M1799621 Mersenne number exponent details

Residue

Status

L-L

1EBD098081B4751D

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	16.5112	68.6567%	2475400	2475400	0.1947	3.6022%	16.7059	69.7858%	1.1290%
PrimeNet	2⁵⁷	0.0107	63.1579%	8000	150000	0.0012	2.8700%	0.0119	64.2153%	1.0574%
GPU72	2⁶¹	0.1707	65.5738%	9000	130000	0.0012	1.5543%	0.1719	66.1089%	0.5351%
Difference	+6	+16.3405	+3.0829%	+2466400	+2345400	+0.1935	+2.0479%	+16.5340	+3.6769%	+3.6769%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.5112

68.6567%

2475400

0.1947

3.6022%

16.7059

69.7858%

1.1290%

PrimeNet

2⁵⁷

0.0107

63.1579%

8000

150000

0.0012

2.8700%

0.0119

64.2153%

1.0574%

GPU72

2⁶¹

0.1707

65.5738%

9000

130000

0.0012

1.5543%

0.1719

66.1089%

0.5351%

Difference

+16.3405

+3.0829%

+2466400

+2345400

+0.1935

+2.0479%

+16.5340

+3.6769%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1799621	105234533384693938304708591	27	86.444	29237971046318624395 5 × 13 × 149 × 11981 × 109049 × 2310643	2015-06-18	109049	2310643	15,597,491	0.0180	0.0185

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1799621

105234533384693938304708591

86.444

29237971046318624395
5 × 13 × 149 × 11981 × 109049 × 2310643

2015-06-18

109049

2310643

15,597,491

0.0180

0.0185

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-11T06:18:00	Carsten Kossendey	leela	100000	1650000		-		-	-	0.015	-	-	2.476%
2014-05-09T20:32:00	Jocelyn Larouche	Manual testing	135665	135665		-		-	-	0.011	-	-	1.060%
2014-09-19T20:39:00	Jocelyn Larouche	Manual testing	171330	171330		-		-	-	0.013	-	-	1.201%
2015-06-18T15:07:00	mikr	MSI	2475400	2475400			105234533384693938304708591	27	86.444	0.195	0.195	0.389	3.602%

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		-	-	0.021	-	-
2010-04-20T13:13:00	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.085	-	-
2010-12-13T03:33:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.887	-	-
2015-05-15T10:56:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.091	-	-
2015-05-15T10:56:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.076	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.787 GHz-days
Estimated T-Level:	24.607

Digits	B1	Curves	Complete	FacMiss
20	11000	258 / 100	2.580	7.480%
25	50000	258 / 280	0.921	39.729%

New Calculation Method

Total ECM effort:	17.787 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	8.323	0.024%
25	50000	0.752	47.133%
30	250000	0.046	95.474%
35	1000000	0.002	99.788%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		258	17.79

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-09-11T00:19:00	Scott Kurowski	HomeOffice	50000	5000000						3	0.207
2009-10-11T05:27:00	SubPrime	mysql0	50000	5000000						3	0.207
2010-12-24T02:26:00	Lupo	yorick	50000	5000000						3	0.207
2012-03-20T18:47:00	S36049	Wolle5	50000	5000000						3	0.207
2013-07-07T02:30:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-03-21T03:40:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2015-02-28T04:24:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-09-13T06:21:46	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.483
2020-11-22T11:22:32	nordi	sweet16	50000	5000000						7	0.483
2020-12-25T11:15:45	TJAOI	Manual testing	50000	5000000						223	15.37

date	userid	compid	res64	spent (GHz-days)
1999-05-23T00:00:00	MadPoo	v4_computers	1EBD098081B4751D	0.098
1999-09-07T00:00:00	ANONYMOUS	v4_computers	1EBD098081B4751D	0.098

date

userid

compid

res64

spent (GHz-days)

1999-05-23T00:00:00

MadPoo

v4_computers

1EBD098081B4751D

0.098

1999-09-07T00:00:00

ANONYMOUS

v4_computers

1EBD098081B4751D

0.098

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 (P-1 stage 1)

B1 = 100000, B2 = 1650000 (P-1 stage 2)

B1 = 171330 (P-1 stage 1)

B1 = 135665 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁷

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