M8213441 Mersenne number exponent details

Residue

Status

L-L

73CA097EB07CA820

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	3.6177	65.6716%	45000	753750	0.0317	2.1993%	3.6494	66.4266%	0.7550%
PrimeNet	2⁶³	0.1943	63.4921%	36000	900000	0.0315	3.6207%	0.2258	64.8139%	1.3219%
GPU72	2⁶⁷	3.6177	65.6716%	55000	1300000	0.0465	2.6271%	3.6642	66.5735%	0.9018%
Difference	-	-	-	-10000	-546250	-0.0148	-0.4278%	-0.0148	-0.1468%	-0.1468%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

3.6177

65.6716%

45000

753750

0.0317

2.1993%

3.6494

66.4266%

0.7550%

PrimeNet

2⁶³

0.1943

63.4921%

36000

900000

0.0315

3.6207%

0.2258

64.8139%

1.3219%

GPU72

2⁶⁷

3.6177

65.6716%

55000

1300000

0.0465

2.6271%

3.6642

66.5735%

0.9018%

Difference

-10000

-546250

-0.0148

-0.4278%

-0.0148

-0.1468%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
8213441	12975374790756951577	20	63.492	789886649868 2² × 3 × 19 × 3464415131	2011-08-10	19	3464415131	0.2744	71.463	133.47

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

8213441

12975374790756951577

63.492

789886649868
2² × 3 × 19 × 3464415131

2011-08-10

3464415131

0.2744

71.463

133.47

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-08-10T00:00:00	Team Prime Rib	v4_computers	45000	753750		-		-	-	0.032	-	-	2.199%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2011-08-10T05:16:00	Carsten Kossendey	Manual testing	?	?	12975374790756951577	63.492	20	0.080	4.363	0.163
1998-11-28T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.075	-	-
1998-12-06T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.194	-	-
2011-08-10T05:16:00	Carsten Kossendey	Manual testing	2⁶³	2⁶⁴	MISSED FACTOR!	-	-	0.239	-	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2000-01-12T00:00:00	EmilS	v4_computers	73CA097EB07CA820	2.145
2003-03-27T00:00:00	Team Prime Rib	v4_computers	73CA097EB07CA820	2.145

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-09-20T00:45:42

Oliver Kruse

GTX-0

12975374790756951577

4342B725A716B4__

2020-03-11T21:22:06

Luigi Morelli

9800X

12975374790756951577

4342B725A716B486

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 = 45000, B2 = 753750 (P-1 stage 2)

B1 = 45000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁷

2⁶⁴

2⁶³

2⁶²

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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