M2120341 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	14.0137	67.1642%	500000	15000000	0.1230	5.1592%	14.1367	68.8582%	1.6941%
PrimeNet	2⁵⁸	0.0181	62.0690%	9000	160000	0.0016	2.6826%	0.0198	63.0865%	1.0175%
GPU72	2⁶²	0.2897	64.5161%	10000	140000	0.0016	1.4542%	0.2914	65.0321%	0.5160%
Difference	+5	+13.7240	+2.6481%	+490000	+14860000	+0.1214	+3.7050%	+13.8454	+3.8261%	+3.8261%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.0137

67.1642%

500000

15000000

0.1230

5.1592%

14.1367

68.8582%

1.6941%

PrimeNet

2⁵⁸

0.0181

62.0690%

9000

160000

0.0016

2.6826%

0.0198

63.0865%

1.0175%

GPU72

2⁶²

0.2897

64.5161%

10000

140000

0.0016

1.4542%

0.2914

65.0321%

0.5160%

Difference

+13.7240

+2.6481%

+490000

+14860000

+0.1214

+3.7050%

+13.8454

+3.8261%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2120341	97535687	8	26.539	23 23	-	1	23	4.237e-12	2.096e-7	2.096e-7
2120341	924099997501440147119	21	69.647	217913061507899 31 × 7029453597029	2022-06-25	31	7029453597029	96.571	36,513	68,196

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2120341

97535687

26.539

23
23

4.237e-12

2.096e-7

2120341

924099997501440147119

69.647

217913061507899
31 × 7029453597029

2022-06-25

7029453597029

96.571

36,513

68,196

exponent	prime factors	composite factor	digits	bits*
2120341	97535687 924099997501440147119	90132728113001248238632735753	29	96.186

exponent

prime factors

composite factor

digits

bits*

2120341

97535687
924099997501440147119

90132728113001248238632735753

96.186

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:12:47	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 97535687	-	-	0.123	-	-	5.159%

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.295 GHz-days
Estimated T-Level:	1.300

Digits	B1	Curves	Complete	FacMiss
20	11000	26 / 100	0.260	77.004%
25	50000	26 / 280	0.093	91.117%

New Calculation Method

Total ECM effort:	2.295 GHz-days
Estimated T-Level:	1.300

Digits	B1	Complete	FacMiss
20	11000	1.019	36.087%
25	50000	0.094	90.989%
30	250000	0.006	99.405%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		20	1.704
50000	6900000	924099997501440147119	6	0.591

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-01-07T06:27:57	ATH	ec2-1xd	50000	5000000						3	0.256
2019-09-28T15:46:00	ATH	ec2-ECMCF	50000	5000000						3	0.256
2021-11-24T17:36:17	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.596
2022-04-11T11:57:32	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.596
2022-06-25T14:14:12	debrouxl	dl380g9-1	50000	6900000	924099997501440147119	69.647	6	2	2895365478838487	6	0.591

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-07T06:27:24

Oliver Kruse

GTX-1

97535687

0F31048FF61F32__

2017-11-17T17:21:31

kkmrkkblmbrbk

c4.xlarge

97535687

0F31048FF61F32__

2022-07-01T11:37:20

Funky Waddle

main

97535687

924099997501440147119

00C612F15DF56B42

2022-07-25T03:33:43

some-students

GIMPS_IN_SHANGHAI

97535687

924099997501440147119

00C612F15DF56B42

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