M1829623 Mersenne number exponent details

Residue

Status

L-L

00882CF150787136

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	16.2405	68.6567%	2780000	15000000	0.2711	5.8436%	16.5115	70.4883%	1.8316%
PrimeNet	2⁵⁷	0.0105	63.1579%	8000	150000	0.0012	2.8790%	0.0117	64.2186%	1.0607%
GPU72	2⁶¹	0.1679	65.5738%	9000	140000	0.0013	1.5945%	0.1692	66.1227%	0.5489%
Difference	+6	+16.0726	+3.0829%	+2771000	+14860000	+0.2698	+4.2491%	+16.3424	+4.3656%	+4.3656%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.2405

68.6567%

2780000

15000000

0.2711

5.8436%

16.5115

70.4883%

1.8316%

PrimeNet

2⁵⁷

0.0105

63.1579%

8000

150000

0.0012

2.8790%

0.0117

64.2186%

1.0607%

GPU72

2⁶¹

0.1679

65.5738%

9000

140000

0.0013

1.5945%

0.1692

66.1227%

0.5489%

Difference

+16.0726

+3.0829%

+2771000

+14860000

+0.2698

+4.2491%

+16.3424

+4.3656%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1829623	111532285241754529727160073	27	86.528	30479581105439352732 2² × 3² × 325463 × 960059 × 2709611	2015-06-17	960059	2709611	12,703,504	0.0830	0.1537

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1829623

111532285241754529727160073

86.528

30479581105439352732
2² × 3² × 325463 × 960059 × 2709611

2015-06-17

960059

2709611

12,703,504

0.0830

0.1537

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-10T06:34:00	Carsten Kossendey	leela	100000	1675000		-		-	-	0.015	-	-	2.491%
2014-05-19T21:00:00	Jocelyn Larouche	Manual testing	135081	135081		-		-	-	0.011	-	-	1.060%
2014-09-22T21:00:00	Jocelyn Larouche	Manual testing	170162	170162		-		-	-	0.013	-	-	1.200%
2015-06-17T17:35:00	mikr	MSI	2780000	15000000			111532285241754529727160073	27	86.528	0.219	0.199	0.437	5.844%
2016-03-16T12:39:19	alpertron	Manual testing	500000	15000000	12	-		-	-	0.101	-	-	5.068%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-16T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.021	-	-
2010-04-10T20:20:00	Architects Cubed	Manual testing	2⁶⁰	2⁶¹		-	-	0.084	-	-
2011-01-21T16:10:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.872	-	-
2015-04-26T04:57:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.073	-	-
2015-04-26T04:57:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.042	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.454 GHz-days
Estimated T-Level:	24.786

Digits	B1	Curves	Complete	FacMiss
20	11000	268 / 100	2.680	6.764%
25	50000	268 / 280	0.957	38.333%

New Calculation Method

Total ECM effort:	20.454 GHz-days
Estimated T-Level:	24.786

Digits	B1	Complete	FacMiss
20	11000	9.137	0.011%
25	50000	0.828	43.707%
30	250000	0.051	95.010%
35	1000000	0.002	99.765%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		47	3.246
50000	6600000		221	17.21

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-02T04:37:00	Lupo	yorick	50000	5000000						3	0.207
2009-07-17T04:36:00	James Hintz	01_071509	50000	5000000						3	0.207
2010-11-07T01:16:00	Mistel		50000	5000000						3	0.207
2012-05-22T05:55:00	OS1	L3	50000	5000000						3	0.207
2013-08-15T22:34:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-05-04T03:13:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-10-20T18:00:00	mikr	MSI	50000	5000000						12	0.829
2021-02-15T12:24:36	MarkS	desktop-i7	50000	5000000						17	1.174
2021-04-23T12:19:17	TJAOI	Manual testing	50000	6600000						221	17.21

date	userid	compid	res64	spent (GHz-days)
1998-12-21T00:00:00	ANONYMOUS	v4_computers	00882CF150787136	0.099

date

userid

compid

res64

spent (GHz-days)

1998-12-21T00:00:00

ANONYMOUS

v4_computers

00882CF150787136

0.099

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T01:23:52

Oliver Kruse

GTX-2

111532285241754529727160073

AFF6F9065CA3DA__

2017-11-06T10:25:13

bayanne

iMac1

111532285241754529727160073

AFF6F9065CA3DA__

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 = 2780000, B2 = 15000000 (P-1 stage 2)

B1 = 2780000 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 100000, B2 = 1675000 (P-1 stage 2)

B1 = 170162 (P-1 stage 1)

B1 = 135081 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁷

10⁴

10⁵

10⁶

10⁷

10⁸

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