M1 597 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	18,606.0849	83.5821%	13000000000	100371492803541960	161,450.6972	35.8071%	180,056.7820	89.4609%
Target	2⁴⁴	0.0015	75.0000%	500	10000	0.0000	0.7066%	0.0015	75.1766%
Difference	+23	+18,606.0834	+8.5821%	+12999999500	+100371492803531960	+161,450.6972	+35.1005%	+180,056.7806	+14.2842%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

2⁶⁷

18,606.0849

83.5821%

13000000000

100371492803541960

161,450.6972

35.8071%

180,056.7820

89.4609%

Target

2⁴⁴

0.0015

75.0000%

500

10000

0.0000

0.7066%

0.0015

75.1766%

Difference

+23

+18,606.0834

+8.5821%

+12999999500

+100371492803531960

+161,450.6972

+35.1005%

+180,056.7806

+14.2842%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1597	46421116904392458242754417331076737	35	115.160	14533850001375221741626304737344 2⁶ × 3 × 6563 × 30937 × 580343 × 642412662963079	2014-04-23	580343	642412662963079	1.130e+14	1,033.3	1,930.0
1597	48316324149219936973422647266327069023371707372348 457	53	175.013	15127214824427030987295756814754874459415061794724 2² × 7² × 19 × 461 × 1997 × 4412353629860619484373265215139146640203	2014-10-17	1997	4412353629860619484373265215139146640203	8.234e+13	7.097e+27	1.326e+28

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1597

46421116904392458242754417331076737

115.160

14533850001375221741626304737344
2⁶ × 3 × 6563 × 30937 × 580343 × 642412662963079

2014-04-23

580343

642412662963079

1.130e+14

1,033.3

1,930.0

1597

48316324149219936973422647266327069023371707372348
457

175.013

15127214824427030987295756814754874459415061794724
2² × 7² × 19 × 461 × 1997 × 4412353629860619484373265215139146640203

2014-10-17

1997

4412353629860619484373265215139146640203

8.234e+13

7.097e+27

1.326e+28

exponent	prime factors	composite factor	digits	bits*
1597	46421116904392458242754417331076737 48316324149219936973422647266327069023371707372348 457	22428977317214591743227203241993581470524603852729 37943877848443238039214840540170544809	88	290.173

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-09-07	kkmrkkblmbrbk	Manual testing	1000000000	100000000000	12	-		-	-	0.189	-	-	14.854%
2022-01-25	Ethan O'Connor	Manual testing	1300000000	10036658384863110		-	skipped known factor: 46421116904392458242754417331076737	-	-	16,144	-	-	30.328%
2022-01-25	Ethan O'Connor	Manual testing	13000000000	100371492803541960		-	skipped known factor: 46421116904392458242754417331076737	-	-	161,451	-	-	35.807%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-09-07

kkmrkkblmbrbk

Manual testing

1000000000

100000000000

0.189

-

-

14.854%

2022-01-25

Ethan O'Connor

Manual testing

1300000000

10036658384863110

skipped known factor: 46421116904392458242754417331076737

16,144

-

-

30.328%

2022-01-25

Ethan O'Connor

Manual testing

13000000000

100371492803541960

skipped known factor: 46421116904392458242754417331076737

161,451

-

-

35.807%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2021-07-22	ViliamF	3	1000000000	221000000000	2	7			-	-	0.457

date

userid

compid

start

factor

Smooth

digits

bits*

ghz-days

2021-07-22

ViliamF

1000000000

221000000000

0.457

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
1998-07-05	ANONYMOUS	v4_computers	2⁵⁰	2⁵²		-	-	0.282	-	-

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

1998-07-05

ANONYMOUS

v4_computers

2⁵⁰

2⁵²

0.282

-

-

ECM factoring results:

Total ECM effort:	53,790.718 GHz-days
Estimated T-Level:	64.029

Digits	B1	Complete	FacMiss
20	11000	108,951.700	0.000%
25	50000	49,044.498	0.000%
30	250000	18,716.560	0.000%
35	1000000	6,015.103	0.000%
40	3000000	1,709.473	0.000%
45	11000000	439.996	0.000%
50	44000000	102.710	0.000%
55	110000000	21.849	0.000%
60	260000000	4.342	1.301%
65	800000000	0.806	44.674%
70	2400000000	0.137	87.162%
75	7200000000	0.021	97.957%

ECM Summary

B1	B2	factor	curves	GHz-days
		48316324149219936973422647266327069023371707372348 457	1	0.00000e+0
44000000	4400000000		14,628	273.4
110000000	110000000		591	18.72
110000000	11000000000		21,227	992.0
110000000	110000000000		1,253	230.0
200000000	2000000000000		1	2.821
260000000	26000000000		59,404	6,562
850000000	85000000000		125,872	45,454
1000000000	100000000000		108	45.88
10000000000	1000000000000		50	212.4

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-10-13	Carsten Kossendey	durandal	44000000	4400000000						1	0.019
2010-12-30	James Hintz	NEW_OMFG	44000000	4400000000						3	0.056
2010-12-30	ANONYMOUS	13_052010	44000000	4400000000						3	0.056
2011-01-01	James Hintz	NEW_OMFG	44000000	4400000000						3	0.056
2011-01-04	James Hintz	NEW_OMFG	44000000	4400000000						3	0.056
2011-01-06	James Hintz	13_052010	44000000	4400000000						3	0.056
2011-01-06	James Hintz	NEW_OMFG	44000000	4400000000						3	0.056
2011-01-10	James Hintz	NEW_OMFG	44000000	4400000000						11	0.206
2011-01-10	James Hintz	17_051310	44000000	4400000000						3	0.056
2011-01-11	James Hintz	lappy_010411	44000000	4400000000						3	0.056
2012-01-01	Michael Kenn	Manual testing	44000000	4400000000						14592	272.8
2013-05-01	Never Odd Or Even	Note	200000000	2000000000000						1	2.821
2014-07-09	Matthias Wurtinger	i5-750	110000000	11000000000						1212	56.64
2014-07-09	Matthias Wurtinger	i5-4670K	110000000	11000000000						890	41.59
2014-09-29	Matthias Wurtinger	i5-4670K	110000000	110000000						227	7.192
2014-09-29	Matthias Wurtinger	i5-750	110000000	110000000						364	11.53
2014-10-17	Matthias Wurtinger	i5-4670K	110000000	110000000000						1253	230.0
2014-10-17	Matthias Wurtinger	i5-750	110000000	11000000000						41	1.916
2014-10-17	Matthias Wurtinger	i5-750			48316324149219936973422647266327069023371707372348 457	175.013		1		1	-
2015-06-25	Craig Meyers	Manual testing	1000000000	100000000000						1	0.425
2015-09-06	Craig Meyers	Manual testing	1000000000	100000000000						107	45.46
2015-12-07	Craig Meyers	Manual testing	10000000000	1000000000000						50	212.4
2019-11-16	Ryan Propper	Manual testing	110000000	11000000000						8492	396.8
2019-11-16	Ryan Propper	Manual testing	260000000	26000000000						25452	2,811
2019-11-16	Ryan Propper	Manual testing	850000000	85000000000						27936	10,088
2019-11-19	Ryan Propper	Manual testing	110000000	11000000000						10592	495.0
2019-11-19	Ryan Propper	Manual testing	260000000	26000000000						33952	3,750
2019-11-19	Ryan Propper	Manual testing	850000000	85000000000						97936	35,366

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

E6CEF3E8CD9C48__

2017-09-21

Oliver Kruse

Manual testing

E6CEF3E8CD9C48__

2017-10-02

kkmrkkblmbrbk

Manual testing

46421116904392458242754417331076737

48316324149219936973422647266327069023371707372348
457

E6CEF3E8CD9C48__

2017-12-07

ATH

Manual testing

46421116904392458242754417331076737

48316324149219936973422647266327069023371707372348
457

E6CEF3E8CD9C48__

2020-04-17

Oliver Kruse

IOS-1

46421116904392458242754417331076737

48316324149219936973422647266327069023371707372348
457

53A93A5FE1E90F95

2020-08-12

_p95holder_

TFL16_PRPt11-E_b

46421116904392458242754417331076737

48316324149219936973422647266327069023371707372348
457

53A93A5FE1E90F95

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 = 13000000000, B2 = 100371492803541960 (P-1 stage 2)

B1 = 1300000000, B2 = 10036658384863110 (P-1 stage 2)

B1 = 13000000000 (P-1 stage 1)

B1 = 1000000000, B2 = 100000000000 (P-1 stage 2)

B1 = 1300000000 (P-1 stage 1)

B1 = 1000000000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

10²¹

10²²

10²³

10²⁴

10²⁵

10²⁶

10²⁷

10²⁸

10²⁹

10³⁰

10³¹

10³²

10³³

10³⁴

10³⁵

10³⁶

10³⁷

10³⁸

10³⁹

10⁴⁰

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