M48004871 Mersenne number exponent details

Residue

Status

L-L

205172F1FE9F2EA0

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	2⁷³	39.8469	64.3836%	1600000	40000000	9.2944	5.7264%	49.1413	66.4231%	2.0396%
PrimeNet	2⁶⁸	1.2416	61.7647%	220000	9000000	1.7580	5.6411%	2.9997	63.9216%	2.1569%
GPU72	2⁷²	19.9216	63.8889%	340000	11000000	2.3180	4.1653%	22.2395	65.3930%	1.5041%
Difference	+1	+19.9253	+0.4947%	+1260000	+29000000	+6.9765	+1.5612%	+26.9018	+1.0301%	+1.0301%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷³

39.8469

64.3836%

1600000

40000000

9.2944

5.7264%

49.1413

66.4231%

2.0396%

PrimeNet

2⁶⁸

1.2416

61.7647%

220000

9000000

1.7580

5.6411%

2.9997

63.9216%

2.1569%

GPU72

2⁷²

19.9216

63.8889%

340000

11000000

2.3180

4.1653%

22.2395

65.3930%

1.5041%

Difference

+19.9253

+0.4947%

+1260000

+29000000

+6.9765

+1.5612%

+26.9018

+1.0301%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
48004871	1755721672554624271611968591	28	90.504	18286911681885618145 5 × 11 × 53 × 337 × 1219433 × 15265603	2018-12-01	1219433	15265603	9,389,492	4.9962	6.2475

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

48004871

1755721672554624271611968591

90.504

18286911681885618145
5 × 11 × 53 × 337 × 1219433 × 15265603

2018-12-01

1219433

15265603

9,389,492

4.9962

6.2475

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-10-27T17:18:00	ANONYMOUS	v4_computers	750000	750000		-		-	-	1.888	-	-	1.920%
2010-01-04T00:00:00	ANONYMOUS	v4_computers	750000	750000		-		-	-	1.888	-	-	1.920%
2018-12-02T02:06:23	mikr	S068	1600000	40000000	6		1755721672554624271611968591	28	90.504	9.294	166.7	18.59	5.726%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-06-09T00:00:00	Thomas Mullen	v4_computers	2¹	2⁵⁹		-	-	0.002	-	-
2003-10-08T00:00:00	Thomas Mullen	v4_computers	2¹	2⁶⁰		-	-	0.003	-	-
2008-04-24T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁹		-	-	2.487	-	-
2015-07-02T14:27:00	Sid & Andy	Manual testing	2⁶⁹	2⁷⁰		-	-	2.491	-	-
2015-12-04T15:23:18	AirSquirrels	Manual testing	2⁷⁰	2⁷¹		-	-	4.981	-	-
2015-12-04T15:23:18	AirSquirrels	Manual testing	2⁷¹	2⁷²		-	-	9.96	-	-
2017-12-13T20:45:07	Sid & Andy	Manual testing	2⁷²	2⁷³		-	-	19.93	-	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2010-05-03T21:10:00	ANONYMOUS	v4_computers	205172F1FE9F2EA0	83.34
2010-07-20T00:00:00	ANONYMOUS	v4_computers	205172F1FE9F2EA0	83.34
2016-09-21T15:03:10	Sebastian Hornbostel	Manual testing	205172F1FE9F2EA0	83.34

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 = 1600000, B2 = 40000000 (P-1 stage 2)

B1 = 1600000 (P-1 stage 1)

B1 = 750000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁷

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁷³

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

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