M2819423 Mersenne number exponent details

Residue

Status

L-L

DDF6493AC0B8EB4D

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	10.5390	67.1642%	336021	3360210	0.0561	3.7399%	10.5951	68.3922%	1.2280%
PrimeNet	2⁵⁹	0.0272	62.7119%	12000	240000	0.0027	2.9308%	0.0300	63.8047%	1.0928%
GPU72	2⁶³	0.5661	65.0794%	15000	260000	0.0032	1.7921%	0.5693	65.7052%	0.6258%
Difference	+4	+9.9729	+2.0848%	+321021	+3100210	+0.0529	+1.9478%	+10.0258	+2.6870%	+2.6870%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

10.5390

67.1642%

336021

3360210

0.0561

3.7399%

10.5951

68.3922%

1.2280%

PrimeNet

2⁵⁹

0.0272

62.7119%

12000

240000

0.0027

2.9308%

0.0300

63.8047%

1.0928%

GPU72

2⁶³

0.5661

65.0794%

15000

260000

0.0032

1.7921%

0.5693

65.7052%

0.6258%

Difference

+9.9729

+2.0848%

+321021

+3100210

+0.0529

+1.9478%

+10.0258

+2.6870%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2819423	109999736277745577489	21	66.576	19507490766328 2³ × 31 × 15331 × 5130731	2017-10-28	15331	5130731	9.3320	0.0329	0.0585

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2819423

109999736277745577489

66.576

19507490766328
2³ × 31 × 15331 × 5130731

2017-10-28

15331

5130731

9.3320

0.0329

0.0585

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-28T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.301%
2016-09-14T01:53:47	Jocelyn Larouche	low 4M	135041	3300000	6	-		-	-	0.034	-	-	3.278%
2016-09-21T12:09:27	Jocelyn Larouche	low 4M	135041	3630000		-		-	-	0.036	-	-	3.346%
2016-12-21T00:33:38	Jocelyn Larouche	low 4M	194458	194458		-		-	-	0.022	-	-	1.383%
2017-01-10T10:25:18	Jocelyn Larouche	low 4M	233349	233349		-		-	-	0.026	-	-	1.512%
2017-03-15T21:54:57	Jocelyn Larouche	low 4M	336021	3360210	6	-		-	-	0.056	-	-	3.740%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:22	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.054	-	-
2009-02-13T19:27:00	Sturle Sunde	fizir.ifi	2⁶⁰	2⁶¹		-	-	0.054	-	-
2012-02-24T04:56:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.109	-	-
2013-01-10T10:21:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.348	-	-
2015-04-21T09:19:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.696	-	-
2015-04-21T09:19:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.325	-	-
2016-02-12T10:12:11	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.650	-	-
2017-10-28T16:39:37	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷	109999736277745577489	66.576	21	4.094	0.443	8.324

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.503 GHz-days
Estimated T-Level:	1.200

Digits	B1	Curves	Complete	FacMiss
20	11000	24 / 100	0.240	78.568%
25	50000	24 / 280	0.086	91.772%

New Calculation Method

Total ECM effort:	2.503 GHz-days
Estimated T-Level:	1.200

Digits	B1	Complete	FacMiss
20	11000	0.923	39.729%
25	50000	0.085	91.814%
30	250000	0.005	99.463%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		24	2.503

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-22T13:36:00	Newro	home	50000	5000000						3	0.313
2010-10-27T01:27:00	Donna Noble	PH2-940-v3-MVB	50000	5000000						3	0.313
2013-04-04T18:09:00	hiems	Laptop	50000	5000000						3	0.313
2015-03-29T03:23:00	Jason U	Server7	50000	5000000						3	0.313
2016-02-17T18:58:02	Sintax	cloud	50000	5000000						3	0.313
2016-06-06T12:22:23	Jason U	Server7	50000	5000000						3	0.313
2017-02-21T22:56:23	Bruce	eleven	50000	5000000						3	0.313
2017-09-01T17:26:59	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.313

date	userid	compid	res64	spent (GHz-days)
1999-10-07T00:00:00	ANONYMOUS	v4_computers	DDF6493AC0B8EB4D	0.218

date

userid

compid

res64

spent (GHz-days)

1999-10-07T00:00:00

ANONYMOUS

v4_computers

DDF6493AC0B8EB4D

0.218

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-29T05:11:35

Oliver Kruse

GTX-2

109999736277745577489

E11C4AB55BAA75__

2017-10-29T17:20:09

YarBer

Manual testing

109999736277745577489

E11C4AB55BAA75__

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 = 336021, B2 = 3360210 (P-1 stage 2)

B1 = 336021 (P-1 stage 1)

B1 = 135041, B2 = 3630000 (P-1 stage 2)

B1 = 135041, B2 = 3300000 (P-1 stage 2)

B1 = 233349 (P-1 stage 1)

B1 = 194458 (P-1 stage 1)

B1 = 135041 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

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