M3336829 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

81E404E0CD204308

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	2⁶⁸	17.8627	67.6471%	4000000	150000000	1.8206	8.7956%	19.6833	70.4927%	2.8456%
PrimeNet	2⁶⁰	0.0460	63.3333%	14000	260000	0.0042	2.7839%	0.0502	64.3541%	1.0208%
GPU72	2⁶⁴	1.0667	65.6250%	18000	300000	0.0051	1.7541%	1.0718	66.2280%	0.6030%
Difference	+4	+16.7961	+2.0221%	+3982000	+149700000	+1.8155	+7.0415%	+18.6115	+4.2647%	+4.2647%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

17.8627

67.6471%

4000000

150000000

1.8206

8.7956%

19.6833

70.4927%

2.8456%

PrimeNet

2⁶⁰

0.0460

63.3333%

14000

260000

0.0042

2.7839%

0.0502

64.3541%

1.0208%

GPU72

2⁶⁴

1.0667

65.6250%

18000

300000

0.0051

1.7541%

1.0718

66.2280%

0.6030%

Difference

+16.7961

+2.0221%

+3982000

+149700000

+1.8155

+7.0415%

+18.6115

+4.2647%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3336829	1130211287412046406009	22	69.937	169354091476076 2² × 13 × 107 × 151 × 201572659	2021-02-13	151	201572659	61.807	1.6725	3.1237

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3336829

1130211287412046406009

69.937

169354091476076
2² × 13 × 107 × 151 × 201572659

2021-02-13

151

201572659

61.807

1.6725

3.1237

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-04T06:46:00	Carsten Kossendey	durandal	15000	206250		-		-	-	0.004	-	-	0.809%
2011-10-07T12:05:00	harlee	P4_2600	55000	893750		-		-	-	0.015	-	-	1.820%
2012-11-28T12:52:00	Squeeky_Squirrel	P4_2600	210000	4672500		-		-	-	0.069	-	-	3.482%
2018-08-18T12:00:13	Jocelyn Larouche	low 4M	420000	3360000		-		-	-	0.088	-	-	3.530%
2020-06-27T08:14:52	mikr	MSI	4000000	150000000	12	-		-	-	1.821	-	-	8.796%
2022-04-02T19:48:47	Jocelyn Larouche	Manual testing	1000000	134316000		-		-	-	1.258	-	-	7.664%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-03-30T04:56:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.046	-	-
2011-08-27T00:18:00	markr	Manual testing	2¹	2⁶²		-	-	0.184	-	-
2012-08-25T21:54:00	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		-	-	1.120	-	-
2016-03-02T10:47:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.239	-	-
2017-03-02T18:04:36	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.479	-	-
2018-11-05T15:44:31	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.958	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.618 GHz-days
Estimated T-Level:	2.950

Digits	B1	Curves	Complete	FacMiss
20	11000	59 / 100	0.590	55.268%
25	50000	59 / 280	0.211	80.970%

New Calculation Method

Total ECM effort:	8.618 GHz-days
Estimated T-Level:	2.950

Digits	B1	Complete	FacMiss
20	11000	1.903	14.909%
25	50000	0.172	84.197%
30	250000	0.011	98.946%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	2.191
50000	5000000	1130211287412046406009	44	6.427

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-07T14:35:00	Martti Järvi	Fiia	50000	5000000						3	0.438
2011-11-15T12:31:00	GrunwalderGIMP	vangelis	50000	5000000						3	0.438
2014-08-26T11:22:00	Lukasz Wrobel	w1	50000	5000000						3	0.438
2016-10-10T19:35:17	Dennis Schreiber	z400	50000	5000000						3	0.438
2019-03-19T04:39:09	IanGlencross	glenx24	50000	5000000						3	0.438
2021-02-13T09:19:51	MarkS	desktop-i7	50000	5000000	1130211287412046406009	69.937	44	2	585196405517482	44	6.427

date	userid	compid	res64	spent (GHz-days)
1999-07-04T00:00:00	ANONYMOUS	v4_computers	196BAD2A3F2A09__	0.350

date

userid

compid

res64

spent (GHz-days)

1999-07-04T00:00:00

ANONYMOUS

v4_computers

196BAD2A3F2A09__

0.350

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 = 134316000 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 420000, B2 = 3360000 (P-1 stage 2)

B1 = 210000, B2 = 4672500 (P-1 stage 2)

B1 = 420000 (P-1 stage 1)

B1 = 210000 (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)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

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