M457829 Mersenne number exponent details

Residue

Status

L-L

A476690BE028DE__

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	64.9018	71.6418%	3000000	100000000	0.1415	7.2135%	65.0433	73.6874%	2.0456%
PrimeNet	2⁴⁰	0.0000	52.5000%	4500	150000	0.0002	18.3953%	0.0002	61.2378%	8.7378%
GPU72	2⁴⁴	0.0000	56.8182%	8000	260000	0.0004	13.8680%	0.0004	62.8066%	5.9884%
Difference	+23	+64.9018	+14.8236%	+2992000	+99740000	+0.1411	-6.6544%	+65.0429	+10.8808%	+10.8808%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

64.9018

71.6418%

3000000

100000000

0.1415

7.2135%

65.0433

73.6874%

2.0456%

PrimeNet

2⁴⁰

0.0000

52.5000%

4500

150000

0.0002

18.3953%

0.0002

61.2378%

8.7378%

GPU72

2⁴⁴

0.0000

56.8182%

8000

260000

0.0004

13.8680%

0.0004

62.8066%

5.9884%

Difference

+23

+64.9018

+14.8236%

+2992000

+99740000

+0.1411

-6.6544%

+65.0429

+10.8808%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
457829	11587618707333379121	20	63.329	12654963651640 2³ × 5 × 41 × 109 × 70793039	2007-09-06	109	70793039	5.9180	0.0659	0.1230

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

457829

11587618707333379121

63.329

12654963651640
2³ × 5 × 41 × 109 × 70793039

2007-09-06

109

70793039

5.9180

0.0659

0.1230

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-12-22T00:00:00	ANONYMOUS	v4_computers	2000	200000		-		-	-	0.000	-	-	0.172%
2001-12-22T00:00:00	ANONYMOUS	v4_computers	50000	1000000		-		-	-	0.002	-	-	1.486%
2002-06-23T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.004	-	-	1.731%
2002-09-07T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.007	-	-	2.460%
2016-03-17T18:48:26	alpertron	Manual testing	3000000	100000000	12	-	skipped known factor: 11587618707333379121	-	-	0.141	-	-	7.214%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-03-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.021	-	-
2002-02-10T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.042	-	-
2004-01-18T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.084	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	12.906 GHz-days
Estimated T-Level:	26.125

Digits	B1	Curves	Complete	FacMiss
20	11000	425 / 100	4.250	1.396%
25	50000	425 / 280	1.518	21.859%
30	250000	144 / 640	0.225	79.838%

New Calculation Method

Total ECM effort:	12.906 GHz-days
Estimated T-Level:	26.125

Digits	B1	Complete	FacMiss
20	11000	23.899	0.000%
25	50000	3.028	4.840%
30	250000	0.287	75.049%
35	1000000	0.022	97.832%
40	3000000	0.001	99.860%

ECM Summary

B1	B2	factor	curves	GHz-days
		11587618707333379121	1	0.00000e+0
50000	5000000		281	3.623
250000	25000000		144	9.283

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-16T13:17:00	ANONYMOUS	Bayes	50000	5000000						1	0.013
2007-09-06T17:37:00	Team_Bundu	bundu1			11587618707333379121	63.329		1		1	-
2013-12-15T17:09:00	Richard B. Woods	Puttputt	50000	5000000						9	0.116
2015-04-17T10:33:00	TJAOI	Manual testing	50000	5000000						90	1.160
2016-02-12T13:31:55	TJAOI	Manual testing	50000	5000000						90	1.160
2016-06-24T03:47:46	TJAOI	Manual testing	50000	5000000						91	1.173
2018-03-09T17:08:02	TJAOI	Manual testing	250000	25000000						44	2.837
2020-05-18T10:33:48	TJAOI	Manual testing	250000	25000000						100	6.447

date	userid	compid	res64	spent (GHz-days)
2002-08-24T00:00:00	ANONYMOUS	v4_computers	A476690BE028DE__	0.005

date

userid

compid

res64

spent (GHz-days)

2002-08-24T00:00:00

ANONYMOUS

v4_computers

A476690BE028DE__

0.005

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-25T07:06:09

Oliver Kruse

Doppelherz

11587618707333379121

E8B0E10112571A__

2017-09-27T07:34:16

Oliver Kruse

Manual testing

11587618707333379121

E8B0E10112571A__

2017-11-07T05:58:17

kkmrkkblmbrbk

c4.xlarge

11587618707333379121

E8B0E10112571A__

2020-04-18T10:08:38

Oliver Kruse

AddPrpType5

11587618707333379121

EA72906D8D396D__

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 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 65536, B2 = 6553600 (P-1 stage 2)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 50000, B2 = 1000000 (P-1 stage 2)

B1 = 65536 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

B1 = 2000, B2 = 200000 (P-1 stage 2)

B1 = 2000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

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