M4307377 Mersenne number exponent details

Residue

Status

L-L

1BECE3881F755D8C

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	6.8984	65.6716%	130000	2632500	0.0482	3.2910%	6.9465	66.8014%	1.1298%
PrimeNet	2⁶¹	0.0713	62.2951%	18000	360000	0.0066	2.9267%	0.0779	63.3986%	1.1035%
GPU72	2⁶⁵	1.6938	64.6154%	24000	500000	0.0090	1.9823%	1.7028	65.3168%	0.7014%
Difference	+2	+5.2046	+1.0563%	+106000	+2132500	+0.0391	+1.3087%	+5.2437	+1.4846%	+1.4846%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6.8984

65.6716%

130000

2632500

0.0482

3.2910%

6.9465

66.8014%

1.1298%

PrimeNet

2⁶¹

0.0713

62.2951%

18000

360000

0.0066

2.9267%

0.0779

63.3986%

1.1035%

GPU72

2⁶⁵

1.6938

64.6154%

24000

500000

0.0090

1.9823%

1.7028

65.3168%

0.7014%

Difference

+5.2046

+1.0563%

+106000

+2132500

+0.0391

+1.3087%

+5.2437

+1.4846%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4307377	43871510123464195783609	23	75.216	5092601613866652 2² × 3 × 1373 × 309092110577	2016-07-19	1373	309092110577	2,057.9	3,045.5	5,688.1

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4307377

43871510123464195783609

75.216

5092601613866652
2² × 3 × 1373 × 309092110577

2016-07-19

1373

309092110577

2,057.9

3,045.5

5,688.1

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-08-03T04:56:00	Carsten Kossendey	durandal	25000	343750		-		-	-	0.008	-	-	1.364%
2011-08-30T03:56:00	harlee	P4_2600	50000	775000		-		-	-	0.016	-	-	2.037%
2013-08-23T18:49:00	Squeeky_Squirrel	T7500_2200	130000	2632500		-		-	-	0.048	-	-	3.291%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2002-01-22T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.071	-	-
2010-12-12T01:43:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.071	-	-
2012-01-14T04:23:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.371	-	-
2016-02-23T16:29:53	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.228	-	-
2014-05-12T04:13:00	Jayder	Manual testing	2⁶³	2⁶⁴		-	-	0.456	-	-
2014-05-13T13:03:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.867	-	-
2015-06-14T11:55:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.735	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.463 GHz-days
Estimated T-Level:	0.400

Digits	B1	Curves	Complete	FacMiss
20	11000	8 / 100	0.080	92.274%
25	50000	8 / 280	0.029	97.178%

New Calculation Method

Total ECM effort:	1.463 GHz-days
Estimated T-Level:	0.400

Digits	B1	Complete	FacMiss
20	11000	0.258	77.255%
25	50000	0.023	97.695%
30	250000	0.001	99.856%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	1.097
50000	5000000	43871510123464195783609	2	0.366

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-12-10T19:49:00	GrunwalderGIMP	compute-0-9	50000	5000000						3	0.549
2013-03-09T20:58:00	Kish	HPtower-office	50000	5000000						3	0.549
2016-07-19T15:59:45	Bruce	desk	50000	5000000	43871510123464195783609	75.216	2	2		2	0.366

date	userid	compid	res64	spent (GHz-days)
2000-02-16T00:00:00	vidmar	v4_computers	1BECE3881F755D8C	0.537

date

userid

compid

res64

spent (GHz-days)

2000-02-16T00:00:00

vidmar

v4_computers

1BECE3881F755D8C

0.537

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T06:18:19

kkmrkkblmbrbk

Manual testing

43871510123464195783609

23EEC760072231__

2018-01-30T01:40:38

Oliver Kruse

GTX-4

43871510123464195783609

23EEC760072231__

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 = 130000, B2 = 2632500 (P-1 stage 2)

B1 = 130000 (P-1 stage 1)

B1 = 50000, B2 = 775000 (P-1 stage 2)

B1 = 50000 (P-1 stage 1)

B1 = 25000, B2 = 343750 (P-1 stage 2)

B1 = 25000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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