M3336803 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

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	17.8629	67.6471%	1000000	134343300	1.2587	7.6642%	19.1215	70.1266%	2.4796%
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	+16.7962	+2.0221%	+982000	+134043300	+1.2536	+5.9101%	+18.0498	+3.8987%	+3.8987%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

17.8629

67.6471%

1000000

134343300

1.2587

7.6642%

19.1215

70.1266%

2.4796%

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

+16.7962

+2.0221%

+982000

+134043300

+1.2536

+5.9101%

+18.0498

+3.8987%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3336803	6673607	7	22.670	1 1	-	1	1	1.675e-13	1.523e-7	3.099e-7
3336803	8944018067882929	16	52.990	1340207688 2³ × 3 × 199 × 280613	2014-08-31	199	280613	0.0002	0.0024	0.0043

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3336803

6673607

22.670

1
1

1.675e-13

1.523e-7

3.099e-7

3336803

8944018067882929

52.990

1340207688
2³ × 3 × 199 × 280613

2014-08-31

199

280613

0.0002

0.0024

0.0043

exponent	prime factors	composite factor	digits	bits*
3336803	6673607 8944018067882929	59688861585949990154903	23	75.660

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2021-03-08T12:47:30	Jocelyn Larouche	Manual testing	333680	3670483	6	-	skipped known factor: 6673607 skipped known factor: 8944018067882929	-	-	0.079	-	-	3.513%
2021-03-09T01:58:00	Jocelyn Larouche	Manual testing	333680	7007286	6	-	skipped known factor: 6673607 skipped known factor: 8944018067882929	-	-	0.106	-	-	4.049%
2022-02-24T19:16:37	Jocelyn Larouche	Manual testing	1000000	134343300		-	skipped known factor: 6673607 skipped known factor: 8944018067882929	-	-	1.259	-	-	7.664%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2014-08-31T10:32:00	TJAOI	Manual testing	?	?	8944018067882929	52.990	16	4.38995e-5	0.758	9.49285e-5
2021-07-27T18:06:57	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	8.958	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.438 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:	0.438 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.438

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-10-03T07:49:56	Niels_Mache_Nextcloud	SuperDry-T	50000	5000000						3	0.438

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-06T08:33:14

kkmrkkblmbrbk

old

6673607

8944018067882929

89910442CA119F__

2017-11-20T07:37:56

Oliver Kruse

GTX-3

6673607

8944018067882929

89910442CA119F__

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 = 1000000, B2 = 134343300 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 333680, B2 = 7007286 (P-1 stage 2)

B1 = 333680, B2 = 3670483 (P-1 stage 2)

B1 = 333680 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁸

2²⁰

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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