M9002671 Mersenne number exponent details

Residue

Status

L-L

D0EF852FFDEBBA07

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	2⁶⁸	6.6208	64.7059%	2500000	72000000	2.5194	8.3817%	9.1402	67.6641%	2.9583%
PrimeNet	2⁶⁴	0.3954	62.5000%	36000	1000000	0.0355	3.3269%	0.4308	63.7476%	1.2476%
GPU72	2⁶⁸	6.6208	64.7059%	60000	1300000	0.0511	2.4000%	6.6719	65.5529%	0.8471%
Difference	-	-	-	+2440000	+70700000	+2.4683	+5.9817%	+2.4683	+2.1112%	+2.1112%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

6.6208

64.7059%

2500000

72000000

2.5194

8.3817%

9.1402

67.6641%

2.9583%

PrimeNet

2⁶⁴

0.3954

62.5000%

36000

1000000

0.0355

3.3269%

0.4308

63.7476%

1.2476%

GPU72

2⁶⁸

6.6208

64.7059%

60000

1300000

0.0511

2.4000%

6.6719

65.5529%

0.8471%

Difference

+2440000

+70700000

+2.4683

+5.9817%

+2.4683

+2.1112%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
9002671	160912509458952521950925521	27	87.056	8936931576137377560 2³ × 3 × 5 × 11 × 739 × 1181527 × 7754011	2018-03-01	1181527	7754011	4,973,594	0.6170	0.9637

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

9002671

160912509458952521950925521

87.056

8936931576137377560
2³ × 3 × 5 × 11 × 739 × 1181527 × 7754011

2018-03-01

1181527

7754011

4,973,594

0.6170

0.9637

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2012-05-22T14:46:00	Squeeky_Squirrel	P4_2600	100000	1675000		-		-	-	0.074	-	-	2.816%
2018-03-01T09:07:07	mikr	Color	2500000	72000000	12		160912509458952521950925521	27	87.056	2.519	4.976	5.039	8.382%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-28T00:00:00	Lars Fricke	v4_computers	2¹	2⁶¹		-	-	0.034	-	-
1998-12-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.177	-	-
2016-02-23T16:39:27	Mark Rose	Manual testing	2⁶³	2⁶⁴		-	-	0.218	-	-
2009-12-09T06:52:00	Bud	annan	2⁶⁴	2⁶⁵		-	-	0.415	-	-
2015-05-12T08:17:00	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	0.830	-	-
2016-03-16T23:47:03	snme2pm1	Manual testing	2⁶⁶	2⁶⁷		-	-	1.660	-	-
2016-12-17T09:23:56	snme2pm1	Manual testing	2⁶⁷	2⁶⁸		-	-	3.320	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.261 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	1.261 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.097	90.776%
25	50000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	1.261

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2014-01-30T09:26:00	Dogbert948	Haswell	50000	5000000						3	1.261

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2003-05-19T00:00:00	Team Prime Rib	v4_computers	D0EF852FFDEBBA07	2.488

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-05-29T17:40:26

vnatin

160912509458952521950925521

955B43B054E5C7__

2020-10-20T15:57:58

oodaira

com2

160912509458952521950925521

955B43B054E5C798

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 = 2500000, B2 = 72000000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 100000, B2 = 1675000 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁷

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶¹

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