M10044017 Mersenne number exponent details

Residue

Status

L-L

77D6068298853424

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	2⁶⁹	11.8864	65.2174%	110000	1952500	0.0890	2.6875%	11.9753	66.1522%	0.9348%
PrimeNet	2⁶⁴	0.3544	62.5000%	45000	1300000	0.0479	3.7469%	0.4023	63.9051%	1.4051%
GPU72	2⁶⁸	5.9344	64.7059%	65000	1500000	0.0606	2.5696%	5.9949	65.6128%	0.9069%
Difference	+1	+5.9520	+0.5115%	+45000	+452500	+0.0284	+0.1179%	+5.9804	+0.5394%	+0.5394%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

11.8864

65.2174%

110000

1952500

0.0890

2.6875%

11.9753

66.1522%

0.9348%

PrimeNet

2⁶⁴

0.3544

62.5000%

45000

1300000

0.0479

3.7469%

0.4023

63.9051%

1.4051%

GPU72

2⁶⁸

5.9344

64.7059%

65000

1500000

0.0606

2.5696%

5.9949

65.6128%

0.9069%

Difference

+5.9520

+0.5115%

+45000

+452500

+0.0284

+0.1179%

+5.9804

+0.5394%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
10044017	149914778264519815607	21	67.023	7462889512459 29 × 233 × 1104467887	2016-06-16	233	1104467887	3.8982	25.449	47.531

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

10044017

149914778264519815607

67.023

7462889512459
29 × 233 × 1104467887

2016-06-16

233

1104467887

3.8982

25.449

47.531

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-09T00:00:00	Martti Järvi	v4_computers	55000	838750		-		-	-	0.041	-	-	1.891%
2011-12-23T15:56:00	bcp19	acer-Q8200	110000	1952500		-		-	-	0.089	-	-	2.688%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-11-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.354	-	-
2011-09-27T13:13:00	David Campeau	Manual testing	2⁶⁴	2⁶⁵		-	-	0.372	-	-
2015-04-20T13:22:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	0.744	-	-
2015-11-10T09:03:34	VictordeHollander	Manual testing	2⁶⁶	2⁶⁷		-	-	1.488	-	-
2016-06-16T17:45:23	mikr	Manual testing	2⁶⁷	2⁶⁸	skipped known factors(?)	-	-	2.976	-	-
2016-06-16T17:50:15	mikr	Manual testing	2⁶⁷	2⁶⁸*	149914778264519815607	67.023	21	0.940	5.955	1.910
2021-12-28T17:29:08	ViliamF	Manual testing	2⁶⁸	2⁶⁹		-	-	5.952	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.444 GHz-days
Estimated T-Level:	0.050

Digits	B1	Curves	Complete	FacMiss
20	11000	1 / 100	0.010	99.000%
25	50000	1 / 280	0.004	99.643%

New Calculation Method

Total ECM effort:	0.444 GHz-days
Estimated T-Level:	0.050

Digits	B1	Complete	FacMiss
20	11000	0.032	96.826%
25	50000	0.003	99.709%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		1	0.444

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-04-05T00:48:00	Marco-DK84	i7-3770	50000	5000000						1	0.444

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2000-08-31T00:00:00	ANONYMOUS	v4_computers	77D6068298853424	2.930
2003-11-28T00:00:00	Martti Järvi	v4_computers	77D6068298853424	2.930

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-12-21T12:02:42

Alvin Bunk

BADCAT

149914778264519815607

8B4BEF51579568__

2021-01-22T22:17:34

XZT

M900Tiny2

149914778264519815607

8B4BEF5157956812

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 = 110000, B2 = 1952500 (P-1 stage 2)

B1 = 110000 (P-1 stage 1)

B1 = 55000, B2 = 838750 (P-1 stage 2)

B1 = 55000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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