M8211479 Mersenne number exponent details

Residue

Status

L-L

448FB9F5116FCEFC

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	3.6186	65.6716%	45000	753750	0.0317	2.1993%	3.6502	66.4266%	0.7550%
PrimeNet	2⁶³	0.1944	63.4921%	36000	900000	0.0315	3.6206%	0.2258	64.8139%	1.3218%
GPU72	2⁶⁷	3.6186	65.6716%	55000	1300000	0.0465	2.6270%	3.6651	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

3.6186

65.6716%

45000

753750

0.0317

2.1993%

3.6502

66.4266%

0.7550%

PrimeNet

2⁶³

0.1944

63.4921%

36000

900000

0.0315

3.6206%

0.2258

64.8139%

1.3218%

GPU72

2⁶⁷

3.6186

65.6716%

55000

1300000

0.0465

2.6270%

3.6651

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
8211479	10379665247642655031	20	63.170	632021664285 3² × 5 × 11 × 23 × 55513541	2011-08-11	23	55513541	0.2029	1.1451	2.1388

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

8211479

10379665247642655031

63.170

632021664285
3² × 5 × 11 × 23 × 55513541

2011-08-11

55513541

0.2029

1.1451

2.1388

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-08-03T00:00:00	Team Prime Rib	v4_computers	45000	697500		-		-	-	0.030	-	-	2.155%
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
2011-08-11T05:14:00	Carsten Kossendey	Manual testing	?	?	10379665247642655031	63.170	20	0.009	4.362	0.017
1998-08-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.075	-	-
1999-05-09T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.194	-	-
1999-11-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.194	-	-
2011-08-11T05:13:00	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	ANONYMOUS	v4_computers	448FB9F5116FCEFC	2.144
2003-03-27T00:00:00	Team Prime Rib	v4_computers	448FB9F5116FCEFC	2.144

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-09-15T14:55:19

Dylan Delgado

desktop

10379665247642655031

34CA469660CC33__

2020-03-09T09:44:43

marssystems

system11

10379665247642655031

34CA469660CC3331

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, B2 = 697500 (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

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