M10319423 Mersenne number exponent details

Residue

Status

L-L

B895E304DDFAE2BC

double-checked

PRP

48E04A4840414B__

unverified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	2.8794	64.1791%	125000	2531250	0.1213	3.6690%	3.0007	65.4934%	1.3143%
PrimeNet	2⁶⁴	0.3449	62.5000%	45000	1300000	0.0537	3.7623%	0.3986	63.9109%	1.4109%
GPU72	2⁶⁸	5.7760	64.7059%	70000	1600000	0.0726	2.6598%	5.8486	65.6446%	0.9388%
Difference	-1	-2.8966	-0.5268%	+55000	+931250	+0.0487	+1.0091%	-2.8479	-0.1513%	-0.1513%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

2.8794

64.1791%

125000

2531250

0.1213

3.6690%

3.0007

65.4934%

1.3143%

PrimeNet

2⁶⁴

0.3449

62.5000%

45000

1300000

0.0537

3.7623%

0.3986

63.9109%

1.4109%

GPU72

2⁶⁸

5.7760

64.7059%

70000

1600000

0.0726

2.6598%

5.8486

65.6446%

0.9388%

Difference

-1

-2.8966

-0.5268%

+55000

+931250

+0.0487

+1.0091%

-2.8479

-0.1513%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
10319423	48579276822594477690351907045124143	35	115.226	2353778734653792062325185577 3 × 47 × 113 × 4703 × 62001493 × 506630057911	2016-09-28	62001493	506630057911	1.268e+10	13,102	24,419

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

10319423

48579276822594477690351907045124143

115.226

2353778734653792062325185577
3 × 47 × 113 × 4703 × 62001493 × 506630057911

2016-09-28

62001493

506630057911

1.268e+10

13,102

24,419

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-23T00:00:00	Team Prime Rib	v4_computers	55000	632500		-		-	-	0.041	-	-	2.272%
2004-04-29T00:00:00	Team Prime Rib	v4_computers	50000	737500		-		-	-	0.041	-	-	2.322%
2013-06-09T23:06:00	Nesowa	Outback	125000	2531250		-		-	-	0.121	-	-	3.669%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-09-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.345	-	-
2013-09-25T09:16:00	Nesowa	Manual testing	2⁶⁴	2⁶⁵		-	-	0.362	-	-
2015-04-29T08:20:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	0.724	-	-
2015-12-11T23:17:24	VictordeHollander	Manual testing	2⁶⁶	2⁶⁷		-	-	1.448	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.993 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:	0.993 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	0.497
50000	5000000	48579276822594477690351907045124143	1	0.497

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-05-10T16:55:00	WileECoyote	Beaker	50000	5000000						1	0.497
2016-09-29T00:31:00	Bruce	Desk10	50000	5000000	48579276822594477690351907045124143	115.226	1	2		1	0.497

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2000-08-01T00:00:00	ANONYMOUS	v4_computers	B895E304DDFAE2BC	3.371
2004-04-29T00:00:00	Team Prime Rib	v4_computers	B895E304DDFAE2BC	3.371

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-04-02T18:49:54

Oliver Kruse

Threadripper-PC

48579276822594477690351907045124143

48E04A4840414B__

2021-02-21T17:24:34

monsted

liane

48579276822594477690351907045124143

48E04A4840414B42

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 = 125000, B2 = 2531250 (P-1 stage 2)

B1 = 125000 (P-1 stage 1)

B1 = 50000, B2 = 737500 (P-1 stage 2)

B1 = 55000, B2 = 632500 (P-1 stage 2)

B1 = 55000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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