M8000357 Mersenne number exponent details

Residue

Status

L-L

657D251CE7AD0F1D

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	2⁷⁰	29.8675	67.1429%	2400000	2400000	0.9087	3.1883%	30.7762	68.1904%	1.0476%
PrimeNet	2⁶³	0.1995	63.4921%	34000	900000	0.0307	3.5661%	0.2302	64.7940%	1.3019%
GPU72	2⁶⁷	3.7141	65.6716%	55000	1200000	0.0444	2.5668%	3.7585	66.5528%	0.8812%
Difference	+3	+26.1534	+1.4712%	+2345000	+1200000	+0.8642	+0.6214%	+27.0176	+1.6376%	+1.6376%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷⁰

29.8675

67.1429%

2400000

0.9087

3.1883%

30.7762

68.1904%

1.0476%

PrimeNet

2⁶³

0.1995

63.4921%

34000

900000

0.0307

3.5661%

0.2302

64.7940%

1.3019%

GPU72

2⁶⁷

3.7141

65.6716%

55000

1200000

0.0444

2.5668%

3.7585

66.5528%

0.8812%

Difference

+26.1534

+1.4712%

+2345000

+1200000

+0.8642

+0.6214%

+27.0176

+1.6376%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
8000357	19471169201268296583877802369	29	93.975	1216893771194728971712 2⁶ × 67 × 457 × 4967 × 205307 × 608953	2018-02-10	205307	608953	488,005,474	0.0861	0.1582

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

8000357

19471169201268296583877802369

93.975

1216893771194728971712
2⁶ × 67 × 457 × 4967 × 205307 × 608953

2018-02-10

205307

608953

488,005,474

0.0861

0.1582

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2012-04-07T21:20:00	Squeeky_Squirrel	T7500_2200	100000	1950000		-		-	-	0.076	-	-	2.265%
2018-02-10T11:15:58	mikr	Y12	2400000	2400000			19471169201268296583877802369	29	93.975	0.909	4.178	1.817	3.188%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-08-16T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.038	-	-
1998-08-16T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.199	-	-
2013-07-24T15:40:00	c10ck3r	Manual testing	2⁶³	2⁶⁴		-	-	0.245	-	-
2013-09-01T01:11:00	David Campeau	Manual testing	2⁶⁴	2⁶⁵		-	-	0.467	-	-
2015-04-20T23:58:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	0.934	-	-
2015-11-13T03:49:04	snme2pm1	Manual testing	2⁶⁶	2⁶⁷		-	-	1.868	-	-
2016-11-04T17:56:49	Conductor	Manual testing	2⁶⁷	2⁶⁸		-	-	3.736	-	-
2017-05-12T06:53:09	Yxinity	Manual testing	2⁶⁸	2⁶⁹		-	-	7.472	-	-
2017-05-12T06:53:09	Yxinity	Manual testing	2⁶⁹	2⁷⁰		-	-	14.94	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.191 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	1.191 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.097	90.776%
25	50000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	1.191

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2013-02-04T06:17:00	Florimond C.	ichthys3	50000	5000000						3	1.191

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-11-17T00:00:00	Roger_hunt	v4_computers	657D251CE7AD0F1D	2.089
2015-09-18T07:16:00	Vteam	micael	657D251CE7AD0F1D	2.089

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-07-04T08:27:43

Dt12

Core_i5-8250U

19471169201268296583877802369

49FA72B35DB05D__

2019-06-21T18:06:47

timbit

Manual testing

19471169201268296583877802369

49FA72B35DB05D89

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 = 2400000 (P-1 stage 1)

B1 = 100000, B2 = 1950000 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁷

10⁴

10⁵

10⁶

10⁷

TF factor-bounds graph:

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶¹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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