M19 387 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
Actual	2⁶⁷	1,532.6723	77.6119%	5400000000	15129309322837710	351,594.7187	35.6751%	353,127.3910	85.5989%
Target	2⁴⁴	0.0001	65.9091%	500	80000	0.0000	1.5449%	0.0001	66.4358%
Difference	+23	+1,532.6722	+11.7028%	+5399999500	+15129309322757710	+351,594.7187	+34.1302%	+353,127.3909	+19.1631%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

2⁶⁷

1,532.6723

77.6119%

5400000000

15129309322837710

351,594.7187

35.6751%

353,127.3910

85.5989%

Target

2⁴⁴

0.0001

65.9091%

500

80000

0.0000

1.5449%

0.0001

66.4358%

Difference

+23

+1,532.6722

+11.7028%

+5399999500

+15129309322757710

+351,594.7187

+34.1302%

+353,127.3909

+19.1631%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
19387	108010289039	12	36.652	2785637 17 × 163861	-	17	163861	9.216e-7	3.815e-6	7.112e-6
19387	617601887953	12	39.168	15928248 2³ × 3 × 7 × 94811	2008-08-26	8	94811	6.319e-6	2.207e-6	4.115e-6
19387	1759660617495005287995636181683708681077303	43	140.336	45382488716536990973220100626288458273 13 × 19 × 23 × 41 × 277 × 2803 × 4831 × 217852429 × 238439032782077	2023-04-19	217852429	238439032782077	7.563e+12	5,541.2	10,349

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

19387

108010289039

36.652

2785637
17 × 163861

163861

9.216e-7

3.815e-6

7.112e-6

19387

617601887953

39.168

15928248
2³ × 3 × 7 × 94811

2008-08-26

94811

6.319e-6

2.207e-6

4.115e-6

19387

1759660617495005287995636181683708681077303

140.336

45382488716536990973220100626288458273
13 × 19 × 23 × 41 × 277 × 2803 × 4831 × 217852429 × 238439032782077

2023-04-19

217852429

238439032782077

7.563e+12

5,541.2

10,349

exponent	prime factors	composite factor	digits	bits*
19387	108010289039 617601887953	66707358428835622047167	23	75.820
19387	108010289039 1759660617495005287995636181683708681077303	19006145190618074129524210095434369232063296693258 1817	54	176.989
19387	617601887953 1759660617495005287995636181683708681077303	10867697195214570474138233930331745997361978987374 30759	55	179.504
19387	108010289039 617601887953 1759660617495005287995636181683708681077303	11738231152434553645359059212561288743325986819353 4349447839150601	66	216.157

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2022-02-06	Lisander Viaene	Manual testing	50000	50000		-		-	-	2.13271e-5	-	-	0.222%
2023-04-19	JacobZ	GreatLakes	5400000000	15129309322837710			1759660617495005287995636181683708681077303	43	140.336	351,595	1.14060e-5	703,189	35.675%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2022-02-06

Lisander Viaene

Manual testing

50000

2.13271e-5

-

-

0.222%

2023-04-19

JacobZ

GreatLakes

5400000000

15129309322837710

1759660617495005287995636181683708681077303

140.336

351,595

1.14060e-5

703,189

35.675%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-08-26	ANONYMOUS	Manual testing	?	?	617601887953	39.168	12	2.54134e-6	0.000	5.57773e-5

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-08-26

ANONYMOUS

Manual testing

617601887953

39.168

2.54134e-6

0.000

5.57773e-5

ECM factoring results:

Total ECM effort:	21.133 GHz-days
Estimated T-Level:	36.176

Digits	B1	Complete	FacMiss
20	11000	419.539	0.000%
25	50000	88.789	0.000%
30	250000	14.813	0.000%
35	1000000	2.036	13.060%
40	3000000	0.235	79.048%
45	11000000	0.024	97.659%
50	44000000	0.002	99.790%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	163	0.050
250000	25000000	568	0.872
1000000	100000000	1,421	8.722
3000000	300000000	624	11.49

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-07	Matthias Wurtinger	WUR_E6600	50000	5000000						50	0.015
2009-06-08	unconnected	dual5430	250000	25000000						30	0.046
2009-06-15	Rob_Dee	twopc	50000	5000000						80	0.025
2009-06-18	Rob_Dee	twopc	50000	5000000						4	0.001
2009-06-19	Rob_Dee	twopc	50000	5000000						4	0.001
2009-06-19	Rob_Dee	twopc	50000	5000000						4	0.001
2009-06-20	Rob_Dee	twopc	50000	5000000						6	0.002
2009-06-26	Rob_Dee	twopc	50000	5000000						9	0.003
2009-06-27	Rob_Dee	twopc	50000	5000000						6	0.002
2009-06-28	Rob_Dee	twopc	250000	25000000						7	0.011
2011-04-03	James Hintz	17_051310	250000	25000000						11	0.017
2014-09-21	James Hintz	08_04_2014	250000	25000000						520	0.798
2014-09-21	James Hintz	08_04_2014	1000000	100000000						11	0.068
2017-10-07	kkmrkkblmbrbk	r4.2xlarge-4	1000000	100000000						1410	8.654
2019-10-16	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-20	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-23	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-27	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-31	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-11-03	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-11-07	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-11-10	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2020-06-05	James Hintz	work_lappy_5_16_2019	3000000	300000000						100	1.841
2022-03-19	nordi	sweet16_ccx3	3000000	300000000						500	9.207

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

PRP

108010289039

617601887953

56D64A789EF814__

2017-09-21

Oliver Kruse

Manual testing

108010289039

617601887953

56D64A789EF814__

2017-10-12

kkmrkkblmbrbk

Manual testing

108010289039

617601887953

56D64A789EF814__

2020-04-17

Oliver Kruse

Manual testing

108010289039

617601887953

DB8C8FEC79DE8D__

2023-04-19

JacobZ

GreatLakes

108010289039

617601887953

1759660617495005287995636181683708681077303

DB8C8FEC79DE8D85

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 = 5400000000, B2 = 15129309322837710 (P-1 stage 2)

B1 = 5400000000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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