M16800271 Mersenne number exponent details

Residue

Status

L-L

F8B60B65C93A5763

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	1.7687	62.6866%	205000	4458750	0.3463	4.7320%	2.1149	64.4522%	1.7657%
PrimeNet	2⁶⁵	0.4343	61.5385%	80000	2400000	0.1636	4.5227%	0.5979	63.2780%	1.7395%
GPU72	2⁶⁹	7.1062	63.7681%	120000	3200000	0.2282	3.2897%	7.3344	64.9601%	1.1919%
Difference	-2	-5.3376	-1.0815%	+85000	+1258750	+0.1181	+1.4422%	-5.2195	-0.5078%	-0.5078%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

1.7687

62.6866%

205000

4458750

0.3463

4.7320%

2.1149

64.4522%

1.7657%

PrimeNet

2⁶⁵

0.4343

61.5385%

80000

2400000

0.1636

4.5227%

0.5979

63.2780%

1.7395%

GPU72

2⁶⁹

7.1062

63.7681%

120000

3200000

0.2282

3.2897%

7.3344

64.9601%

1.1919%

Difference

-2

-5.3376

-1.0815%

+85000

+1258750

+0.1181

+1.4422%

-5.2195

-0.5078%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
16800271	1541898108320792830799	22	70.385	45889084417769 41 × 379 × 30493 × 96847	2017-06-10	30493	96847	27.437	0.0270	0.0492

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

16800271

1541898108320792830799

70.385

45889084417769
41 × 379 × 30493 × 96847

2017-06-10

30493

96847

27.437

0.0270

0.0492

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-10-19T00:00:00	ANONYMOUS	v4_computers	205000	4458750		-	MISSED FACTOR!	-	-	0.346	-	-	4.732%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-12-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.001	-	-
2001-04-15T00:00:00	Net_Force	v4_computers	2¹	2⁵⁹		-	-	0.005	-	-
2001-07-17T00:00:00	Jocelyn Larouche	v4_computers	2¹	2⁶⁰		-	-	0.009	-	-
2002-01-02T00:00:00	subgenius	v4_computers	2¹	2⁶⁵		-	-	0.434	-	-
2014-03-13T21:08:00	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.445	-	-
2014-09-15T21:07:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	0.890	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.831 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:	0.831 GHz-days
Estimated T-Level:	0.050

Digits	B1	Complete	FacMiss
20	11000	0.038	96.227%
25	50000	0.004	99.645%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	1541898108320792830799	1	0.831

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-06-10T21:43:41	ATH	ec2-1x	50000	5000000	1541898108320792830799	70.385	1	2		1	0.831

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-11-16T00:00:00	ANONYMOUS	v4_computers	F8B60B65C93A5763	9.186
2006-04-14T00:00:00	ANONYMOUS	v4_computers	7E894C72836C8D__	9.186
2007-09-13T00:00:00	shaneamy	v4_computers	F8B60B65C93A5763	9.186

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 = 205000, B2 = 4458750 (P-1 stage 2)

B1 = 205000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁰

2⁵⁹

2⁵⁶

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