M1412447 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	2⁶⁷	21.0372	68.6567%	500000	15000000	0.0714	4.9125%	21.1086	70.1965%	1.5397%
PrimeNet	2⁵⁶	0.0068	62.5000%	6500	110000	0.0007	2.7669%	0.0075	63.5376%	1.0376%
GPU72	2⁶⁰	0.1087	65.0000%	6000	70000	0.0005	1.2450%	0.1093	65.4358%	0.4358%
Difference	+7	+20.9285	+3.6567%	+494000	+14930000	+0.0709	+3.6675%	+20.9993	+4.7607%	+4.7607%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

21.0372

68.6567%

500000

15000000

0.0714

4.9125%

21.1086

70.1965%

1.5397%

PrimeNet

2⁵⁶

0.0068

62.5000%

6500

110000

0.0007

2.7669%

0.0075

63.5376%

1.0376%

GPU72

2⁶⁰

0.1087

65.0000%

6000

70000

0.0005

1.2450%

0.1093

65.4358%

0.4358%

Difference

+20.9285

+3.6567%

+494000

+14930000

+0.0709

+3.6675%

+20.9993

+4.7607%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1412447	122961986033	12	36.839	43528 2³ × 5441	-	8	5441	9.214e-9	1.683e-5	3.065e-5
1412447	1357155138001855587961	22	70.201	480426925046340 2² × 3 × 5 × 35543 × 225279673	2018-09-10	35543	225279673	303.30	0.6814	1.2691

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1412447

122961986033

36.839

43528
2³ × 5441

5441

9.214e-9

1.683e-5

3.065e-5

1412447

1357155138001855587961

70.201

480426925046340
2² × 3 × 5 × 35543 × 225279673

2018-09-10

35543

225279673

303.30

0.6814

1.2691

exponent	prime factors	composite factor	digits	bits*
1412447	122961986033 1357155138001855587961	166878491123598354334943484948713	33	107.040

exponent

prime factors

composite factor

digits

bits*

1412447

122961986033
1357155138001855587961

166878491123598354334943484948713

107.040

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:13:59	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 122961986033	-	-	0.071	-	-	4.913%

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.549 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	304 / 100	3.040	4.711%
25	50000	304 / 280	1.086	33.700%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	25.549 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.360	0.000%
25	50000	1.366	25.525%
30	250000	0.114	89.267%
35	1000000	0.008	99.234%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		251	11.83
50000	5000000	1357155138001855587961	3	0.141
250000	35000000		50	13.58

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-11-16T18:51:18	storm5510	HP-Z220-CMT	50000	5000000						3	0.141
2018-09-10T21:06:47	Chang Chia-Tche	exbpc13	50000	5000000	1357155138001855587961	70.201	3	2		3	0.141
2019-02-01T12:16:25	TJAOI	Manual testing	50000	5000000						245	11.54
2019-02-02T17:49:06	zampel	goldammer	50000	5000000						3	0.141
2021-10-28T13:37:20	TJAOI	Manual testing	250000	35000000						50	13.58

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T18:16:47

Oliver Kruse

GTX-3

122961986033

F0072678726D0E__

2017-10-26T07:20:25

kkmrkkblmbrbk

c4.xlarge

122961986033

F0072678726D0E__

2018-09-11T04:26:03

Oliver Kruse

GTX-2

122961986033

1357155138001855587961

5A4DCB20638288__

2018-09-11T04:37:58

ANONYMOUS

122961986033

1357155138001855587961

5A4DCB20638288__

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

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