M28393 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

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	1,046.5226	77.6119%	500000000	10000000000	0.8128	13.6491%	1,047.3354	80.6677%	3.0558%
PrimeNet	2⁴⁰	0.0000	62.5000%	500	10000	0.0000	4.0462%	0.0000	64.0173%	1.5173%
GPU72	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.7303%	0.0001	66.4990%	0.5899%
Difference	+23	+1,046.5226	+11.7028%	+499999500	+9999990000	+0.8128	+11.9187%	+1,047.3353	+14.1687%	+14.1687%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

1,046.5226

77.6119%

500000000

10000000000

0.8128

13.6491%

1,047.3354

80.6677%

3.0558%

PrimeNet

2⁴⁰

0.0000

62.5000%

500

10000

0.0000

4.0462%

0.0000

64.0173%

1.5173%

GPU72

2⁴⁴

0.0001

65.9091%

500

10000

0.0000

1.7303%

0.0001

66.4990%

0.5899%

Difference

+23

+1,046.5226

+11.7028%

+499999500

+9999990000

+0.8128

+11.9187%

+1,047.3353

+14.1687%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
28393	13304259770581138553	20	63.529	234287672499932 2² × 58571918124983	2014-04-23	4	58571918124983	71.957	2,548.8	4,760.5
28393	4498021793244645861861554830891457	34	111.793	79210048132367940370189040096 2⁵ × 13 × 23 × 41 × 719 × 280831851633456676043	2018-02-18	719	280831851633456676043	6.692e+12	1.222e+10	2.282e+10

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

28393

13304259770581138553

63.529

234287672499932
2² × 58571918124983

2014-04-23

58571918124983

71.957

2,548.8

4,760.5

28393

4498021793244645861861554830891457

111.793

79210048132367940370189040096
2⁵ × 13 × 23 × 41 × 719 × 280831851633456676043

2018-02-18

719

280831851633456676043

6.692e+12

1.222e+10

2.282e+10

exponent	prime factors	composite factor	digits	bits*
28393	13304259770581138553 4498021793244645861861554830891457	59842850391061973584150319917438026462539311021041 721	53	175.321

exponent

prime factors

composite factor

digits

bits*

28393

13304259770581138553
4498021793244645861861554830891457

59842850391061973584150319917438026462539311021041
721

175.321

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-12-28T07:28:38	kkmrkkblmbrbk	Manual testing	500000000	10000000000	12	-		-	-	0.813	-	-	13.649%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-12-28T07:28:38

kkmrkkblmbrbk

Manual testing

500000000

10000000000

0.813

-

-

13.649%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
1999-10-21T00:00:00	ANONYMOUS	v4_computers	2⁵²	2⁵³		-	-	0.021	-	-
2000-03-15T00:00:00	ANONYMOUS	v4_computers	2⁵³	2⁵⁴		-	-	0.042	-	-
2000-10-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.338	-	-

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

1999-10-21T00:00:00

ANONYMOUS

v4_computers

2⁵²

2⁵³

0.021

-

-

2000-03-15T00:00:00

ANONYMOUS

v4_computers

2⁵³

2⁵⁴

0.042

-

-

2000-10-15T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁶

0.338

-

-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.207 GHz-days
Estimated T-Level:	31.617

Digits	B1	Curves	Complete	FacMiss
20	11000	1283 / 100	12.830	0.000%
25	50000	1283 / 280	4.582	1.015%
30	250000	1119 / 640	1.748	17.381%
35	1000000	511 / 1580	0.323	72.360%
40	3000000	500 / 4700	0.106	89.907%

New Calculation Method

Total ECM effort:	19.207 GHz-days
Estimated T-Level:	31.617

Digits	B1	Complete	FacMiss
20	11000	157.528	0.000%
25	50000	31.927	0.000%
30	250000	5.499	0.409%
35	1000000	0.797	45.081%
40	3000000	0.098	90.623%
45	11000000	0.011	98.945%
50	44000000	0.001	99.899%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		164	0.094
250000	25000000		608	1.747
1000000	100000000		11	0.126
3000000	300000000		309	10.65
3000000	300000000	4498021793244645861861554830891457	191	6.586

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-04T14:31:00	Matthias Wurtinger	WUR_E6600	50000	5000000						30	0.017
2009-05-10T17:33:00	Matthias Wurtinger	WUR_E6600	250000	25000000						30	0.086
2010-04-18T21:18:00	James Hintz	10_122109	50000	5000000						3	0.002
2010-04-19T12:53:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-20T08:14:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-21T03:45:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-21T23:04:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-22T19:15:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-23T16:51:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-24T08:24:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-24T23:57:00	James Hintz	14_091909	50000	5000000						32	0.018
2010-04-25T03:50:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-25T23:54:00	James Hintz	10_122109	50000	5000000						11	0.006
2011-03-20T02:13:00	James Hintz	17_051310	250000	25000000						11	0.032
2014-11-18T13:55:00	James Hintz	08_04_2014	250000	25000000						567	1.629
2014-11-18T14:21:00	James Hintz	08_04_2014	1000000	100000000						11	0.126
2018-02-18T16:08:50	nordi	nordiputer	3000000	300000000	4498021793244645861861554830891457	111.793	191	2		191	6.586
2018-02-20T02:34:31	nordi	nordiputer	3000000	300000000						309	10.65

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T19:38:15

Oliver Kruse

Oliver-PC

13304259770581138553

A0569BFEC18225__

2017-09-21T20:27:18

Oliver Kruse

Manual testing

13304259770581138553

A0569BFEC18225__

2017-10-12T16:30:08

kkmrkkblmbrbk

Manual testing

13304259770581138553

A0569BFEC18225__

2018-02-21T03:00:34

Oliver Kruse

GTX-5

13304259770581138553

4498021793244645861861554830891457

EFE338459BE67D__

2018-02-21T17:35:31

kkmrkkblmbrbk

c5.large

13304259770581138553

4498021793244645861861554830891457

EFE338459BE67D__

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 = 500000000, B2 = 10000000000 (P-1 stage 2)

B1 = 500000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

10²¹

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