M1799107 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	16.5159	68.6567%	500000	15000000	0.1015	5.0582%	16.6174	70.2421%	1.5854%
PrimeNet	2⁵⁷	0.0107	63.1579%	8000	150000	0.0012	2.8699%	0.0119	64.2152%	1.0573%
GPU72	2⁶¹	0.1707	65.5738%	9000	130000	0.0012	1.5542%	0.1720	66.1088%	0.5351%
Difference	+6	+16.3452	+3.0829%	+491000	+14870000	+0.1002	+3.5040%	+16.4454	+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

16.5159

68.6567%

500000

15000000

0.1015

5.0582%

16.6174

70.2421%

1.5854%

PrimeNet

2⁵⁷

0.0107

63.1579%

8000

150000

0.0012

2.8699%

0.0119

64.2152%

1.0573%

GPU72

2⁶¹

0.1707

65.5738%

9000

130000

0.0012

1.5542%

0.1720

66.1088%

0.5351%

Difference

+16.3452

+3.0829%

+491000

+14870000

+0.1002

+3.5040%

+16.4454

+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
1799107	38634023719	11	35.169	10737 3² × 1193	-	9	1193	3.369e-9	5.782e-6	9.576e-6
1799107	102632493918040644605401	24	76.442	28523176753256100 2² × 3⁵ × 5² × 1173793282027	2020-06-19	243	1173793282027	9,058.8	5,030.6	9,395.7

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1799107

38634023719

35.169

10737
3² × 1193

1193

3.369e-9

5.782e-6

9.576e-6

1799107

102632493918040644605401

76.442

28523176753256100
2² × 3⁵ × 5² × 1173793282027

2020-06-19

243

1173793282027

9,058.8

5,030.6

9,395.7

exponent	prime factors	composite factor	digits	bits*
1799107	38634023719 102632493918040644605401	3965106204369705505691111629506319	34	111.611

exponent

prime factors

composite factor

digits

bits*

1799107

38634023719
102632493918040644605401

3965106204369705505691111629506319

111.611

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:35:34	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 38634023719	-	-	0.101	-	-	5.058%

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.303 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	17.303 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.097	0.030%
25	50000	0.732	48.105%
30	250000	0.045	95.594%
35	1000000	0.002	99.794%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		119	8.204
50000	5000000	102632493918040644605401	132	9.100

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-09-27T13:00:17	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-03-27T13:56:10	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2019-09-05T02:21:48	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-04-09T00:22:03	Team_Inspector	SpudBoy4	50000	5000000						3	0.207
2020-05-02T03:25:22	Greg Hogan	azure4	50000	5000000						3	0.207
2020-06-19T19:45:38	nordi	sweet16	50000	5000000	102632493918040644605401	76.442	132	2	2461192804861783	132	9.100
2020-12-18T11:12:54	TJAOI	Manual testing	50000	5000000						106	7.307

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T18:37:46

Oliver Kruse

GTX-2

38634023719

F40C49AA029656__

2017-11-05T10:29:27

kkmrkkblmbrbk

c4.xlarge

38634023719

F40C49AA029656__

2020-06-22T05:39:37

Justine V.

Gible_Desktop_1

38634023719

102632493918040644605401

805ED9CD417AA6A5

2020-06-22T05:48:13

ATH

ec2-PRPCFDC

38634023719

102632493918040644605401

805ED9CD417AA6A5

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

10¹¹

10¹²

10¹³

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