M4834231 Mersenne number exponent details

Residue

Status

L-L

9F3A1332968BAD47

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	6.1466	65.6716%	30000	435000	0.0099	1.5679%	6.1565	66.2099%	0.5382%
PrimeNet	2⁶¹	0.0635	62.2951%	20000	450000	0.0083	3.2285%	0.0718	63.5124%	1.2173%
GPU72	2⁶⁵	1.5092	64.6154%	32000	650000	0.0125	2.3250%	1.5217	65.4381%	0.8227%
Difference	+2	+4.6374	+1.0563%	-2000	-215000	-0.0026	-0.7571%	+4.6348	+0.7718%	+0.7718%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6.1466

65.6716%

30000

435000

0.0099

1.5679%

6.1565

66.2099%

0.5382%

PrimeNet

2⁶¹

0.0635

62.2951%

20000

450000

0.0083

3.2285%

0.0718

63.5124%

1.2173%

GPU72

2⁶⁵

1.5092

64.6154%

32000

650000

0.0125

2.3250%

1.5217

65.4381%

0.8227%

Difference

+4.6374

+1.0563%

-2000

-215000

-0.0026

-0.7571%

+4.6348

+0.7718%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4834231	15097599307229829569	20	63.711	1561530604064 2⁵ × 48797831377	2017-04-18	32	48797831377	0.4290	507.58	948.02
4834231	16354555660418892193	20	63.826	1691536426416 2⁴ × 3² × 24151 × 486389	2017-05-18	24151	486389	0.5865	0.0094	0.0094
4834231	6836096688125586082916881	25	82.499	707051099557053240 2³ × 3 × 5 × 11² × 61 × 43403 × 18392239	2010-04-04	43403	18392239	347,333	0.1991	0.3573

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4834231

15097599307229829569

63.711

1561530604064
2⁵ × 48797831377

2017-04-18

48797831377

0.4290

507.58

948.02

4834231

16354555660418892193

63.826

1691536426416
2⁴ × 3² × 24151 × 486389

2017-05-18

24151

486389

0.5865

0.0094

4834231

6836096688125586082916881

82.499

707051099557053240
2³ × 3 × 5 × 11² × 61 × 43403 × 18392239

2010-04-04

43403

18392239

347,333

0.1991

0.3573

exponent	prime factors	composite factor	digits	bits*
4834231	15097599307229829569 16354555660418892193	246914528208791954581365094603174654817	39	127.537
4834231	15097599307229829569 6836096688125586082916881	103208648622800980729888977991510652023054289	45	146.210
4834231	16354555660418892193 6836096688125586082916881	111801323785955146196434469281779792118810033	45	146.326
4834231	15097599307229829569 16354555660418892193 6836096688125586082916881	16879315885382142816077282488031699006313256050610 22837677265777	64	210.037

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-08-31T20:34:00	Carsten Kossendey	durandal	30000	435000		-		-	-	0.010	-	-	1.568%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2017-04-18T15:17:55	TJAOI	Manual testing	2⁶³	2⁶⁴*	15097599307229829569	63.711	20	0.099	1.294	0.201
2017-05-18T16:20:50	TJAOI	Manual testing	2⁶³	2⁶⁴*	16354555660418892193	63.826	20	0.256	1.294	0.521

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
		6836096688125586082916881	1	0.00000e+0

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-04-04T01:46:00	Aca Arsov	backo6400			6836096688125586082916881	82.499		1		1	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-07-11T00:00:00	ANONYMOUS	v4_computers	9F3A1332968BAD47	0.637
2000-03-15T00:00:00	ANONYMOUS	v4_computers	9F3A1332968BAD47	0.637

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T13:08:57

alpertron

Manual testing

15097599307229829569

16354555660418892193

6836096688125586082916881

514E786D5C195A__

2018-01-08T16:03:03

kkmrkkblmbrbk

c4.xlarge

15097599307229829569

16354555660418892193

6836096688125586082916881

514E786D5C195A__

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 = 30000, B2 = 435000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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