M2061149 Mersenne number exponent details

Residue

Status

L-L

AC29E1ECF09A3485

double-checked

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	14.4162	68.6567%	500000	15000000	0.1230	5.1416%	14.5392	70.2683%	1.6116%
PrimeNet	2⁵⁸	0.0186	63.7931%	9000	160000	0.0016	2.6684%	0.0203	64.7592%	0.9661%
GPU72	2⁶²	0.2981	66.1290%	9000	130000	0.0015	1.3651%	0.2996	66.5914%	0.4624%
Difference	+5	+14.1181	+2.5277%	+491000	+14870000	+0.1215	+3.7765%	+14.2396	+3.6769%	+3.6769%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.4162

68.6567%

500000

15000000

0.1230

5.1416%

14.5392

70.2683%

1.6116%

PrimeNet

2⁵⁸

0.0186

63.7931%

9000

160000

0.0016

2.6684%

0.0203

64.7592%

0.9661%

GPU72

2⁶²

0.2981

66.1290%

9000

130000

0.0015

1.3651%

0.2996

66.5914%

0.4624%

Difference

+14.1181

+2.5277%

+491000

+14870000

+0.1215

+3.7765%

+14.2396

+3.6769%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2061149	224155191484390455073	21	67.603	54376270586064 2⁴ × 3⁵ × 7 × 30553 × 65393	2008-12-09	30553	65393	15.998	0.0031	0.0059

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2061149

224155191484390455073

67.603

54376270586064
2⁴ × 3⁵ × 7 × 30553 × 65393

2008-12-09

30553

65393

15.998

0.0031

0.0059

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-24T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.275%
2016-03-16T13:42:43	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 224155191484390455073	-	-	0.123	-	-	5.142%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
1999-01-10T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

1999-01-10T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁸

0.019

-

-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.641 GHz-days
Estimated T-Level:	1.900

Digits	B1	Curves	Complete	FacMiss
20	11000	38 / 100	0.380	68.255%
25	50000	38 / 280	0.136	87.288%

New Calculation Method

Total ECM effort:	3.641 GHz-days
Estimated T-Level:	1.900

Digits	B1	Complete	FacMiss
20	11000	1.525	21.757%
25	50000	0.139	86.988%
30	250000	0.009	99.128%

ECM Summary

B1	B2	factor	curves	GHz-days
		224155191484390455073	1	0.00000e+0
50000	50000		7	0.355
50000	5000000		24	2.038
50000	5600000		7	0.623
50000	5645903		7	0.625

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-09T18:26:00	SubPrime	dijkstra			224155191484390455073	67.603		1		1	-
2018-11-24T02:47:43	rucio		50000	5000000						3	0.255
2021-07-26T09:50:23	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.594
2021-10-14T12:18:39	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.594
2022-03-04T04:29:36	JackBlock	school10	50000	50000						7	0.355
2022-03-16T06:35:56	MarkS	laptop64	50000	5000000						7	0.594
2022-06-10T01:06:57	Eric	miniPCWindows	50000	5600000						7	0.623
2022-08-10T09:38:01	debrouxl	z400	50000	5645903						7	0.625

date	userid	compid	res64	spent (GHz-days)
1999-02-07T00:00:00	ANONYMOUS	v4_computers	AC29E1ECF09A3485	0.136

date

userid

compid

res64

spent (GHz-days)

1999-02-07T00:00:00

ANONYMOUS

v4_computers

AC29E1ECF09A3485

0.136

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)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

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