M2127761 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	13.9649	67.1642%	500000	15000000	0.1230	5.1613%	14.0879	68.8589%	1.6948%
PrimeNet	2⁵⁸	0.0180	62.0690%	9000	160000	0.0016	2.6844%	0.0197	63.0872%	1.0182%
GPU72	2⁶²	0.2887	64.5161%	10000	140000	0.0016	1.4552%	0.2904	65.0325%	0.5164%
Difference	+5	+13.6761	+2.6481%	+490000	+14860000	+0.1214	+3.7061%	+13.7975	+3.8265%	+3.8265%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.9649

67.1642%

500000

15000000

0.1230

5.1613%

14.0879

68.8589%

1.6948%

PrimeNet

2⁵⁸

0.0180

62.0690%

9000

160000

0.0016

2.6844%

0.0197

63.0872%

1.0182%

GPU72

2⁶²

0.2887

64.5161%

10000

140000

0.0016

1.4552%

0.2904

65.0325%

0.5164%

Difference

+13.6761

+2.6481%

+490000

+14860000

+0.1214

+3.7061%

+13.7975

+3.8265%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2127761	76493331807990767	17	56.086	17975076103 19 × 367 × 431 × 5981	-	431	5981	0.0050	6.992e-5	8.363e-5
2127761	71163997651189139280967	23	75.914	16722742274905203 3⁴ × 71 × 571783 × 5085491	2021-12-19	571783	5085491	5,093.1	0.0780	0.1109

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2127761

76493331807990767

56.086

17975076103
19 × 367 × 431 × 5981

431

5981

0.0050

6.992e-5

8.363e-5

2127761

71163997651189139280967

75.914

16722742274905203
3⁴ × 71 × 571783 × 5085491

2021-12-19

571783

5085491

5,093.1

0.0780

0.1109

exponent	prime factors	composite factor	digits	bits*
2127761	76493331807990767 71163997651189139280967	5443571285115486419594621840775354831689	40	132.000

exponent

prime factors

composite factor

digits

bits*

2127761

76493331807990767
71163997651189139280967

5443571285115486419594621840775354831689

132.000

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-15T15:11:33	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 76493331807990767	-	-	0.123	-	-	5.161%

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.705 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:	1.705 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	1.108
50000	5000000	71163997651189139280967	7	0.597

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-01-09T02:40:47	Oliver Kruse	ECM-HTC	50000	5000000						3	0.256
2019-10-10T18:29:44	wazuma	G751	50000	5000000						3	0.256
2021-12-19T11:32:05	MarkS	desktop-i7	50000	5000000	71163997651189139280967	75.914	7	2	85124396090488	7	0.597
2022-05-10T02:45:08	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.597

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-08T13:51:59

Oliver Kruse

GTX-2

76493331807990767

9EEC650C20B41D__

2017-11-17T22:41:21

kkmrkkblmbrbk

c4.xlarge

76493331807990767

9EEC650C20B41D__

2021-12-19T11:46:56

MarkS

desktop-i7

76493331807990767

71163997651189139280967

462F207C585C60C1

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)

10¹

10²

10³

10⁴

10⁵

10⁶

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