M2 935 019 Mersenne number exponent details

Residue

Status

L-L

DCFFE470FD490368

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁹	40.6767	68.1159%	10000000	19223759100	130.4232	14.9444%	171.0998	72.8808%
Target	2⁶³	0.5438	65.0794%	17000	1500000	0.0121	1.9458%	0.5559	65.7588%
Difference	+6	+40.1329	+3.0366%	+9983000	+19222259100	+130.4111	+12.9987%	+170.5440	+7.1220%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

2⁶⁹

40.6767

68.1159%

10000000

19223759100

130.4232

14.9444%

171.0998

72.8808%

Target

2⁶³

0.5438

65.0794%

17000

1500000

0.0121

1.9458%

0.5559

65.7588%

Difference

+40.1329

+3.0366%

+9983000

+19222259100

+130.4111

+12.9987%

+170.5440

+7.1220%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2935019	1111457314453146563292087589390697826577	40	129.708	189344142994158907198230674041752 2³ × 3 × 13 × 53 × 139627 × 8601097 × 8709373 × 1094740711	2022-11-02	8709373	1094740711	5.459e+10	8.3771	13.748

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2935019

1111457314453146563292087589390697826577

129.708

189344142994158907198230674041752
2³ × 3 × 13 × 53 × 139627 × 8601097 × 8709373 × 1094740711

2022-11-02

8709373

1094740711

5.459e+10

8.3771

13.748

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-12-13	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.198%
2010-11-08	markr	tiny	105000	2283750		-		-	-	0.028	-	-	2.295%
2015-04-29	VictordeHollander	Manual testing	1000000	20000000		-		-	-	0.251	-	-	5.053%
2022-09-05	Wentao Huang	Biolake	1200000	3268104840		-		-	-	22.11	-	-	10.470%
2022-11-02	mikr	MSI	10000000	19223759100			1111457314453146563292087589390697826577	40	129.708	130.4	0.500	260.8	14.944%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-02-08	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.026	-	-
2016-02-23	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.026	-	-
2009-02-14	Sturle Sunde	golli.ifi	2⁶⁰	2⁶¹		-	-	0.052	-	-
2012-01-03	markr	oldgamer	2⁶¹	2⁶²		-	-	0.105	-	-
2013-01-07	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.334	-	-
2015-04-25	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.669	-	-
2015-04-25	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.273	-	-
2016-02-23	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.546	-	-
2017-11-23	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.092	-	-
2018-12-21	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.18	-	-
2021-05-24	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	20.37	-	-

ECM factoring results:

Total ECM effort:	14.535 GHz-days
Estimated T-Level:	22.214

Digits	B1	Complete	FacMiss
20	11000	4.786	0.834%
25	50000	0.443	64.228%
30	250000	0.028	97.242%
35	1000000	0.001	99.869%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	102	11.80
50000	6296669	7	0.902
50000	6450000	7	0.913
50000	6550000	7	0.920

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-31	Net_Force	Vista64	50000	5000000						3	0.347
2011-04-10	Rob		50000	5000000						3	0.347
2013-06-20	Bruce	E6510	50000	5000000						3	0.347
2015-12-28	Bruce	Desk7	50000	5000000						3	0.347
2017-05-29	Conductor	NataW	50000	5000000						3	0.347
2019-08-31	Corey	Computer	50000	5000000						3	0.347
2020-09-03	mnd9	kitchen	50000	5000000						7	0.810
2020-10-10	mnd9	75204b	50000	5000000						7	0.810
2020-11-03	lycorn	colab_A_1	50000	5000000						7	0.810
2020-12-08	C.D.B.	i7-6850K	50000	5000000						7	0.810
2021-01-10	Zenzoma	AM3700X_1	50000	5000000						7	0.810
2021-02-09	lycorn	colab_A	50000	6450000						7	0.913
2021-03-14	mnd9	75204	50000	5000000						7	0.810
2021-04-22	daveward2005	Dave2	50000	5000000						7	0.810
2021-06-12	kutens	capella	50000	6550000						7	0.920
2021-07-28	daveward2005	Dave2	50000	5000000						7	0.810
2021-10-06	mnd9	office2	50000	5000000						7	0.810
2021-12-23	daveward2005	Dave2	50000	5000000						7	0.810
2022-04-13	J.R. Allen	lapasus	50000	6296669						7	0.902
2022-07-23	daveward2005	Davy	50000	5000000						7	0.810
2022-10-20	C.D.B.	i7-6850K	50000	5000000						7	0.810

date	userid	compid	res64	spent (GHz-days)
1998-06-01	ANONYMOUS	v4_computers	DCFFE470FD490368	0.250
1999-05-02	foxkid	v4_computers	DCFFE470FD490368	0.250
2018-10-08	kkmrkkblmbrbk	old	DCFFE470FD490368	0.250

date

userid

compid

res64

spent (GHz-days)

1998-06-01

ANONYMOUS

v4_computers

DCFFE470FD490368

0.250

1999-05-02

foxkid

v4_computers

DCFFE470FD490368

0.250

2018-10-08

kkmrkkblmbrbk

old

DCFFE470FD490368

0.250

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 = 10000000, B2 = 19223759100 (P-1 stage 2)

B1 = 1200000, B2 = 3268104840 (P-1 stage 2)

B1 = 10000000 (P-1 stage 1)

B1 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 1200000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 105000, B2 = 2283750 (P-1 stage 2)

B1 = 105000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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