M2039761 Mersenne number exponent details

Residue

Status

L-L

CA4DA7487A50CFC0

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	14.5674	68.6567%	500000	15000000	0.1230	5.1352%	14.6903	70.2663%	1.6095%
PrimeNet	2⁵⁸	0.0188	63.7931%	9000	160000	0.0016	2.6631%	0.0205	64.7573%	0.9642%
GPU72	2⁶²	0.3012	66.1290%	9000	120000	0.0014	1.3289%	0.3026	66.5791%	0.4501%
Difference	+5	+14.2662	+2.5277%	+491000	+14880000	+0.1216	+3.8063%	+14.3877	+3.6871%	+3.6871%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.5674

68.6567%

500000

15000000

0.1230

5.1352%

14.6903

70.2663%

1.6095%

PrimeNet

2⁵⁸

0.0188

63.7931%

9000

160000

0.0016

2.6631%

0.0205

64.7573%

0.9642%

GPU72

2⁶²

0.3012

66.1290%

9000

120000

0.0014

1.3289%

0.3026

66.5791%

0.4501%

Difference

+14.2662

+2.5277%

+491000

+14880000

+0.1216

+3.8063%

+14.3877

+3.6871%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2039761	55473244238441916881	20	65.588	13597976488040 2³ × 5 × 7 × 31 × 1566587153	2009-10-16	31	1566587153	4.0208	8.1372	15.198

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2039761

55473244238441916881

65.588

13597976488040
2³ × 5 × 7 × 31 × 1566587153

2009-10-16

1566587153

4.0208

8.1372

15.198

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-24T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.274%
2009-02-10T22:35:00	markr	Manual testing	100000	3000000		-		-	-	0.025	-	-	2.899%
2016-03-17T19:19:50	alpertron	Manual testing	500000	15000000	12	-		-	-	0.123	-	-	5.135%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-10T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-
2022-03-09T07:29:22	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.075	-	-
2009-01-02T13:51:00	Sturle Sunde	giny.ifi	2⁶⁰	2⁶¹		-	-	0.075	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.486 GHz-days
Estimated T-Level:	1.900

Digits	B1	Curves	Complete	FacMiss
20	11000	38 / 100	0.380	68.255%
25	50000	38 / 280	0.136	87.288%

New Calculation Method

Total ECM effort:	3.486 GHz-days
Estimated T-Level:	1.900

Digits	B1	Complete	FacMiss
20	11000	1.517	21.933%
25	50000	0.141	86.807%
30	250000	0.009	99.107%

ECM Summary

B1	B2	factor	curves	GHz-days
		55473244238441916881	1	0.00000e+0
50000	5000000		17	1.441
50000	6447579		7	0.663
50000	6878062		7	0.684
50000	7150000		7	0.697

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-08T15:32:00	ClknGo Software	plms3	50000	5000000						3	0.254
2009-10-16T11:09:00	SubPrime	stor			55473244238441916881	65.588		1		1	-
2021-07-05T20:36:49	Jonathan Webb	Desktop2021	50000	5000000						7	0.594
2021-09-22T00:51:43	Ahmed Azhad	c5.4xlarge.azf	50000	6447579						7	0.663
2022-01-28T23:25:28	MarkS	desktop-i7	50000	5000000						7	0.594
2022-05-23T06:15:42	debrouxl	dl380g9-1	50000	6878062						7	0.684
2022-07-22T15:46:32	debrouxl	dl380g9-1	50000	7150000						7	0.697

date	userid	compid	res64	spent (GHz-days)
1999-01-29T00:00:00	ANONYMOUS	v4_computers	CA4DA7487A50CFC0	0.134

date

userid

compid

res64

spent (GHz-days)

1999-01-29T00:00:00

ANONYMOUS

v4_computers

CA4DA7487A50CFC0

0.134

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 = 500000 (P-1 stage 1)

B1 = 100000, B2 = 3000000 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

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