M1799527 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

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	16.5121	68.6567%	500000	15000000	0.1015	5.0583%	16.6135	70.2422%	1.5854%
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	+16.3414	+3.0829%	+491000	+14870000	+0.1002	+3.5041%	+16.4416	+4.1333%	+4.1333%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.5121

68.6567%

500000

15000000

0.1015

5.0583%

16.6135

70.2422%

1.5854%

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

+16.3414

+3.0829%

+491000

+14870000

+0.1002

+3.5041%

+16.4416

+4.1333%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1799527	388697833	9	28.534	108 2² × 3³	-	27	27	2.034e-11	2.124e-6	4.322e-6

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1799527

388697833

28.534

108
2² × 3³

2.034e-11

2.124e-6

4.322e-6

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:35:36	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 388697833	-	-	0.101	-	-	5.058%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:35:36

alpertron

Manual testing

500000

15000000

skipped known factor: 388697833

0.101

-

-

5.058%

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.786 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:	17.786 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	9.923	0.005%
25	50000	0.918	39.926%
30	250000	0.058	94.373%
35	1000000	0.003	99.730%

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
2015-09-28T09:29:11	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-03-28T03:11:10	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2019-09-05T15:58:15	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-04-07T20:43:45	Oliver Kruse	Melissa	50000	5000000						3	0.207
2020-05-02T08:17:09	Greg Hogan	azure	50000	5000000						3	0.207
2020-05-29T19:55:39	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						3	0.207
2020-06-28T09:42:39	nordi	sweet16	50000	5000000						3	0.207
2020-07-25T09:24:49	Ahmed Azhad	c5.4xlarge.azf	50000	5000000						3	0.207
2020-10-02T04:52:04	nordi	sweet16	50000	5000000						7	0.483
2020-11-29T20:33:50	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.483
2020-12-18T11:12:54	TJAOI	Manual testing	50000	5000000						222	15.30

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

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