M28409 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	unknown	500000000	10000000000	0.8128	50.1529%	0.8128	50.1529%	50.1529%
PrimeNet	2⁴⁰	0.0000	62.5000%	500	10000	0.0000	4.0468%	0.0000	64.0175%	1.5175%
GPU72	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.7306%	0.0001	66.4991%	0.5900%
Difference	-44	-0.0001	-65.9091%	+499999500	+9999990000	+0.8128	+48.4223%	+0.8127	-16.3461%	-16.3461%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

unknown

500000000

10000000000

0.8128

50.1529%

0.8128

50.1529%

PrimeNet

2⁴⁰

0.0000

62.5000%

500

10000

0.0000

4.0468%

0.0000

64.0175%

1.5175%

GPU72

2⁴⁴

0.0001

65.9091%

500

10000

0.0000

1.7306%

0.0001

66.4991%

0.5900%

Difference

-44

-0.0001

-65.9091%

+499999500

+9999990000

+0.8128

+48.4223%

+0.8127

-16.3461%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
28409	909089	6	19.794	16 2⁴	-	16	16	2.467e-12	1.278e-8	2.601e-8
28409	132600469588498919984130147144103	33	106.709	2333775732839926079484144939 3 × 7 × 73211026051 × 1517970499100309	2018-02-13	73211026051	1517970499100309	5.741e+12	66,111	123,374

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

28409

909089

19.794

16
2⁴

2.467e-12

1.278e-8

2.601e-8

28409

132600469588498919984130147144103

106.709

2333775732839926079484144939
3 × 7 × 73211026051 × 1517970499100309

2018-02-13

73211026051

1517970499100309

5.741e+12

66,111

123,374

exponent	prime factors	composite factor	digits	bits*
28409	909089 132600469588498919984130147144103	120545628297738894669452891337085452167	39	126.503

exponent

prime factors

composite factor

digits

bits*

28409

909089
132600469588498919984130147144103

120545628297738894669452891337085452167

126.503

	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	-	skipped known factor: 909089	-	-	0.813	-	-	42.827%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-12-28T07:28:38

kkmrkkblmbrbk

Manual testing

500000000

10000000000

skipped known factor: 909089

0.813

-

-

42.827%

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		356	12.27
3000000	300000000	132600469588498919984130147144103	144	4.965

	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
2010-04-18T21:21:00	James Hintz	10_122109	50000	5000000						3	0.002
2010-04-19T13:03:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-20T08:25:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-21T03:56:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-21T23:15:00	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
2010-04-24T08:34:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-25T00:29:00	James Hintz	14_091909	50000	5000000						32	0.018
2010-04-25T04:01:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-26T00:05:00	James Hintz	10_122109	50000	5000000						11	0.006
2011-03-20T01:48:00	James Hintz	17_051310	250000	25000000						11	0.032
2014-11-19T02:39:00	James Hintz	08_04_2014	250000	25000000						567	1.629
2014-11-19T03:04:00	James Hintz	08_04_2014	1000000	100000000						11	0.126
2018-02-13T18:37:36	nordi	nordiputer	3000000	300000000	132600469588498919984130147144103	106.709	144	2		144	4.965
2018-02-15T17:22:16	nordi	nordiputer	3000000	300000000						356	12.27

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T19:38:10

Oliver Kruse

PRP

909089

21BA922BD99A3C__

2017-09-21T21:28:57

Oliver Kruse

Manual testing

909089

21BA922BD99A3C__

2017-10-12T16:30:08

kkmrkkblmbrbk

Manual testing

909089

21BA922BD99A3C__

2018-02-15T22:43:29

Oliver Kruse

GTX-7

909089

132600469588498919984130147144103

94375CEC983AC8__

2018-02-17T07:38:19

Chang Chia-Tche

exbpc13

909089

132600469588498919984130147144103

94375CEC983AC8__

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

10¹⁰

10¹¹

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

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