M1757267 Mersenne number exponent details

Residue

Status

L-L

532D415119A54897

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	16.9092	68.6567%	500000	15000000	0.1015	5.0439%	17.0106	70.2376%	1.5809%
PrimeNet	2⁵⁷	0.0109	63.1579%	8000	140000	0.0012	2.8047%	0.0121	64.1912%	1.0333%
GPU72	2⁶¹	0.1748	65.5738%	8000	110000	0.0011	1.4139%	0.1759	66.0605%	0.4868%
Difference	+6	+16.7344	+3.0829%	+492000	+14890000	+0.1004	+3.6300%	+16.8348	+4.1771%	+4.1771%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.9092

68.6567%

500000

15000000

0.1015

5.0439%

17.0106

70.2376%

1.5809%

PrimeNet

2⁵⁷

0.0109

63.1579%

8000

140000

0.0012

2.8047%

0.0121

64.1912%

1.0333%

GPU72

2⁶¹

0.1748

65.5738%

8000

110000

0.0011

1.4139%

0.1759

66.0605%

0.4868%

Difference

+16.7344

+3.0829%

+492000

+14890000

+0.1004

+3.6300%

+16.8348

+4.1771%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1757267	17691115255786723031	20	63.940	5033701553545 5 × 7 × 17 × 25759 × 328429	2010-08-30	25759	328429	1.8139	0.0033	0.0041
1757267	196917184462617896231	21	67.416	56029386673345 5 × 472477 × 23717297	2020-06-16	472477	23717297	17.222	0.1368	0.1898
1757267	1342661435639314055633	22	70.186	382031141437048 2³ × 257 × 185812811983	2020-08-14	257	185812811983	241.07	796.35	1,487.4

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1757267

17691115255786723031

63.940

5033701553545
5 × 7 × 17 × 25759 × 328429

2010-08-30

25759

328429

1.8139

0.0033

0.0041

1757267

196917184462617896231

67.416

56029386673345
5 × 472477 × 23717297

2020-06-16

472477

23717297

17.222

0.1368

0.1898

1757267

1342661435639314055633

70.186

382031141437048
2³ × 257 × 185812811983

2020-08-14

257

185812811983

241.07

796.35

1,487.4

exponent	prime factors	composite factor	digits	bits*
1757267	17691115255786723031 196917184462617896231	3483684606173187725464667961422695796161	40	131.356
1757267	17691115255786723031 1342661435639314055633	23753178207395172241597857558023496383623	41	134.125
1757267	196917184462617896231 1342661435639314055633	264393109592630172232823372404846955019223	42	137.602
1757267	17691115255786723031 196917184462617896231 1342661435639314055633	46774089746390706241156081596329928431068577890907 08781824913	61	201.541

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:29:58	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 17691115255786723031	-	-	0.101	-	-	5.044%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:29:58

alpertron

Manual testing

500000

15000000

skipped known factor: 17691115255786723031

0.101

-

-

5.044%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.022	-	-
2022-03-08T23:06:25	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.066	-	-
2022-03-09T03:01:43	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.087	-	-
2010-04-23T06:20:00	Architects Cubed	i4l_1	2⁶⁰	2⁶¹		-	-	0.087	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.978 GHz-days
Estimated T-Level:	24.929

Digits	B1	Curves	Complete	FacMiss
20	11000	276 / 100	2.760	6.242%
25	50000	276 / 280	0.986	37.251%

New Calculation Method

Total ECM effort:	18.978 GHz-days
Estimated T-Level:	24.929

Digits	B1	Complete	FacMiss
20	11000	8.903	0.014%
25	50000	0.805	44.724%
30	250000	0.050	95.166%
35	1000000	0.002	99.773%

ECM Summary

B1	B2	factor	curves	GHz-days
		17691115255786723031	1	0.00000e+0
50000	5000000		225	15.47
50000	5000000	196917184462617896231	27	1.857
50000	5000000	1342661435639314055633	24	1.650

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-08-02T02:09:00	Scott Kurowski	UW2	50000	5000000						3	0.206
2009-10-12T00:54:00	Conductor	home	50000	5000000						3	0.206
2010-08-30T19:01:00	Wolfgang Fluck	C91F72025			17691115255786723031	63.940		1		1	-
2020-02-29T09:28:01	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-03-12T05:48:13	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-04-06T20:44:37	Team_Inspector	SpudBoy4	50000	5000000						3	0.206
2020-05-02T04:04:02	Oliver Kruse	IOS-2	50000	5000000						3	0.206
2020-06-16T15:02:57	nordi	sweet16	50000	5000000	196917184462617896231	67.416	27	2	6485878272135096	27	1.857
2020-08-14T09:28:58	TJAOI	Manual testing	50000	5000000	1342661435639314055633	70.186	24	2		24	1.650
2020-08-14T09:28:58	TJAOI	Manual testing	50000	5000000						207	14.23

date	userid	compid	res64	spent (GHz-days)
1998-12-13T00:00:00	ANONYMOUS	v4_computers	532D415119A54897	0.095

date

userid

compid

res64

spent (GHz-days)

1998-12-13T00:00:00

ANONYMOUS

v4_computers

532D415119A54897

0.095

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T08:15:08

Oliver Kruse

GTX-0

17691115255786723031

3A146C009635CB__

2017-11-04T00:13:17

kkmrkkblmbrbk

c4.xlarge

17691115255786723031

3A146C009635CB__

2020-06-17T08:00:32

LaurV

3tits

17691115255786723031

196917184462617896231

E521E0F1863DCF44

2020-06-17T08:19:55

ATH

ec2-PRPCFDC

17691115255786723031

196917184462617896231

E521E0F1863DCF44

2020-08-15T09:20:32

CrypticClue

cruncher

17691115255786723031

196917184462617896231

1342661435639314055633

E521E0F1863DCF44

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

10¹⁰

10¹¹

10¹²

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