M49408277 Mersenne number exponent details

Residue

Status

L-L

DCF3767D8E3062AA

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	2⁷⁴	77.4337	64.8649%	1000000	20000000	5.4061	4.4096%	82.8398	69.2745%	6.9557%
PrimeNet	2⁶⁹	2.4163	62.3188%	220000	9000000	1.8551	5.1241%	4.2714	67.4429%	5.1241%
GPU72	2⁷³	38.7151	64.3836%	320000	10000000	2.2509	3.6771%	40.9660	68.0607%	3.6771%
Difference	+1	+38.7186	+0.4813%	+680000	+10000000	+3.1551	+0.7325%	+41.8738	+1.2138%	+1.2138%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷⁴

77.4337

64.8649%

1000000

20000000

5.4061

4.4096%

82.8398

69.2745%

6.9557%

PrimeNet

2⁶⁹

2.4163

62.3188%

220000

9000000

1.8551

5.1241%

4.2714

67.4429%

5.1241%

GPU72

2⁷³

38.7151

64.3836%

320000

10000000

2.2509

3.6771%

40.9660

68.0607%

3.6771%

Difference

+38.7186

+0.4813%

+680000

+10000000

+3.1551

+0.7325%

+41.8738

+1.2138%

	GHz-days
exponent	factor	digits	bits*	k	min B1	min B2	date found	min. TF	min. P-1	normal P-1
49408277	514893217876959731931639882779892462835273	42	138.563	5210596777913948830189321141272468 2² × 3³ × 53 × 137 × 487 × 5717 × 29021 × 78929 × 191473 × 5441437	191473	5441437	2020-10-22	3.321e+9	1.2684	1.4708

GHz-days

exponent

factor

digits

bits*

min B1

min B2

date found

min. TF

min. P-1

normal P-1

49408277

514893217876959731931639882779892462835273

138.563

5210596777913948830189321141272468
2² × 3³ × 53 × 137 × 487 × 5717 × 29021 × 78929 × 191473 × 5441437

191473

5441437

2020-10-22

3.321e+9

1.2684

1.4708

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2010-03-29T06:28:00	ANONYMOUS		785000	785000		-		-	-	2.085	-	-	1.755%
2020-10-22T21:43:05	Sid & Andy	Magic_8_Ball	1000000	20000000	12		514893217876959731931639882779892462835273	42	138.563	5.406	181.0	10.81	4.410%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-11-28T00:00:00	Team Prime Rib	v4_computers	?	2⁵⁹		-	-	0.001	-	-
2007-08-14T00:00:00	1997rj7	v4_computers	?	2⁶³		-	-	0.020	-	-
2008-06-03T14:50:00	ANONYMOUS	Manual testing	?	2⁶⁴		-	-	0.040	-	-
2008-08-07T00:00:00	tmorrow	v4_computers	?	2⁶⁹		-	-	1.210	-	-
2015-08-13T08:13:00	LaurV	Manual testing	2⁶⁹	2⁷⁰		-	-	2.420	-	-
2015-10-17T05:48:44	LaurV	Manual testing	2⁷⁰	2⁷¹		-	-	4.840	-	-
2015-11-10T11:59:57	LaurV	Manual testing	2⁷¹	2⁷²		-	-	9.68	-	-
2017-09-14T20:45:07	Sid & Andy	Manual testing	2⁷²	2⁷³		-	-	19.36	-	-
2019-07-22T06:40:05	Sid & Andy	Manual testing	2⁷³	2⁷⁴		-	-	38.72	-	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2011-04-04T11:20:00	Bruce	TIGGER	DCF3767D8E3062AA	90.51
2018-09-10T05:07:42	Dax Mickelson	GPO-RTP-mprime110	DCF3767D8E3062AA	90.51

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 = 1000000, B2 = 20000000 (stage 2)

B1 = 1000000 (stage 1)

B1 = 785000 (stage 1)

10⁴

10⁵

10⁶

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁷⁴

2⁷³

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁴

2⁶³

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

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	<	123M	PrimeNet wavefront