M3716857 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

4DCE921FCEE372D0

verified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁷⁰	64.2884	68.5714%	14000000	700000000	7.8239	10.2462%	72.1123	71.7917%	3.2202%
PrimeNet	2⁶⁰	0.0413	63.3333%	16000	320000	0.0050	3.0861%	0.0463	64.4649%	1.1316%
GPU72	2⁶⁴	0.9576	65.6250%	22000	450000	0.0069	2.1073%	0.9645	66.3494%	0.7244%
Difference	+6	+63.3307	+2.9464%	+13978000	+699550000	+7.8170	+8.1389%	+71.1478	+5.4423%	+5.4423%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷⁰

64.2884

68.5714%

14000000

700000000

7.8239

10.2462%

72.1123

71.7917%

3.2202%

PrimeNet

2⁶⁰

0.0413

63.3333%

16000

320000

0.0050

3.0861%

0.0463

64.4649%

1.1316%

GPU72

2⁶⁴

0.9576

65.6250%

22000

450000

0.0069

2.1073%

0.9645

66.3494%

0.7244%

Difference

+63.3307

+2.9464%

+13978000

+699550000

+7.8170

+8.1389%

+71.1478

+5.4423%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3716857	142926226343284456539919	24	76.920	19226758837276287 3³ × 11 × 227 × 285183091373	2021-10-09	227	285183091373	6,440.9	2,366.2	4,419.4

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3716857

142926226343284456539919

76.920

19226758837276287
3³ × 11 × 227 × 285183091373

2021-10-09

227

285183091373

6,440.9

2,366.2

4,419.4

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-06T10:52:00	Carsten Kossendey	leela	20000	265000		-		-	-	0.005	-	-	0.729%
2012-12-14T13:29:00	Squeeky_Squirrel	T7500_2200	245000	7717500		-		-	-	0.099	-	-	3.248%
2021-05-19T10:48:38	axn	Manual testing	14000000	700000000		-		-	-	7.824	-	-	10.246%
2022-03-04T04:17:48	Jocelyn Larouche	Manual testing	90000	90000		-		-	-	0.014	-	-	0.623%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-01-05T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.041	-	-
2009-03-06T05:54:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.041	-	-
2011-04-24T00:37:00	Grant McCracken	home	2⁶¹	2⁶²		-	-	0.083	-	-
2012-04-19T23:29:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.429	-	-
2016-02-23T16:29:37	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.264	-	-
2015-01-22T10:39:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.528	-	-
2015-01-22T10:39:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.005	-	-
2016-02-24T09:33:34	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.010	-	-
2016-11-01T13:30:55	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.021	-	-
2019-01-14T11:03:45	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.042	-	-
2020-12-15T01:55:31	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	16.08	-	-
2021-03-08T13:56:20	axn	Manual testing	2⁶⁹	2⁷⁰		-	-	32.17	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.451 GHz-days
Estimated T-Level:	1.100

Digits	B1	Curves	Complete	FacMiss
20	11000	22 / 100	0.220	80.163%
25	50000	22 / 280	0.079	92.431%

New Calculation Method

Total ECM effort:	3.451 GHz-days
Estimated T-Level:	1.100

Digits	B1	Complete	FacMiss
20	11000	0.725	48.420%
25	50000	0.066	93.624%
30	250000	0.004	99.594%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.790
50000	5000000	142926226343284456539919	3	0.448
50000	6750000		7	1.213

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-09-11T18:38:00	Aca Arsov	backo6400	50000	5000000						3	0.448
2012-05-19T14:56:00	oodaira	Linux01	50000	5000000						3	0.448
2015-11-13T01:03:55	WileECoyote	Beaker	50000	5000000						3	0.448
2017-06-18T00:05:17	bayanne	iMac	50000	5000000						3	0.448
2021-07-31T02:22:07	kutens	terra	50000	6750000						7	1.213
2021-10-09T15:05:10	daveward2005	Dave2	50000	5000000	142926226343284456539919	76.920	3	2	5646309864067284	3	0.448

date	userid	compid	res64	spent (GHz-days)
1998-01-16T00:00:00	ANONYMOUS	v4_computers	598A7D0D72D359__	0.390
1999-09-14T00:00:00	ANONYMOUS	v4_computers	CAF1B6FBE4622A__	0.390

date

userid

compid

res64

spent (GHz-days)

1998-01-16T00:00:00

ANONYMOUS

v4_computers

598A7D0D72D359__

0.390

1999-09-14T00:00:00

ANONYMOUS

v4_computers

CAF1B6FBE4622A__

0.390

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 = 14000000, B2 = 700000000 (P-1 stage 2)

B1 = 14000000 (P-1 stage 1)

B1 = 245000, B2 = 7717500 (P-1 stage 2)

B1 = 245000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

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

B1 = 20000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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