M5608033 Mersenne number exponent details

Residue

Status

L-L

353970B3DADB4470

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	5.2985	65.6716%	65000	1023750	0.0268	2.4141%	5.3253	66.5004%	0.8287%
PrimeNet	2⁶²	0.1096	62.9032%	24000	550000	0.0121	3.1715%	0.1216	64.0798%	1.1765%
GPU72	2⁶⁶	2.6334	65.1515%	36000	700000	0.0165	2.1904%	2.6500	65.9149%	0.7633%
Difference	+1	+2.6650	+0.5201%	+29000	+323750	+0.0103	+0.2237%	+2.6753	+0.5855%	+0.5855%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

5.2985

65.6716%

65000

1023750

0.0268

2.4141%

5.3253

66.5004%

0.8287%

PrimeNet

2⁶²

0.1096

62.9032%

24000

550000

0.0121

3.1715%

0.1216

64.0798%

1.1765%

GPU72

2⁶⁶

2.6334

65.1515%

36000

700000

0.0165

2.1904%

2.6500

65.9149%

0.7633%

Difference

+2.6650

+0.5201%

+29000

+323750

+0.0103

+0.2237%

+2.6753

+0.5855%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5608033	23460136500719806745527	23	74.313	2091654640826811 3⁵ × 2039 × 4221496943	2015-08-13	2039	4221496943	725.18	52.665	98.363

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5608033

23460136500719806745527

74.313

2091654640826811
3⁵ × 2039 × 4221496943

2015-08-13

2039

4221496943

725.18

52.665

98.363

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-06-06T06:59:00	Carsten Kossendey	leela	30000	397500		-		-	-	0.011	-	-	1.570%
2011-01-10T20:42:00	harlee	P4_2600	65000	1023750		-		-	-	0.027	-	-	2.414%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-02-09T04:43:00	GrunwalderGIMP	Manual testing	2⁶²	2⁶³		-	-	0.175	-	-
2014-11-10T12:42:00	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.350	-	-
2014-11-11T11:59:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	0.666	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.441 GHz-days
Estimated T-Level:	0.300

Digits	B1	Curves	Complete	FacMiss
20	11000	6 / 100	0.060	94.148%
25	50000	6 / 280	0.021	97.876%

New Calculation Method

Total ECM effort:	1.441 GHz-days
Estimated T-Level:	0.300

Digits	B1	Complete	FacMiss
20	11000	0.194	82.403%
25	50000	0.017	98.266%
30	250000	0.001	99.892%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.720
50000	5000000	23460136500719806745527	3	0.720

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2011-04-27T11:37:00	Lukin Dmitry	Dmitry	50000	5000000						3	0.720
2015-08-13T05:48:00	Bruce	d975xbx2	50000	5000000	23460136500719806745527	74.313	3	2		3	0.720

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-11-24T00:00:00	ANONYMOUS	v4_computers	353970B3DADB4470	0.886
2000-09-29T00:00:00	ANONYMOUS	v4_computers	353970B3DADB4470	0.886

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-12-08T22:20:12

Oliver Kruse

Threadripper

23460136500719806745527

C218513C3637AF__

2018-04-05T10:47:16

kkmrkkblmbrbk

c5.xlarge

23460136500719806745527

C218513C3637AF__

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 = 65000, B2 = 1023750 (P-1 stage 2)

B1 = 65000 (P-1 stage 1)

B1 = 30000, B2 = 397500 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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