M28619 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	50.1646%	0.8128	50.1646%	50.1646%
PrimeNet	2⁴⁰	0.0000	62.5000%	500	10000	0.0000	4.0544%	0.0000	64.0204%	1.5204%
GPU72	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.7344%	0.0001	66.5004%	0.5913%
Difference	-44	-0.0001	-65.9091%	+499999500	+9999990000	+0.8128	+48.4302%	+0.8127	-16.3358%	-16.3358%

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

50.1646%

0.8128

50.1646%

PrimeNet

2⁴⁰

0.0000

62.5000%

500

10000

0.0000

4.0544%

0.0000

64.0204%

1.5204%

GPU72

2⁴⁴

0.0001

65.9091%

500

10000

0.0000

1.7344%

0.0001

66.5004%

0.5913%

Difference

-44

-0.0001

-65.9091%

+499999500

+9999990000

+0.8128

+48.4302%

+0.8127

-16.3358%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
28619	1101030169	10	30.036	19236 2² × 3 × 7 × 229	-	7	229	5.816e-9	1.525e-8	1.827e-8
28619	16739378603290845640074917144813791	35	113.689	292452192656816199728762660205 3 × 5 × 1559454730591 × 12502326910380317	2018-01-19	1559454730591	12502326910380317	5.294e+12	545,227	1,016,132

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

28619

1101030169

30.036

19236
2² × 3 × 7 × 229

229

5.816e-9

1.525e-8

1.827e-8

28619

16739378603290845640074917144813791

113.689

292452192656816199728762660205
3 × 5 × 1559454730591 × 12502326910380317

2018-01-19

1559454730591

12502326910380317

5.294e+12

545,227

1,016,132

exponent	prime factors	composite factor	digits	bits*
28619	1101030169 16739378603290845640074917144813791	18430560852536303731244599196615325778260679	44	143.725

exponent

prime factors

composite factor

digits

bits*

28619

1101030169
16739378603290845640074917144813791

18430560852536303731244599196615325778260679

143.725

	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: 1101030169	-	-	0.813	-	-	42.840%

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: 1101030169

0.813

-

-

42.840%

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		23	0.793
3000000	300000000	16739378603290845640074917144813791	477	16.45

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-04T14:32:00	Matthias Wurtinger	WUR_E6600	50000	5000000						30	0.017
2009-05-10T17:33:00	Matthias Wurtinger	WUR_E6600	250000	25000000						30	0.086
2010-04-18T21:45:00	James Hintz	10_122109	50000	5000000						3	0.002
2010-04-19T15:32:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-20T10:10:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-21T05:41:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-22T01:00:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-23T00:21:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-23T16:51:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-24T10:19:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-25T05:47:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-25T05:52:00	James Hintz	14_091909	50000	5000000						32	0.018
2010-04-26T01:45:00	James Hintz	10_122109	50000	5000000						11	0.006
2011-03-19T20:59:00	James Hintz	17_051310	250000	25000000						11	0.032
2014-11-20T02:01:00	James Hintz	08_04_2014	250000	25000000						567	1.629
2014-11-20T02:29:00	James Hintz	08_04_2014	1000000	100000000						11	0.126
2018-01-19T18:04:14	nordi	nordiputer	3000000	300000000	16739378603290845640074917144813791	113.689	477	2		477	16.45
2018-01-19T21:31:26	nordi	nordiputer	3000000	300000000						23	0.793

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T19:38:30

Oliver Kruse

PRP

1101030169

60C73FA4E97875__

2017-09-21T20:27:18

Oliver Kruse

Manual testing

1101030169

60C73FA4E97875__

2017-10-12T16:30:08

kkmrkkblmbrbk

Manual testing

1101030169

60C73FA4E97875__

2018-01-19T18:05:54

ATH

ec2-1xd

1101030169

16739378603290845640074917144813791

59762FD08ED84E__

2018-01-19T22:41:20

Squeeky_Squirrel

i5-5250U_1600

1101030169

16739378603290845640074917144813791

0925996A3DE3FE__

2018-01-19T22:45:54

Squeeky_Squirrel

i5-5250U_1600

1101030169

60C73FA4E97875__

2018-01-20T13:17:39

Squeeky_Squirrel

i5-5250U_1600

1101030169

16739378603290845640074917144813791

59762FD08ED84E__

2018-01-22T03:56:57

Oliver Kruse

GTX-4

1101030169

16739378603290845640074917144813791

59762FD08ED84E__

2018-02-28T19:54:12

kkmrkkblmbrbk

c5.xlarge

1101030169

16739378603290845640074917144813791

0925996A3DE3FE__

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

10¹²

10¹³

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

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