M2116757 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	14.0375	67.1642%	500000	15000000	0.1230	5.1581%	14.1605	68.8579%	1.6937%
PrimeNet	2⁵⁸	0.0181	62.0690%	9000	160000	0.0016	2.6818%	0.0198	63.0862%	1.0172%
GPU72	2⁶²	0.2902	64.5161%	10000	140000	0.0016	1.4537%	0.2919	65.0319%	0.5158%
Difference	+5	+13.7472	+2.6481%	+490000	+14860000	+0.1214	+3.7045%	+13.8686	+3.8259%	+3.8259%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.0375

67.1642%

500000

15000000

0.1230

5.1581%

14.1605

68.8579%

1.6937%

PrimeNet

2⁵⁸

0.0181

62.0690%

9000

160000

0.0016

2.6818%

0.0198

63.0862%

1.0172%

GPU72

2⁶²

0.2902

64.5161%

10000

140000

0.0016

1.4537%

0.2919

65.0319%

0.5158%

Difference

+13.7472

+2.6481%

+490000

+14860000

+0.1214

+3.7045%

+13.8686

+3.8259%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2116757	29634599	8	24.821	7 7	-	1	7	1.057e-12	1.265e-7	1.940e-7
2116757	367151257169934595753	21	68.315	86724942251268 2² × 3 × 122347 × 59070337	2021-11-14	122347	59070337	54.127	0.3179	0.5731

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2116757

29634599

24.821

7
7

1.057e-12

1.265e-7

1.940e-7

2116757

367151257169934595753

68.315

86724942251268
2² × 3 × 122347 × 59070337

2021-11-14

122347

59070337

54.127

0.3179

0.5731

exponent	prime factors	composite factor	digits	bits*
2116757	29634599 367151257169934595753	10880380278576886601367258047	29	93.136

exponent

prime factors

composite factor

digits

bits*

2116757

29634599
367151257169934595753

10880380278576886601367258047

93.136

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-25T16:40:44	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 29634599	-	-	0.123	-	-	5.158%

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.704 GHz-days
Estimated T-Level:	1.000

Digits	B1	Curves	Complete	FacMiss
20	11000	20 / 100	0.200	81.791%
25	50000	20 / 280	0.071	93.094%

New Calculation Method

Total ECM effort:	1.704 GHz-days
Estimated T-Level:	1.000

Digits	B1	Complete	FacMiss
20	11000	0.645	52.458%
25	50000	0.058	94.336%
30	250000	0.004	99.642%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		13	1.107
50000	5000000	367151257169934595753	7	0.596

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-01-08T01:58:29	Oliver Kruse	ECM-HTC	50000	5000000						3	0.256
2019-09-23T06:58:49	J.R. Allen	lapacer	50000	5000000						3	0.256
2021-11-14T04:43:40	MarkS	desktop-i7	50000	5000000	367151257169934595753	68.315	7	2	1468352327143464	7	0.596
2022-04-01T12:55:05	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.596

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-07T05:39:37

Oliver Kruse

GTX-3

29634599

7E4069B6C72DB6__

2017-11-17T14:57:40

kkmrkkblmbrbk

c4.xlarge

29634599

7E4069B6C72DB6__

2021-11-14T06:44:05

SRJ2877

LTOS

29634599

367151257169934595753

10C524B551AD7C23

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