M10520669 Mersenne number exponent details

Residue

Status

L-L

4D5194B8F6A8ED7A

double-checked

PRP

1B48C2542E1FC9__

unverified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	2.8243	64.1791%	120000	2130000	0.1087	3.5179%	2.9330	65.4393%	1.2601%
PrimeNet	2⁶⁴	0.3383	62.5000%	45000	1300000	0.0537	3.7734%	0.3920	63.9150%	1.4150%
GPU72	2⁶⁸	5.6655	64.7059%	70000	1700000	0.0752	2.7057%	5.7407	65.6608%	0.9549%
Difference	-1	-2.8412	-0.5268%	+50000	+430000	+0.0335	+0.8122%	-2.8077	-0.2216%	-0.2216%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

2.8243

64.1791%

120000

2130000

0.1087

3.5179%

2.9330

65.4393%

1.2601%

PrimeNet

2⁶⁴

0.3383

62.5000%

45000

1300000

0.0537

3.7734%

0.3920

63.9150%

1.4150%

GPU72

2⁶⁸

5.6655

64.7059%

70000

1700000

0.0752

2.7057%

5.7407

65.6608%

0.9549%

Difference

-1

-2.8412

-0.5268%

+50000

+430000

+0.0335

+0.8122%

-2.8077

-0.2216%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
10520669	56226822596718569296079	23	75.574	2672207565731731 857 × 3118095175883	2016-11-21	857	3118095175883	1,119.5	80,468	150,291

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

10520669

56226822596718569296079

75.574

2672207565731731
857 × 3118095175883

2016-11-21

857

3118095175883

1,119.5

80,468

150,291

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-28T00:00:00	ANONYMOUS	v4_computers	45000	270000		-		-	-	0.027	-	-	1.707%
2013-07-23T02:57:00	Nesowa	Outback	120000	2130000		-		-	-	0.109	-	-	3.518%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-01-19T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.338	-	-
2013-07-04T15:41:00	David Campeau	Manual testing	2⁶⁴	2⁶⁵		-	-	0.355	-	-
2015-05-06T09:43:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	0.710	-	-
2015-11-14T12:38:42	VictordeHollander	Manual testing	2⁶⁶	2⁶⁷		-	-	1.421	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.993 GHz-days
Estimated T-Level:	0.100

Digits	B1	Curves	Complete	FacMiss
20	11000	2 / 100	0.020	98.010%
25	50000	2 / 280	0.007	99.287%

New Calculation Method

Total ECM effort:	0.993 GHz-days
Estimated T-Level:	0.100

Digits	B1	Complete	FacMiss
20	11000	0.065	93.752%
25	50000	0.006	99.419%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		1	0.497
50000	5000000	56226822596718569296079	1	0.497

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-06-19T02:31:00	Kish	HPLaptop	50000	5000000						1	0.497
2016-11-21T19:36:59	Bruce	Desk7	50000	5000000	56226822596718569296079	75.574	1	2		1	0.497

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2000-08-24T00:00:00	ANONYMOUS	v4_computers	4D5194B8F6A8ED7A	3.437
2004-03-26T00:00:00	ANONYMOUS	v4_computers	2B4A9E72B75A03__	3.437
2004-07-02T00:00:00	shaneamy	v4_computers	4D5194B8F6A8ED7A	3.437

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-09-15T20:17:05

fre_games

gpu

56226822596718569296079

1B48C2542E1FC9__

2021-03-08T05:35:48

rucio

56226822596718569296079

1B48C2542E1FC958

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 = 120000, B2 = 2130000 (P-1 stage 2)

B1 = 120000 (P-1 stage 1)

B1 = 45000, B2 = 270000 (P-1 stage 2)

B1 = 45000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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