M3754099 Mersenne number exponent details

Residue

Status

L-L

D445E4E029BFE209

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	7.9151	67.1642%	200000	130364850	1.1105	6.8113%	9.0255	69.4007%	2.2365%
PrimeNet	2⁶⁰	0.0409	63.3333%	16000	320000	0.0050	3.0914%	0.0459	64.4669%	1.1335%
GPU72	2⁶⁴	0.9481	65.6250%	22000	450000	0.0069	2.1111%	0.9550	66.3507%	0.7257%
Difference	+3	+6.9669	+1.5392%	+178000	+129914850	+1.1036	+4.7002%	+8.0705	+3.0500%	+3.0500%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

7.9151

67.1642%

200000

130364850

1.1105

6.8113%

9.0255

69.4007%

2.2365%

PrimeNet

2⁶⁰

0.0409

63.3333%

16000

320000

0.0050

3.0914%

0.0459

64.4669%

1.1335%

GPU72

2⁶⁴

0.9481

65.6250%

22000

450000

0.0069

2.1111%

0.9550

66.3507%

0.7257%

Difference

+6.9669

+1.5392%

+178000

+129914850

+1.1036

+4.7002%

+8.0705

+3.0500%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3754099	4936698399640271691863	22	72.064	657507753476969 293 × 185063 × 12125891	2009-09-06	185063	12125891	454.88	0.1273	0.1879

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3754099

4936698399640271691863

72.064

657507753476969
293 × 185063 × 12125891

2009-09-06

185063

12125891

454.88

0.1273

0.1879

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-07T17:50:00	Carsten Kossendey	leela	20000	265000		-		-	-	0.005	-	-	1.150%
2022-05-25T14:13:49	Jocelyn Larouche	Manual testing	200000	130364850		-	skipped known factor: 4936698399640271691863	-	-	1.110	-	-	6.811%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-03-04T08:03:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.041	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:

0.000 GHz-days

Digits	B1	Curves	Complete	FacMiss

New Calculation Method

Total ECM effort:

0.000 GHz-days

Digits	B1	Complete	FacMiss

ECM Summary

B1	B2	factor	curves	GHz-days
		4936698399640271691863	1	0.00000e+0

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-09-06T09:20:00	JimBa	D600			4936698399640271691863	72.064		1		1	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-07-30T00:00:00	LEE Sau Dan	v4_computers	D445E4E029BFE209	0.394

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T19:28:12

kkmrkkblmbrbk

Manual testing

4936698399640271691863

14C76620A1830B__

2017-12-04T23:09:12

Oliver Kruse

GTX-3

4936698399640271691863

14C76620A1830B__

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 = 200000, B2 = 130364850 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 20000, B2 = 265000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁷

2⁶¹

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