M2122039 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	14.0025	67.1642%	500000	15000000	0.1230	5.1597%	14.1255	68.8584%	1.6942%
PrimeNet	2⁵⁸	0.0181	62.0690%	9000	160000	0.0016	2.6830%	0.0197	63.0867%	1.0177%
GPU72	2⁶²	0.2895	64.5161%	10000	140000	0.0016	1.4544%	0.2911	65.0322%	0.5161%
Difference	+5	+13.7130	+2.6481%	+490000	+14860000	+0.1214	+3.7053%	+13.8344	+3.8262%	+3.8262%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.0025

67.1642%

500000

15000000

0.1230

5.1597%

14.1255

68.8584%

1.6942%

PrimeNet

2⁵⁸

0.0181

62.0690%

9000

160000

0.0016

2.6830%

0.0197

63.0867%

1.0177%

GPU72

2⁶²

0.2895

64.5161%

10000

140000

0.0016

1.4544%

0.2911

65.0322%

0.5161%

Difference

+13.7130

+2.6481%

+490000

+14860000

+0.1214

+3.7053%

+13.8344

+3.8262%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2122039	21220391	8	24.339	5 5	-	1	5	1.054e-12	1.161e-7	1.940e-7
2122039	145818135940601054311	21	66.983	34358024508645 3 × 5 × 4013 × 570778711	2018-01-07	4013	570778711	11.876	2.9651	5.5374

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2122039

21220391

24.339

5
5

1.054e-12

1.161e-7

1.940e-7

2122039

145818135940601054311

66.983

34358024508645
3 × 5 × 4013 × 570778711

2018-01-07

4013

570778711

11.876

2.9651

5.5374

exponent	prime factors	composite factor	digits	bits*
2122039	21220391 145818135940601054311	3094317859550707147491655601	28	91.322

exponent

prime factors

composite factor

digits

bits*

2122039

21220391
145818135940601054311

3094317859550707147491655601

91.322

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:12:58	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 21220391	-	-	0.123	-	-	5.160%

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.473 GHz-days
Estimated T-Level:	1.350

Digits	B1	Curves	Complete	FacMiss
20	11000	27 / 100	0.270	76.234%
25	50000	27 / 280	0.096	90.792%

New Calculation Method

Total ECM effort:	3.473 GHz-days
Estimated T-Level:	1.350

Digits	B1	Complete	FacMiss
20	11000	1.187	30.529%
25	50000	0.107	89.894%
30	250000	0.007	99.342%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	50000		21	1.065
50000	5000000		11	0.937
50000	5000000	145818135940601054311	2	0.170
50000	5965834		7	0.644
50000	6219073		7	0.656

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-01-07T10:42:19	ATH	ec2-1xd	50000	5000000	145818135940601054311	66.983	2	2		2	0.170
2018-11-28T08:31:18	rucio		50000	5000000						3	0.256
2021-11-10T00:00:05	JackBlock	school2	50000	50000						7	0.355
2021-11-24T08:00:00	JackBlock	school10	50000	50000						7	0.355
2021-12-08T05:57:34	JackBlock	school2	50000	50000						7	0.355
2022-01-01T21:57:02	MarkS	desktop-i7	50000	5000000						8	0.682
2022-05-20T19:41:48	debrouxl	dl380g9-1	50000	6219073						7	0.656
2022-07-17T13:25:43	debrouxl	z400	50000	5965834						7	0.644

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-08T12:03:12

Oliver Kruse

GTX-1

21220391

B0619CD176B223__

2017-11-17T18:32:49

kkmrkkblmbrbk

c4.xlarge

21220391

B0619CD176B223__

2018-01-09T16:49:34

AdolfNor

Manual testing

21220391

145818135940601054311

1AB32453E33BD0__

2018-01-10T19:54:30

Oliver Kruse

GTX-5

21220391

145818135940601054311

1AB32453E33BD0__

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

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