M1839737 Mersenne number exponent details

Residue

Status

L-L

4547A654E66AC540

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	16.1512	68.6567%	500000	15000000	0.1015	5.0718%	16.2527	70.2464%	1.5897%
PrimeNet	2⁵⁷	0.0104	63.1579%	8000	150000	0.0012	2.8820%	0.0117	64.2197%	1.0618%
GPU72	2⁶¹	0.1670	65.5738%	9000	140000	0.0013	1.5963%	0.1682	66.1233%	0.5496%
Difference	+6	+15.9842	+3.0829%	+491000	+14860000	+0.1002	+3.4755%	+16.0844	+4.1231%	+4.1231%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.1512

68.6567%

500000

15000000

0.1015

5.0718%

16.2527

70.2464%

1.5897%

PrimeNet

2⁵⁷

0.0104

63.1579%

8000

150000

0.0012

2.8820%

0.0117

64.2197%

1.0618%

GPU72

2⁶¹

0.1670

65.5738%

9000

140000

0.0013

1.5963%

0.1682

66.1233%

0.5496%

Difference

+15.9842

+3.0829%

+491000

+14860000

+0.1002

+3.4755%

+16.0844

+4.1231%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1839737	3828378903055597889	19	61.731	1040469073312 2⁵ × 17² × 112507469	2009-07-19	289	112507469	0.1884	0.4822	0.9006

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1839737

3828378903055597889

61.731

1040469073312
2⁵ × 17² × 112507469

2009-07-19

289

112507469

0.1884

0.4822

0.9006

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-18T00:38:11	alpertron	Manual testing	500000	15000000	12	-		-	-	0.101	-	-	5.072%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-18T00:38:11

alpertron

Manual testing

500000

15000000

0.101

-

-

5.072%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2003-01-16T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.021	-	-

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2003-01-16T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁸

0.021

-

-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.559 GHz-days
Estimated T-Level:	24.536

Digits	B1	Curves	Complete	FacMiss
20	11000	254 / 100	2.540	7.786%
25	50000	254 / 280	0.907	40.302%

New Calculation Method

Total ECM effort:	19.559 GHz-days
Estimated T-Level:	24.536

Digits	B1	Complete	FacMiss
20	11000	10.497	0.003%
25	50000	0.966	38.063%
30	250000	0.061	94.053%
35	1000000	0.003	99.712%

ECM Summary

B1	B2	factor	curves	GHz-days
		3828378903055597889	1	0.00000e+0
50000	5000000		27	1.866
50000	6600000		220	17.14
50000	6750000		7	0.551

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-10-10T17:49:00	James Heinrich	Q6600	50000	5000000						3	0.207
2009-07-19T11:26:00	KAMCOBILL	PC01			3828378903055597889	61.731		1		1	-
2020-06-04T13:57:10	Oliver Kruse	IOS-1	50000	5000000						10	0.691
2020-10-09T13:53:08	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.484
2020-12-04T22:05:39	George Woltman	x64-debug	50000	6750000						7	0.551
2021-03-28T00:53:53	MarkS	desktop-i7	50000	5000000						7	0.484
2021-06-04T15:56:34	TJAOI	Manual testing	50000	6600000						220	17.14

date	userid	compid	res64	spent (GHz-days)
1998-12-27T00:00:00	ANONYMOUS	v4_computers	4547A654E66AC540	0.100

date

userid

compid

res64

spent (GHz-days)

1998-12-27T00:00:00

ANONYMOUS

v4_computers

4547A654E66AC540

0.100

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

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