M4835321 Mersenne number exponent details

Residue

Status

L-L

FCA2D8AC3A6174DB

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	6.1452	65.6716%	-	-	-	-	6.1452	65.6716%	0.0000%
PrimeNet	2⁶¹	0.0635	62.2951%	20000	450000	0.0083	3.2287%	0.0718	63.5124%	1.2174%
GPU72	2⁶⁵	1.5088	64.6154%	32000	650000	0.0125	2.3251%	1.5214	65.4381%	0.8227%
Difference	+2	+4.6363	+1.0563%	-32000	-650000	-0.0125	-2.3251%	+4.6238	+0.2335%	+0.2335%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6.1452

65.6716%

6.1452

65.6716%

0.0000%

PrimeNet

2⁶¹

0.0635

62.2951%

20000

450000

0.0083

3.2287%

0.0718

63.5124%

1.2174%

GPU72

2⁶⁵

1.5088

64.6154%

32000

650000

0.0125

2.3251%

1.5214

65.4381%

0.8227%

Difference

+4.6363

+1.0563%

-32000

-650000

-0.0125

-2.3251%

+4.6238

+0.2335%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4835321	14592897432263572057	20	63.662	1508989520268 2² × 3² × 379 × 3373 × 32789	2000-07-03	3373	32789	0.4450	0.0009	0.0013
4835321	10446980670742304231038719986047	32	103.043	1080277883385850104991863 3 × 31193 × 11544020382626979397	2019-06-21	31193	11544020382626979397	3.225e+10	1.201e+11	2.243e+11

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4835321

14592897432263572057

63.662

1508989520268
2² × 3² × 379 × 3373 × 32789

2000-07-03

3373

32789

0.4450

0.0009

0.0013

4835321

10446980670742304231038719986047

103.043

1080277883385850104991863
3 × 31193 × 11544020382626979397

2019-06-21

31193

11544020382626979397

3.225e+10

1.201e+11

2.243e+11

exponent	prime factors	composite factor	digits	bits*
4835321	14592897432263572057 10446980670742304231038719986047	15245171740498254113171446042004702080467341908867 9	51	166.705

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-07-03T00:00:00	ANONYMOUS	v4_computers	?	?	14592897432263572057	63.662	20	0.115	1.294	0.234

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.596 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:	0.596 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.097	90.776%
25	50000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	10446980670742304231038719986047	3	0.596

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2019-06-21T05:01:55	MarkS	laptop64	50000	5000000	10446980670742304231038719986047	103.043	3	2		3	0.596

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-09-13T00:00:00	ANONYMOUS	v4_computers	FCA2D8AC3A6174DB	0.637

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T06:28:34

kkmrkkblmbrbk

Manual testing

14592897432263572057

D59364A5A98054__

2018-03-29T03:29:04

Oliver Kruse

GTX-4

14592897432263572057

D59364A5A98054__

2019-06-21T19:49:17

Niels_Mache_Nextcloud

SuperDry3

14592897432263572057

10446980670742304231038719986047

1A24F80AF1D4A24D

2019-06-21T20:49:01

ATH

ec2-PRPCFDC

14592897432263572057

10446980670742304231038719986047

1A24F80AF1D4A24D

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

10²

10³

10⁴

10⁵

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

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