M3642559 Mersenne number exponent details

Residue

Status

L-L

13EA3E43C41E2BAA

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	8.1574	67.1642%	100000	130364850	1.0961	5.9863%	9.2535	69.1298%	1.9657%
PrimeNet	2⁶⁰	0.0422	63.3333%	16000	320000	0.0050	3.0753%	0.0471	64.4609%	1.1276%
GPU72	2⁶⁴	0.9772	65.6250%	22000	400000	0.0065	2.0355%	0.9836	66.3247%	0.6997%
Difference	+3	+7.1803	+1.5392%	+78000	+129964850	+1.0896	+3.9508%	+8.2699	+2.8051%	+2.8051%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

8.1574

67.1642%

100000

130364850

1.0961

5.9863%

9.2535

69.1298%

1.9657%

PrimeNet

2⁶⁰

0.0422

63.3333%

16000

320000

0.0050

3.0753%

0.0471

64.4609%

1.1276%

GPU72

2⁶⁴

0.9772

65.6250%

22000

400000

0.0065

2.0355%

0.9836

66.3247%

0.6997%

Difference

+7.1803

+1.5392%

+78000

+129964850

+1.0896

+3.9508%

+8.2699

+2.8051%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3642559	10838674223971788270673	23	73.199	1487782932818904 2³ × 3² × 29 × 712539718783	2015-09-10	29	712539718783	834.79	5,912.1	11,042

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3642559

10838674223971788270673

73.199

1487782932818904
2³ × 3² × 29 × 712539718783

2015-09-10

712539718783

834.79

5,912.1

11,042

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-07T04:41:00	Carsten Kossendey	leela	20000	245000		-		-	-	0.005	-	-	1.116%
2012-01-26T01:13:00	Squeeky_Squirrel	P4_2600	90000	1620000		-		-	-	0.026	-	-	2.691%
2022-03-05T05:36:53	Jocelyn Larouche	Manual testing	90000	90000		-		-	-	0.014	-	-	0.956%
2022-03-22T11:10:30	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.015	-	-	1.016%
2022-05-25T14:13:42	Jocelyn Larouche	Manual testing	100000	130364850		-		-	-	1.096	-	-	5.986%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-03-10T16:50:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.042	-	-
2011-05-19T09:47:00	markr	Manual testing	2¹	2⁶²		-	-	0.169	-	-
2012-06-20T01:22:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.438	-	-
2015-01-22T10:40:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.539	-	-
2015-01-22T10:40:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.026	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.040 GHz-days
Estimated T-Level:	0.350

Digits	B1	Curves	Complete	FacMiss
20	11000	7 / 100	0.070	93.207%
25	50000	7 / 280	0.025	97.527%

New Calculation Method

Total ECM effort:	1.040 GHz-days
Estimated T-Level:	0.350

Digits	B1	Complete	FacMiss
20	11000	0.226	79.787%
25	50000	0.020	97.980%
30	250000	0.001	99.874%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	0.891
50000	5000000	10838674223971788270673	1	0.149

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-10-22T22:16:00	arnaud	SPR11	50000	5000000						3	0.446
2012-05-14T15:29:00	Lukasz Wrobel	u-w	50000	5000000						3	0.446
2015-09-10T06:21:00	Bruce	agent86	50000	5000000	10838674223971788270673	73.199	1	2		1	0.149

date	userid	compid	res64	spent (GHz-days)
1999-07-30T00:00:00	ANONYMOUS	v4_computers	13EA3E43C41E2BAA	0.383

date

userid

compid

res64

spent (GHz-days)

1999-07-30T00:00:00

ANONYMOUS

v4_computers

13EA3E43C41E2BAA

0.383

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-11T07:23:31

Oliver Kruse

GTX-2

10838674223971788270673

AD1D23000253A8__

2017-12-19T03:05:21

kkmrkkblmbrbk

c4.xlarge

10838674223971788270673

AD1D23000253A8__

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 = 100000, B2 = 130364850 (P-1 stage 2)

B1 = 90000, B2 = 1620000 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 20000, B2 = 245000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁰

10¹

10²

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