M3339521 Mersenne number exponent details

Residue

Status

L-L

70E9A88AFCEB54FC

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	2⁶⁸	17.8483	67.6471%	4000000	150000000	1.8206	8.7963%	19.6689	70.4929%	2.8459%
PrimeNet	2⁶⁰	0.0460	63.3333%	14000	260000	0.0042	2.7843%	0.0502	64.3543%	1.0209%
GPU72	2⁶⁴	1.0658	65.6250%	18000	300000	0.0051	1.7544%	1.0709	66.2281%	0.6031%
Difference	+4	+16.7825	+2.0221%	+3982000	+149700000	+1.8155	+7.0419%	+18.5980	+4.2649%	+4.2649%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

17.8483

67.6471%

4000000

150000000

1.8206

8.7963%

19.6689

70.4929%

2.8459%

PrimeNet

2⁶⁰

0.0460

63.3333%

14000

260000

0.0042

2.7843%

0.0502

64.3543%

1.0209%

GPU72

2⁶⁴

1.0658

65.6250%

18000

300000

0.0051

1.7544%

1.0709

66.2281%

0.6031%

Difference

+16.7825

+2.0221%

+3982000

+149700000

+1.8155

+7.0419%

+18.5980

+4.2649%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3339521	14630571171777105537385753319	29	93.563	2190519414577286014579 7 × 23 × 277 × 40699 × 110039 × 10967587	2020-07-11	110039	10967587	907,374,942	0.1068	0.1700

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3339521

14630571171777105537385753319

93.563

2190519414577286014579
7 × 23 × 277 × 40699 × 110039 × 10967587

2020-07-11

110039

10967587

907,374,942

0.1068

0.1700

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-04T14:07:00	Carsten Kossendey	durandal	15000	206250		-		-	-	0.004	-	-	0.809%
2011-10-08T03:59:00	harlee	P4_2600	55000	893750		-		-	-	0.015	-	-	1.820%
2012-12-01T00:58:00	Squeeky_Squirrel	P4_2600	230000	6612500		-		-	-	0.088	-	-	3.796%
2020-07-11T18:08:23	mikr	MSI	4000000	150000000	12		14630571171777105537385753319	29	93.563	1.821	0.701	3.641	8.796%
2022-04-08T06:40:59	Jocelyn Larouche	Manual testing	1000000	115661700		-	skipped known factor: 14630571171777105537385753319	-	-	1.104	-	-	7.502%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-03-29T11:32:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.046	-	-
2011-08-23T20:26:00	markr	Manual testing	2¹	2⁶²		-	-	0.184	-	-
2012-08-25T21:55:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.478	-	-
2016-02-23T16:29:26	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.294	-	-
2015-02-11T09:06:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.588	-	-
2015-02-11T09:06:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.119	-	-
2016-03-02T17:18:07	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.238	-	-
2017-03-02T18:04:37	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.475	-	-
2018-11-05T15:44:30	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.951	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.191 GHz-days
Estimated T-Level:	0.750

Digits	B1	Curves	Complete	FacMiss
20	11000	15 / 100	0.150	86.006%
25	50000	15 / 280	0.054	94.775%

New Calculation Method

Total ECM effort:	2.191 GHz-days
Estimated T-Level:	0.750

Digits	B1	Complete	FacMiss
20	11000	0.484	61.639%
25	50000	0.044	95.721%
30	250000	0.003	99.731%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	2.191

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-06-02T00:34:00	Smurgs	Praca	50000	5000000						3	0.438
2012-01-19T01:24:00	Smurgs	Praca	50000	5000000						3	0.438
2014-08-28T00:44:00	joe b.	Pandora	50000	5000000						3	0.438
2016-10-12T05:30:55	Dennis Schreiber	z400	50000	5000000						3	0.438
2019-03-20T15:43:56	furkell	furkell1	50000	5000000						3	0.438

date	userid	compid	res64	spent (GHz-days)
2000-01-19T00:00:00	ANONYMOUS	v4_computers	70E9A88AFCEB54FC	0.351

date

userid

compid

res64

spent (GHz-days)

2000-01-19T00:00:00

ANONYMOUS

v4_computers

70E9A88AFCEB54FC

0.351

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-07-15T05:20:22

Klaus Nordmann

no1

14630571171777105537385753319

4AFBEA73A9D9E1E7

2020-07-16T05:12:53

pew

laptop

14630571171777105537385753319

4AFBEA73A9D9E1E7

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 = 4000000, B2 = 150000000 (P-1 stage 2)

B1 = 1000000, B2 = 115661700 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 230000, B2 = 6612500 (P-1 stage 2)

B1 = 230000 (P-1 stage 1)

B1 = 55000, B2 = 893750 (P-1 stage 2)

B1 = 55000 (P-1 stage 1)

B1 = 15000, B2 = 206250 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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