M2399821 Mersenne number exponent details

Residue

Status

L-L

6C7FDE515A5C9694

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	12.3817	67.1642%	2000000	60000000	0.5055	7.6152%	12.8872	69.6647%	2.5005%
PrimeNet	2⁵⁹	0.0320	62.7119%	10000	170000	0.0018	2.4796%	0.0338	63.6365%	0.9246%
GPU72	2⁶³	0.6651	65.0794%	10000	140000	0.0017	1.2748%	0.6667	65.5245%	0.4452%
Difference	+4	+11.7167	+2.0848%	+1990000	+59860000	+0.5038	+6.3404%	+12.2204	+4.1402%	+4.1402%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

12.3817

67.1642%

2000000

60000000

0.5055

7.6152%

12.8872

69.6647%

2.5005%

PrimeNet

2⁵⁹

0.0320

62.7119%

10000

170000

0.0018

2.4796%

0.0338

63.6365%

0.9246%

GPU72

2⁶³

0.6651

65.0794%

10000

140000

0.0017

1.2748%

0.6667

65.5245%

0.4452%

Difference

+11.7167

+2.0848%

+1990000

+59860000

+0.5038

+6.3404%

+12.2204

+4.1402%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2399821	33871002269318429287	20	64.877	7056985139583 3 × 53 × 21961 × 2021017	2018-02-15	21961	2021017	2.9602	0.0128	0.0201
2399821	73011776172931861297	20	65.985	15211921258488 2³ × 3 × 1999 × 317073563	2009-01-30	1999	317073563	3.1129	1.6924	3.1605

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2399821

33871002269318429287

64.877

7056985139583
3 × 53 × 21961 × 2021017

2018-02-15

21961

2021017

2.9602

0.0128

0.0201

2399821

73011776172931861297

65.985

15211921258488
2³ × 3 × 1999 × 317073563

2009-01-30

1999

317073563

3.1129

1.6924

3.1605

exponent	prime factors	composite factor	digits	bits*
2399821	33871002269318429287 73011776172931861297	2472982036440344298202430564185386605239	40	130.861

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-21T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.287%
2018-09-28T16:25:27	alpertron	Manual testing	2000000	60000000	12	-	skipped known factor: 33871002269318429287	-	-	0.505	-	-	7.615%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.032	-	-
2022-03-09T16:37:58	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.064	-	-
2009-01-15T19:30:00	Sturle Sunde	ghibu.ifi	2⁶⁰	2⁶¹		-	-	0.064	-	-
2022-03-09T16:37:58	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	0.128	-	-
2022-03-09T16:37:58	LordJulius	Manual testing	2⁶²	2⁶³		-	-	0.409	-	-
2022-03-09T16:37:58	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	0.818	-	-
2018-02-15T14:22:15	TJAOI	Manual testing	2⁶⁴	2⁶⁵*	33871002269318429287	64.877	20	1.477	0.329	2.997

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.267 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	0.267 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
		73011776172931861297	1	0.00000e+0
50000	5000000		3	0.267

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-30T19:34:00	Aca Arsov	backo6400			73011776172931861297	65.985		1		1	-
2019-03-01T23:56:51	oodaira	com1	50000	5000000						3	0.267

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	6C7FDE515A5C9694	0.162

date

userid

compid

res64

spent (GHz-days)

1999-03-15T00:00:00

ANONYMOUS

v4_computers

6C7FDE515A5C9694

0.162

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-12T22:30:29

Oliver Kruse

GTX-1

86822AFB58949D__

2017-11-26T08:01:40

kkmrkkblmbrbk

c4.xlarge

73011776172931861297

86822AFB58949D__

2018-02-17T12:32:15

AdolfNor

Manual testing

33871002269318429287

73011776172931861297

86822AFB58949D__

2018-02-17T17:12:18

Oliver Kruse

GTX-0

33871002269318429287

73011776172931861297

86822AFB58949D__

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 = 2000000, B2 = 60000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁷

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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