M9485893 Mersenne number exponent details

Residue

Status

L-L

7D6D6BDE94FFAA5B

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	2⁶⁷	3.1324	64.1791%	180000	3960000	0.1547	4.2101%	3.2871	65.6872%	1.5081%
PrimeNet	2⁶⁴	0.3752	62.5000%	40000	1100000	0.0392	3.4998%	0.4144	63.8124%	1.3124%
GPU72	2⁶⁸	6.2835	64.7059%	60000	1400000	0.0533	2.4634%	6.3368	65.5753%	0.8694%
Difference	-1	-3.1511	-0.5268%	+120000	+2560000	+0.1014	+1.7468%	-3.0497	+0.1119%	+0.1119%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

3.1324

64.1791%

180000

3960000

0.1547

4.2101%

3.2871

65.6872%

1.5081%

PrimeNet

2⁶⁴

0.3752

62.5000%

40000

1100000

0.0392

3.4998%

0.4144

63.8124%

1.3124%

GPU72

2⁶⁸

6.2835

64.7059%

60000

1400000

0.0533

2.4634%

6.3368

65.5753%

0.8694%

Difference

-1

-3.1511

-0.5268%

+120000

+2560000

+0.1014

+1.7468%

-3.0497

+0.1119%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
9485893	52468081244118870487	20	65.508	2765584707951 3 × 13 × 727 × 97541167	2014-09-17	727	97541167	1.2791	2.1301	3.9778

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

9485893

52468081244118870487

65.508

2765584707951
3 × 13 × 727 × 97541167

2014-09-17

727

97541167

1.2791

2.1301

3.9778

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-05-11T00:00:00	S00030	v4_computers	50000	50000		-		-	-	0.020	-	-	0.806%
2011-07-27T14:46:00	James Heinrich	Q6600	180000	3960000		-		-	-	0.155	-	-	4.210%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-12-06T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.001	-	-
1999-04-23T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.375	-	-
2013-09-04T08:11:00	Nesowa	Manual testing	2⁶⁴	2⁶⁵		-	-	0.394	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.841 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:	0.841 GHz-days
Estimated T-Level:	0.100

Digits	B1	Complete	FacMiss
20	11000	0.077	92.596%
25	50000	0.007	99.291%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	52468081244118870487	2	0.841

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2014-09-17T01:41:00	swildner	ultra	50000	5000000	52468081244118870487	65.508	2	2		2	0.841

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2000-05-05T00:00:00	ANONYMOUS	v4_computers	7D6D6BDE94FFAA5B	2.622
2003-05-19T00:00:00	S00030	v4_computers	7D6D6BDE94FFAA5B	2.622

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-09-14T21:45:33

mnd9

27016b

52468081244118870487

7090F1977AF04C__

2020-12-05T20:23:00

tanaydin

iMac

52468081244118870487

7090F1977AF04C5D

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 = 180000, B2 = 3960000 (P-1 stage 2)

B1 = 180000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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