559
2022-02-17T11:37:43	TJAOI	Manual testing	50000	6600000	152596530979779280317151	77.014	45	2		45	3.529
2022-02-17T11:37:43	TJAOI	Manual testing	50000	6600000						168	13.17

date	userid	compid	res64	spent (GHz-days)
1999-01-17T00:00:00	ANONYMOUS	v4_computers	5C712485B8EC2407	0.105
2015-07-01T17:35:00	MadPoo	Manual testing	5C712485B8EC2407	0.105

date

userid

compid

res64

spent (GHz-days)

1999-01-17T00:00:00

ANONYMOUS

v4_computers

5C712485B8EC2407

0.105

2015-07-01T17:35:00

MadPoo

Manual testing

5C712485B8EC2407

0.105

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T00:26:08

Oliver Kruse

GTX-2

2511680180800080268926719

FE488C0224CC4E__

2017-11-10T17:39:13

kkmrkkblmbrbk

old

2511680180800080268926719

FE488C0224CC4E__

2022-02-22T07:37:26

LordJulius

WhiteBox

152596530979779280317151

2511680180800080268926719

DD7025A51AB2FC7F

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 = 300000, B2 = 9000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 300000 (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

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

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