M12817757 Mersenne number exponent details

Residue

Status

L-L

FFD16D2AECD4B324

double-checked

PRP

42CAA1582221676A

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	2⁶⁹	9.3142	65.2174%	165000	3918750	0.2189	3.4864%	9.5330	66.4301%	1.2127%
PrimeNet	2⁶⁴	0.2777	62.5000%	60000	1700000	0.0885	4.3284%	0.3661	64.1231%	1.6231%
GPU72	2⁶⁸	4.6502	64.7059%	90000	2400000	0.1278	3.1623%	4.7780	65.8220%	1.1161%
Difference	+1	+4.6640	+0.5115%	+75000	+1518750	+0.0910	+0.3242%	+4.7550	+0.6081%	+0.6081%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

9.3142

65.2174%

165000

3918750

0.2189

3.4864%

9.5330

66.4301%

1.2127%

PrimeNet

2⁶⁴

0.2777

62.5000%

60000

1700000

0.0885

4.3284%

0.3661

64.1231%

1.6231%

GPU72

2⁶⁸

4.6502

64.7059%

90000

2400000

0.1278

3.1623%

4.7780

65.8220%

1.1161%

Difference

+4.6640

+0.5115%

+75000

+1518750

+0.0910

+0.3242%

+4.7550

+0.6081%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
12817757	6848635433566410359353	22	72.536	267154207774668 2² × 3² × 1493 × 4970495791	2019-10-07	1493	4970495791	105.43	160.40	299.57

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

12817757

6848635433566410359353

72.536

267154207774668
2² × 3² × 1493 × 4970495791

2019-10-07

1493

4970495791

105.43

160.40

299.57

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-16T00:00:00	Mason	v4_computers	165000	3918750		-		-	-	0.219	-	-	3.486%

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		-	-	0.278	-	-
2013-06-04T08:18:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.291	-	-
2014-04-27T15:09:00	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.583	-	-
2015-04-08T09:43:00	Tha	Manual testing	2⁶⁶	2⁶⁷		-	-	1.166	-	-
2018-01-07T23:29:42	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	2.332	-	-
2018-01-07T23:29:42	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	4.664	-	-

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	6848635433566410359353	1	0.621

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-04-25T01:28:01	cerkiner	cerkiner_s_desktop	50000	5000000						1	0.621
2019-10-08T03:38:29	Keysarecool	HPLaptop	50000	5000000	6848635433566410359353	72.536	1	2	4825329358199358	1	0.621

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2003-03-27T00:00:00	Mason	v4_computers	FFD16D2AECD4B324	5.236
2004-11-22T00:00:00	Team Prime Rib	v4_computers	FFD16D2AECD4B324	5.236
2004-11-30T00:00:00	Team Prime Rib	v4_computers	FFD16D2AECD4B324	5.236

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 = 165000, B2 = 3918750 (P-1 stage 2)

B1 = 165000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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