M1788539 Mersenne number exponent details

Residue

Status

L-L

53BC036F05D700CD

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	16.6135	68.6567%	500000	15000000	0.1015	5.0546%	16.7150	70.2410%	1.5843%
PrimeNet	2⁵⁷	0.0107	63.1579%	8000	140000	0.0012	2.8141%	0.0119	64.1947%	1.0368%
GPU72	2⁶¹	0.1717	65.5738%	8000	130000	0.0012	1.4931%	0.1729	66.0878%	0.5140%
Difference	+6	+16.4418	+3.0829%	+492000	+14870000	+0.1003	+3.5615%	+16.5421	+4.1532%	+4.1532%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.6135

68.6567%

500000

15000000

0.1015

5.0546%

16.7150

70.2410%

1.5843%

PrimeNet

2⁵⁷

0.0107

63.1579%

8000

140000

0.0012

2.8141%

0.0119

64.1947%

1.0368%

GPU72

2⁶¹

0.1717

65.5738%

8000

130000

0.0012

1.4931%

0.1729

66.0878%

0.5140%

Difference

+16.4418

+3.0829%

+492000

+14870000

+0.1003

+3.5615%

+16.5421

+4.1532%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1788539	197448826346792903	18	57.454	55198356409 7 × 7885479487	2003-01-25	7	7885479487	0.0128	33.795	63.120
1788539	339204580775038346231	21	68.201	94827281030785 5 × 349 × 607 × 89525999	2020-12-01	607	89525999	50.002	0.3837	0.7166

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1788539

197448826346792903

57.454

55198356409
7 × 7885479487

2003-01-25

7885479487

0.0128

33.795

63.120

1788539

339204580775038346231

68.201

94827281030785
5 × 349 × 607 × 89525999

2020-12-01

607

89525999

50.002

0.3837

0.7166

exponent	prime factors	composite factor	digits	bits*
1788539	197448826346792903 339204580775038346231	66975546365487232846166012831767598593	38	125.655

exponent

prime factors

composite factor

digits

bits*

1788539

197448826346792903
339204580775038346231

66975546365487232846166012831767598593

125.655

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:34:10	alpertron	Manual testing	500000	15000000	12	-		-	-	0.101	-	-	5.055%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:34:10

alpertron

Manual testing

500000

15000000

0.101

-

-

5.055%

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	?	?	197448826346792903	57.454	18	0.002	0.197	0.004
2003-08-25T00:00:00	ANONYMOUS	v4_computers	?	?	197448826346792903	57.454	18	0.002	0.197	0.004

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.843 GHz-days
Estimated T-Level:	24.625

Digits	B1	Curves	Complete	FacMiss
20	11000	259 / 100	2.590	7.405%
25	50000	259 / 280	0.925	39.588%

New Calculation Method

Total ECM effort:	17.843 GHz-days
Estimated T-Level:	24.625

Digits	B1	Complete	FacMiss
20	11000	8.355	0.024%
25	50000	0.755	46.996%
30	250000	0.046	95.457%
35	1000000	0.002	99.787%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		258	17.77
50000	5000000	339204580775038346231	1	0.069

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-14T05:20:23	Oliver Kruse	O2.261	50000	5000000						3	0.207
2018-12-11T20:54:19	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-03-13T11:25:40	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.207
2020-04-09T15:14:38	Oliver Kruse	Melissa	50000	5000000						3	0.207
2020-05-02T23:04:37	Greg Hogan	azure3	50000	5000000						3	0.207
2020-06-01T08:42:04	nordi	sweet16	50000	5000000						3	0.207
2020-06-30T04:35:58	debrouxl	p4	50000	5000000						3	0.207
2020-07-26T03:32:39	Ahmed Azhad	c5.4xlarge.azf	50000	5000000						3	0.207
2020-10-05T15:42:37	Chang Chia-Tche	exbpc13	50000	5000000						7	0.482
2020-12-01T22:42:13	nordi	sweet16	50000	5000000	339204580775038346231	68.201	1	2	7346816019865715	1	0.069
2020-12-11T12:25:27	TJAOI	Manual testing	50000	5000000						227	15.64

date	userid	compid	res64	spent (GHz-days)
1999-03-01T00:00:00	Ethan O'Connor	v4_computers	53BC036F05D700CD	0.097

date

userid

compid

res64

spent (GHz-days)

1999-03-01T00:00:00

Ethan O'Connor

v4_computers

53BC036F05D700CD

0.097

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T20:13:07

Oliver Kruse

Doppelherz

197448826346792903

1E6BEC6AA4291C__

2017-11-05T04:02:26

kkmrkkblmbrbk

c4.xlarge

197448826346792903

1E6BEC6AA4291C__

2020-12-02T04:48:04

mrh

lanai

197448826346792903

339204580775038346231

D8AE630EA192804B

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 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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