M1995061 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	14.8937	68.6567%	-	-	-	-	14.8937	68.6567%	0.0000%
PrimeNet	2⁵⁸	0.0192	63.7931%	8000	140000	0.0014	2.4777%	0.0207	64.6902%	0.8971%
GPU72	2⁶²	0.3079	66.1290%	8000	110000	0.0013	1.2360%	0.3092	66.5477%	0.4186%
Difference	+5	+14.5858	+2.5277%	-8000	-110000	-0.0013	-1.2360%	+14.5845	+2.1090%	+2.1090%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.8937

68.6567%

14.8937

68.6567%

0.0000%

PrimeNet

2⁵⁸

0.0192

63.7931%

8000

140000

0.0014

2.4777%

0.0207

64.6902%

0.8971%

GPU72

2⁶²

0.3079

66.1290%

8000

110000

0.0013

1.2360%

0.3092

66.5477%

0.4186%

Difference

+14.5858

+2.5277%

-8000

-110000

-0.0013

-1.2360%

+14.5845

+2.1090%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1995061	44609563961	11	35.377	11180 2² × 5 × 13 × 43	-	13	43	3.258e-9	1.395e-6	2.522e-6
1995061	5626756177310906111	19	62.287	1410171462755 5 × 11 × 17 × 67 × 22510519	2016-07-21	67	22510519	0.4778	0.1169	0.2184
1995061	1788857082783350971543	22	70.600	448321400394111 3⁴ × 17327 × 319433953	2021-07-10	17327	319433953	188.03	1.6608	3.0990

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1995061

44609563961

35.377

11180
2² × 5 × 13 × 43

3.258e-9

1.395e-6

2.522e-6

1995061

5626756177310906111

62.287

1410171462755
5 × 11 × 17 × 67 × 22510519

2016-07-21

22510519

0.4778

0.1169

0.2184

1995061

1788857082783350971543

70.600

448321400394111
3⁴ × 17327 × 319433953

2021-07-10

17327

319433953

188.03

1.6608

3.0990

exponent	prime factors	composite factor	digits	bits*
1995061	44609563961 5626756177310906111	251007139584702723141520265671	30	97.664
1995061	44609563961 1788857082783350971543	79800134451511767070958949361823	32	105.976
1995061	5626756177310906111 1788857082783350971543	10065462640877587030631503177221505799273	41	132.887
1995061	44609563961 5626756177310906111 1788857082783350971543	44901589947528469181430010720583748121740132080035 3	51	168.263

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2016-07-20T14:32:22	TJAOI	Manual testing	2⁶²	2⁶³*	5626756177310906111	62.287	19	0.170	0.266	0.345

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2016-07-20T14:32:22

TJAOI

Manual testing

2⁶²

2⁶³*

5626756177310906111

62.287

0.170

0.266

0.345

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.534 GHz-days
Estimated T-Level:	2.050

Digits	B1	Curves	Complete	FacMiss
20	11000	41 / 100	0.410	66.228%
25	50000	41 / 280	0.146	86.356%

New Calculation Method

Total ECM effort:	3.534 GHz-days
Estimated T-Level:	2.050

Digits	B1	Complete	FacMiss
20	11000	1.599	20.203%
25	50000	0.147	86.290%
30	250000	0.009	99.073%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	4800000		7	0.582
50000	5000000		20	1.691
50000	5000000	1788857082783350971543	7	0.592
50000	6597468		7	0.668

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-23T23:58:10	ATH	ec2-1xe	50000	5000000						3	0.254
2019-05-02T15:36:38	ATH	ec2-ECMCF	50000	5000000						3	0.254
2021-03-18T00:35:09	Ducho_YYZ	Dutch	50000	4800000						7	0.582
2021-07-10T17:37:40	_p95holder_	TFL17_PRPt12pE_k	50000	5000000	1788857082783350971543	70.600	7	2		7	0.592
2021-09-23T06:10:40	Ahmed Azhad	c5.4xlarge.azf	50000	6597468						7	0.668
2022-02-06T09:21:15	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.592
2022-05-26T20:21:32	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.592

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T17:10:32

Oliver Kruse

GTX-2

44609563961

5626756177310906111

BD2785F3C41EE1__

2017-11-13T00:59:41

kkmrkkblmbrbk

c4.xlarge

44609563961

5626756177310906111

BD2785F3C41EE1__

2021-07-15T10:55:59

GURA LOVE

44609563961

5626756177310906111

1788857082783350971543

BC5742C974F94764

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

10⁰

10¹

10²

10³

10⁴

10⁵

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