M5553269 Mersenne number exponent details

Residue

Status

L-L

30739F176EF901E0

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	5.3507	65.6716%	65000	1121250	0.0281	2.4659%	5.3788	66.5181%	0.8465%
PrimeNet	2⁶²	0.1106	62.9032%	24000	550000	0.0121	3.1664%	0.1227	64.0778%	1.1746%
GPU72	2⁶⁶	2.6594	65.1515%	34000	700000	0.0161	2.1571%	2.6755	65.9032%	0.7517%
Difference	+1	+2.6913	+0.5201%	+31000	+421250	+0.0120	+0.3088%	+2.7033	+0.6149%	+0.6149%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

5.3507

65.6716%

65000

1121250

0.0281

2.4659%

5.3788

66.5181%

0.8465%

PrimeNet

2⁶²

0.1106

62.9032%

24000

550000

0.0121

3.1664%

0.1227

64.0778%

1.1746%

GPU72

2⁶⁶

2.6594

65.1515%

34000

700000

0.0161

2.1571%

2.6755

65.9032%

0.7517%

Difference

+2.6913

+0.5201%

+31000

+421250

+0.0120

+0.3088%

+2.7033

+0.6149%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5553269	12815048016712780759546943	26	83.406	1153829214532267459 1217303 × 947857036853	2015-06-25	1217303	947857036853	537,452	11,825	22,086

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5553269

12815048016712780759546943

83.406

1153829214532267459
1217303 × 947857036853

2015-06-25

1217303

947857036853

537,452

11,825

22,086

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-06-06T07:41:00	Carsten Kossendey	leela	25000	356250		-		-	-	0.010	-	-	1.445%
2010-11-25T15:36:00	Squeeky_Squirrel	P4_2600	65000	1121250		-		-	-	0.028	-	-	2.466%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-02-11T05:10:00	GrunwalderGIMP	Manual testing	2⁶²	2⁶³		-	-	0.177	-	-
2014-12-14T20:34:00	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.354	-	-
2014-12-15T04:13:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	0.673	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.201 GHz-days
Estimated T-Level:	0.250

Digits	B1	Curves	Complete	FacMiss
20	11000	5 / 100	0.050	95.099%
25	50000	5 / 280	0.018	98.227%

New Calculation Method

Total ECM effort:	1.201 GHz-days
Estimated T-Level:	0.250

Digits	B1	Complete	FacMiss
20	11000	0.161	85.104%
25	50000	0.015	98.553%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.720
50000	5000000	12815048016712780759546943	2	0.480

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2011-01-31T21:24:00	Sebastian Hornbostel	Toshiba-NB	50000	5000000						3	0.720
2015-06-25T04:22:00	Bruce	desk16	50000	5000000	12815048016712780759546943	83.406	2	2		2	0.480

date	userid	compid	res64	spent (GHz-days)
2000-09-23T00:00:00	ANONYMOUS	v4_computers	30739F176EF901E0	0.877

date

userid

compid

res64

spent (GHz-days)

2000-09-23T00:00:00

ANONYMOUS

v4_computers

30739F176EF901E0

0.877

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T19:27:20

kkmrkkblmbrbk

Manual testing

12815048016712780759546943

7B2D0D561D3F30__

2018-07-07T23:56:27

Andrew B

my_custom_pc_x64

12815048016712780759546943

7B2D0D561D3F30__

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 = 1121250 (P-1 stage 2)

B1 = 65000 (P-1 stage 1)

B1 = 25000, B2 = 356250 (P-1 stage 2)

B1 = 25000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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