M334 014 209 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
Actual	2⁷⁸	183.2752	62.8205%	2970000	2970000	64.0592	2.4756%	247.3343	63.7409%
Target	2⁸¹	1,466.2050	64.1975%	2000000	400000000	510.8373	4.0587%	1,977.0422	65.6507%
Difference	-3	-1,282.9298	-1.3770%	+970000	-397030000	-446.7781	-1.5831%	-1,729.7079	-1.9097%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

2⁷⁸

183.2752

62.8205%

2970000

64.0592

2.4756%

247.3343

63.7409%

Target

2⁸¹

1,466.2050

64.1975%

2000000

400000000

510.8373

4.0587%

1,977.0422

65.6507%

Difference

-3

-1,282.9298

-1.3770%

+970000

-397030000

-446.7781

-1.5831%

-1,729.7079

-1.9097%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
334014209	1149360148529793636649753	25	79.927	1720525830279564 2² × 3 × 7 × 11 × 139 × 80341 × 166739	2020-12-06	80341	166739	439.86	1.8344	3.5267

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

334014209

1149360148529793636649753

79.927

1720525830279564
2² × 3 × 7 × 11 × 139 × 80341 × 166739

2020-12-06

80341

166739

439.86

1.8344

3.5267

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2020-12-06	GAN	Manual testing	2970000	2970000			1149360148529793636649753	25	79.927	64.06	9,937	128.1	2.476%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2012-12-08	kracker	Manual testing	2⁶⁶	2⁶⁷		-	-	0.045	-	-
2014-11-24	mikr	Manual testing	2⁶⁷	2⁶⁹		-	-	0.268	-	-
2014-11-24	mikr	Manual testing	2⁶⁹	2⁷⁰		-	-	0.358	-	-
2016-01-07	Jacques MOLNE	Manual testing	2⁷⁰	2⁷¹		-	-	0.716	-	-
2016-01-07	Jacques MOLNE	Manual testing	2⁷¹	2⁷²		-	-	1.432	-	-
2019-09-23	GAN	Manual testing	2⁷²	2⁷³		-	-	2.864	-	-
2019-11-10	GAN	Manual testing	2⁷³	2⁷⁴		-	-	5.727	-	-
2019-11-21	GAN	Manual testing	2⁷⁴	2⁷⁵		-	-	11.45	-	-
2019-12-06	GAN	Manual testing	2⁷⁵	2⁷⁶		-	-	22.91	-	-
2020-02-25	GAN	Manual testing	2⁷⁵	2⁷⁶		-	-	22.91	-	-
2020-07-11	GAN	Manual testing	2⁷⁶	2⁷⁷		-	-	45.82	-	-
2020-07-11	GAN	Manual testing	2⁷⁷	2⁷⁸		-	-	91.64	-	-

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 = 2970000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

TF factor-bounds graph:

2⁷⁸

2⁷⁷

2⁷⁶

2⁷⁵

2⁷⁴

2⁷³

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁷

this exponent TF target: 81

TF double-checked to: 67.9

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

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