M749129 Mersenne number exponent details

Residue

Status

L-L

E4D53386BAB080__

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	39.6646	70.1493%	500000	15000000	0.0374	4.5470%	39.7020	71.5066%	1.3573%
PrimeNet	2⁴⁰	0.0000	50.0000%	7000	280000	0.0006	21.9541%	0.0006	60.9770%	10.9770%
GPU72	2⁴⁴	0.0000	54.5455%	12000	450000	0.0010	16.6281%	0.0010	62.1037%	7.5582%
Difference	+23	+39.6646	+15.6038%	+488000	+14550000	+0.0363	-12.0811%	+39.7009	+9.4029%	+9.4029%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

39.6646

70.1493%

500000

15000000

0.0374

4.5470%

39.7020

71.5066%

1.3573%

PrimeNet

2⁴⁰

0.0000

50.0000%

7000

280000

0.0006

21.9541%

0.0006

60.9770%

10.9770%

GPU72

2⁴⁴

0.0000

54.5455%

12000

450000

0.0010

16.6281%

0.0010

62.1037%

7.5582%

Difference

+23

+39.6646

+15.6038%

+488000

+14550000

+0.0363

-12.0811%

+39.7009

+9.4029%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
749129	568810652571212479	18	58.981	379647999591 3 × 7² × 97 × 26625149	2007-08-30	97	26625149	0.0864	0.0420	0.0785

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

749129

568810652571212479

58.981

379647999591
3 × 7² × 97 × 26625149

2007-08-30

26625149

0.0864

0.0420

0.0785

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-12-07T00:00:00	Alex Kruppa	v4_computers	100000	4000000		-		-	-	0.009	-	-	2.656%
2002-05-25T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.003	-	-	1.257%
2002-07-20T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.006	-	-	1.888%
2002-11-24T00:00:00	ANONYMOUS	v4_computers	65537	6553700		-		-	-	0.012	-	-	2.659%
2003-06-30T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.024	-	-	3.558%
2016-03-17T18:51:51	alpertron	Manual testing	500000	15000000	12	-		-	-	0.037	-	-	4.547%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-09-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.006	-	-
2001-03-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.013	-	-
2001-12-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.026	-	-
2003-09-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.051	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	11.371 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	325 / 100	3.250	3.815%
25	50000	325 / 280	1.161	31.261%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	11.371 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	14.808	0.000%
25	50000	1.620	19.795%
30	250000	0.132	87.678%
35	1000000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
		568810652571212479	1	0.00000e+0
50000	5000000		281	6.378
250000	25000000		44	4.993

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-30T17:44:00	Team_Bundu	bundu1			568810652571212479	58.981		1		1	-
2015-10-23T13:50:12	TJAOI	Manual testing	50000	5000000						100	2.270
2016-07-22T12:44:08	TJAOI	Manual testing	50000	5000000						90	2.043
2017-02-03T18:28:46	TJAOI	Manual testing	50000	5000000						91	2.065
2019-01-11T18:43:59	TJAOI	Manual testing	250000	25000000						44	4.993

date	userid	compid	res64	spent (GHz-days)
2003-05-19T00:00:00	ANONYMOUS	v4_computers	E4D53386BAB080__	0.015

date

userid

compid

res64

spent (GHz-days)

2003-05-19T00:00:00

ANONYMOUS

v4_computers

E4D53386BAB080__

0.015

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27T18:04:25

Oliver Kruse

GTX-0

568810652571212479

4BDC256FD2AA76__

2017-10-13T16:53:30

Oliver Kruse

Threadripper

4BDC256FD2AA76__

2017-12-16T18:22:50

ATH

work

568810652571212479

4BDC256FD2AA76__

2020-04-20T22:17:33

Oliver Kruse

AddPrpType5

568810652571212479

4072B0436C2883__

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 65537, B2 = 6553700 (P-1 stage 2)

B1 = 100000, B2 = 4000000 (P-1 stage 2)

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

B1 = 131072 (P-1 stage 1)

B1 = 16384, B2 = 1638400 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 65537 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

B1 = 16384 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

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