M12288439 Mersenne number exponent details

Residue

Status

L-L

8B6D0021540877F7

double-checked

PRP

8298728F3CEB8D4B

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	4.8505	64.7059%	400000	303696120	9.4481	8.7781%	14.2985	67.8041%	3.0982%
PrimeNet	2⁶⁴	0.2896	62.5000%	55000	1500000	0.0747	4.1282%	0.3643	64.0481%	1.5481%
GPU72	2⁶⁸	4.8505	64.7059%	90000	2200000	0.1144	3.0825%	4.9649	65.7938%	1.0880%
Difference	-	-	-	+310000	+301496120	+9.3336	+5.6956%	+9.3336	+2.0102%	+2.0102%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

4.8505

64.7059%

400000

303696120

9.4481

8.7781%

14.2985

67.8041%

3.0982%

PrimeNet

2⁶⁴

0.2896

62.5000%

55000

1500000

0.0747

4.1282%

0.3643

64.0481%

1.5481%

GPU72

2⁶⁸

4.8505

64.7059%

90000

2200000

0.1144

3.0825%

4.9649

65.7938%

1.0880%

Difference

+310000

+301496120

+9.3336

+5.6956%

+9.3336

+2.0102%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
12288439	6434018638883403597503	22	72.446	261791535885209 11 × 563 × 42272167913	2016-03-11	563	42272167913	92.465	1,285.7	2,401.3

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

12288439

6434018638883403597503

72.446

261791535885209
11 × 563 × 42272167913

2016-03-11

563

42272167913

92.465

1,285.7

2,401.3

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-05-20T00:00:00	Team_Deutschland	v4_computers	185000	185000		-		-	-	0.103	-	-	1.516%
2001-08-24T00:00:00	ANONYMOUS	v4_computers	140000	1505000		-		-	-	0.120	-	-	3.029%
2022-02-08T10:42:05	nordi	sweet16_30.8b10	400000	400000		-		-	-	0.223	-	-	2.148%
2022-02-22T16:09:29	nordi	sweet16_30.8b10	400000	303696120		-		-	-	9.448	-	-	8.778%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-03-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.290	-	-
2013-08-03T20:51:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.304	-	-
2013-09-29T05:23:00	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.608	-	-
2015-03-07T09:56:00	Tha	Manual testing	2⁶⁶	2⁶⁷		-	-	1.216	-	-
2015-07-25T09:25:00	Tha	Manual testing	2⁶⁷	2⁶⁸		-	-	2.432	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.585 GHz-days
Estimated T-Level:	0.050

Digits	B1	Curves	Complete	FacMiss
20	11000	1 / 100	0.010	99.000%
25	50000	1 / 280	0.004	99.643%

New Calculation Method

Total ECM effort:	0.585 GHz-days
Estimated T-Level:	0.050

Digits	B1	Complete	FacMiss
20	11000	0.032	96.826%
25	50000	0.003	99.709%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	6434018638883403597503	1	0.585

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-03-11T11:58:03	Bruce	Desk10	50000	5000000	6434018638883403597503	72.446	1	2		1	0.585

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-02-24T00:00:00	ANONYMOUS	v4_computers	8B6D0021540877F7	4.731
2004-08-06T00:00:00	ANONYMOUS	v4_computers	8B6D0021540877F7	4.731

PRP results:

date

userid

compid

cofactors

res64

PRP

2022-02-26T05:11:02

Poao

office-CN2

6434018638883403597503

8298728F3CEB8D4B

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 = 303696120 (P-1 stage 2)

B1 = 400000 (P-1 stage 1)

B1 = 140000, B2 = 1505000 (P-1 stage 2)

B1 = 185000 (P-1 stage 1)

B1 = 140000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

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