M12707413 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

E1ECEDA5B13E9C85

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	4.6906	64.7059%	400000	428459850	14.0501	9.1811%	18.7407	67.9463%	3.2404%
PrimeNet	2⁶⁴	0.2801	62.5000%	55000	1700000	0.0857	4.2602%	0.3658	64.0976%	1.5976%
GPU72	2⁶⁸	4.6906	64.7059%	90000	2200000	0.1214	3.0979%	4.8120	65.7992%	1.0934%
Difference	-	-	-	+310000	+426259850	+13.9287	+6.0833%	+13.9287	+2.1470%	+2.1470%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

4.6906

64.7059%

400000

428459850

14.0501

9.1811%

18.7407

67.9463%

3.2404%

PrimeNet

2⁶⁴

0.2801

62.5000%

55000

1700000

0.0857

4.2602%

0.3658

64.0976%

1.5976%

GPU72

2⁶⁸

4.6906

64.7059%

90000

2200000

0.1214

3.0979%

4.8120

65.7992%

1.0934%

Difference

+310000

+426259850

+13.9287

+6.0833%

+13.9287

+2.1470%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
12707413	76244479	8	26.184	3 3	-	1	3	7.040e-13	6.568e-7	1.205e-6
12707413	18736003591492729	17	54.057	737207628 2² × 3 × 139 × 441971	2014-10-30	139	441971	0.0003	0.0143	0.0266

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

12707413

76244479

26.184

3
3

7.040e-13

6.568e-7

1.205e-6

12707413

18736003591492729

54.057

737207628
2² × 3 × 139 × 441971

2014-10-30

139

441971

0.0003

0.0143

0.0266

exponent	prime factors	composite factor	digits	bits*
12707413	76244479 18736003591492729	1428516832375491954893191	25	80.241

exponent

prime factors

composite factor

digits

bits*

12707413

76244479
18736003591492729

1428516832375491954893191

80.241

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-05-02T00:19:28	nordi	sweet16_30.8b14	400000	400000		-	skipped known factor: 76244479	-	-	0.237	-	-	2.159%
2022-05-02T06:22:55	nordi	sweet16_30.8b14	400000	428459850		-	skipped known factor: 76244479 skipped known factor: 18736003591492729	-	-	14.05	-	-	9.181%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2014-10-30T12:07:00	TJAOI	Manual testing	2⁵⁴	2⁵⁵*	18736003591492729	54.057	17	0.000	10.84	0.000
2022-06-25T04:02:11	LordJulius	Manual testing	2¹	2⁶⁴	18736003591492729	54.057	17	0.000	10.84	0.001
2022-06-25T04:02:11	LordJulius	Manual testing	2¹	2⁶⁴	76244479	26.184	8	7.03993e-13	10.84	1.47085e-12
2022-06-25T04:02:11	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	0.294	-	-
2022-06-25T04:02:11	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	0.588	-	-
2022-06-25T04:02:11	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	1.176	-	-
2022-04-11T21:21:53	Lisander Viaene	Manual testing	2⁶⁷	2⁶⁸		-	-	2.352	-	-

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 = 400000, B2 = 428459850 (P-1 stage 2)

B1 = 400000 (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

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁵⁵

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