M1725593 Mersenne number exponent details

Residue

Status

L-L

64F69C4E0AF64BED

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	17.2195	68.6567%	500000	15000000	0.1015	5.0328%	17.3210	70.2342%	1.5774%
PrimeNet	2⁵⁷	0.0111	63.1579%	8000	140000	0.0012	2.7950%	0.0123	64.1876%	1.0297%
GPU72	2⁶¹	0.1780	65.5738%	7000	110000	0.0010	1.3446%	0.1790	66.0367%	0.4629%
Difference	+6	+17.0415	+3.0829%	+493000	+14890000	+0.1005	+3.6882%	+17.1420	+4.1975%	+4.1975%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.2195

68.6567%

500000

15000000

0.1015

5.0328%

17.3210

70.2342%

1.5774%

PrimeNet

2⁵⁷

0.0111

63.1579%

8000

140000

0.0012

2.7950%

0.0123

64.1876%

1.0297%

GPU72

2⁶¹

0.1780

65.5738%

7000

110000

0.0010

1.3446%

0.1790

66.0367%

0.4629%

Difference

+17.0415

+3.0829%

+493000

+14890000

+0.1005

+3.6882%

+17.1420

+4.1975%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1725593	446127673409034604303	21	68.596	129267930911007 3 × 7 × 263 × 23405383109	2020-06-01	263	23405383109	60.840	100.31	187.35
1725593	602191870770744066487	21	69.029	174488384796051 3 × 58162794932017	2008-07-08	3	58162794932017	79.849	249,271	465,569

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1725593

446127673409034604303

68.596

129267930911007
3 × 7 × 263 × 23405383109

2020-06-01

263

23405383109

60.840

100.31

187.35

1725593

602191870770744066487

69.029

174488384796051
3 × 58162794932017

2008-07-08

58162794932017

79.849

249,271

465,569

exponent	prime factors	composite factor	digits	bits*
1725593	446127673409034604303 602191870770744066487	268654458252786080435597205615395168293561	42	137.625

exponent

prime factors

composite factor

digits

bits*

1725593

446127673409034604303
602191870770744066487

268654458252786080435597205615395168293561

137.625

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:31:39	alpertron	Manual testing	500000	15000000	12	-		-	-	0.101	-	-	5.033%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:31:39

alpertron

Manual testing

500000

15000000

0.101

-

-

5.033%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
1998-11-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.011	-	-
2003-02-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.022	-	-

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

1998-11-21T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁷

0.011

-

-

2003-02-02T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁸

0.022

-

-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.431 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:	17.431 GHz-days
Estimated T-Level:	24.536

Digits	B1	Complete	FacMiss
20	11000	9.769	0.006%
25	50000	0.904	40.498%
30	250000	0.057	94.458%
35	1000000	0.003	99.734%

ECM Summary

B1	B2	factor	curves	GHz-days
		602191870770744066487	1	0.00000e+0
50000	5000000		220	15.10
50000	5000000	446127673409034604303	34	2.333

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-08T15:51:00	James Heinrich	Q6600			602191870770744066487	69.029		1		1	-
2015-03-07T08:31:00	Richard B. Woods	Puttputt	50000	5000000						2	0.137
2020-02-07T01:12:55	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-02-15T02:02:45	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-02-22T23:11:12	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-03-02T09:21:19	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-03-14T18:34:39	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-04-11T08:41:38	Oliver Kruse	IOS-1	50000	5000000						3	0.206
2020-05-03T20:43:03	Greg Hogan	azure3	50000	5000000						3	0.206
2020-06-01T14:16:39	TJAOI	Manual testing	50000	5000000	446127673409034604303	68.596	34	2		34	2.333
2020-06-01T14:16:39	TJAOI	Manual testing	50000	5000000						197	13.52

date	userid	compid	res64	spent (GHz-days)
1998-12-06T00:00:00	ANONYMOUS	v4_computers	64F69C4E0AF64BED	0.094

date

userid

compid

res64

spent (GHz-days)

1998-12-06T00:00:00

ANONYMOUS

v4_computers

64F69C4E0AF64BED

0.094

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:16:06

alpertron

Manual testing

602191870770744066487

8ACBE66AE660FC__

2017-10-19T05:48:13

Oliver Kruse

GTX-3

602191870770744066487

8ACBE66AE660FC__

2020-06-02T08:31:06

Klaus Nordmann

no1

446127673409034604303

602191870770744066487

8C786BCFAD0C9994

2020-06-03T06:52:20

marssystems

system03

446127673409034604303

602191870770744066487

8C786BCFAD0C9994

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

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

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