M12905411 Mersenne number exponent details

Residue

Status

L-L

13ED7A94DBDA0FA4

double-checked

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	2⁶⁹	9.2509	65.2174%	300000	6000000	0.3616	4.1557%	9.6125	66.6628%	1.4455%
PrimeNet	2⁶⁴	0.2758	62.5000%	60000	1700000	0.0885	4.3326%	0.3643	64.1247%	1.6247%
GPU72	2⁶⁸	4.6186	64.7059%	90000	2400000	0.1278	3.1654%	4.7464	65.8231%	1.1172%
Difference	+1	+4.6323	+0.5115%	+210000	+3600000	+0.2338	+0.9903%	+4.8661	+0.8398%	+0.8398%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

9.2509

65.2174%

300000

6000000

0.3616

4.1557%

9.6125

66.6628%

1.4455%

PrimeNet

2⁶⁴

0.2758

62.5000%

60000

1700000

0.0885

4.3326%

0.3643

64.1247%

1.6247%

GPU72

2⁶⁸

4.6186

64.7059%

90000

2400000

0.1278

3.1654%

4.7464

65.8231%

1.1172%

Difference

+4.6323

+0.5115%

+210000

+3600000

+0.2338

+0.9903%

+4.8661

+0.8398%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
12905411	71852971562718591832919	23	75.927	2783831199282169 30133 × 92384800693	2019-10-17	30133	92384800693	884.13	2,981.2	5,568.0

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

12905411

71852971562718591832919

75.927

2783831199282169
30133 × 92384800693

2019-10-17

30133

92384800693

884.13

2,981.2

5,568.0

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-09-22T00:00:00	ANONYMOUS	v4_computers	135000	1046250		-		-	-	0.109	-	-	2.461%
2015-12-18T19:27:30	Tha	Riet-Ubuntu	300000	6000000	12	-		-	-	0.362	-	-	4.156%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-04-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.276	-	-
2013-06-01T06:14:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.290	-	-
2014-05-12T08:07:00	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.579	-	-
2015-04-14T11:46:00	Tha	Manual testing	2⁶⁶	2⁶⁷		-	-	1.158	-	-
2018-01-07T23:35:08	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	2.316	-	-
2018-01-07T23:35:08	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	4.632	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.242 GHz-days
Estimated T-Level:	0.100

Digits	B1	Curves	Complete	FacMiss
20	11000	2 / 100	0.020	98.010%
25	50000	2 / 280	0.007	99.287%

New Calculation Method

Total ECM effort:	1.242 GHz-days
Estimated T-Level:	0.100

Digits	B1	Complete	FacMiss
20	11000	0.065	93.752%
25	50000	0.006	99.419%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		1	0.621
50000	5000000	71852971562718591832919	1	0.621

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-05-03T06:03:15	Christian S	DOSe9	50000	5000000						1	0.621
2019-10-17T15:29:20	Keysarecool	HPLaptop	50000	5000000	71852971562718591832919	75.927	1	2	8007081004100198	1	0.621

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-07-27T00:00:00	ANONYMOUS	v4_computers	13ED7A94DBDA0FA4	5.272
2004-10-03T00:00:00	Donna Noble	v4_computers	13ED7A94DBDA0FA4	5.272

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 = 300000, B2 = 6000000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 135000, B2 = 1046250 (P-1 stage 2)

B1 = 135000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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