M5005643 Mersenne number exponent details

Residue

Status

L-L

DE182E09A0F2554F

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	2⁶⁸	11.9075	66.1765%	3600000	120000000	1.9982	8.7783%	13.9057	69.1456%	2.9691%
PrimeNet	2⁶¹	0.0614	62.2951%	22000	450000	0.0091	3.3139%	0.0705	63.5446%	1.2495%
GPU72	2⁶⁵	1.4575	64.6154%	34000	700000	0.0141	2.4165%	1.4716	65.4704%	0.8551%
Difference	+3	+10.4500	+1.5611%	+3566000	+119300000	+1.9840	+6.3618%	+12.4341	+3.6752%	+3.6752%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

11.9075

66.1765%

3600000

120000000

1.9982

8.7783%

13.9057

69.1456%

2.9691%

PrimeNet

2⁶¹

0.0614

62.2951%

22000

450000

0.0091

3.3139%

0.0705

63.5446%

1.2495%

GPU72

2⁶⁵

1.4575

64.6154%

34000

700000

0.0141

2.4165%

1.4716

65.4704%

0.8551%

Difference

+10.4500

+1.5611%

+3566000

+119300000

+1.9840

+6.3618%

+12.4341

+3.6752%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5005643	1119428951822542798364656510601	31	99.821	111816698855925482337100 2² × 5² × 7² × 13 × 4019 × 4657 × 9109 × 10296089	2018-06-06	9109	10296089	3.342e+10	0.1145	0.2106

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5005643

1119428951822542798364656510601

99.821

111816698855925482337100
2² × 5² × 7² × 13 × 4019 × 4657 × 9109 × 10296089

2018-06-06

9109

10296089

3.342e+10

0.1145

0.2106

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-05-13T00:00:00	delta_t	v4_computers	25000	200000		-		-	-	0.007	-	-	1.024%
2009-08-04T15:53:00	harlee	P4_2600	55000	907500		-		-	-	0.020	-	-	1.955%
2013-05-11T04:04:00	Squeeky_Squirrel	P4_2600	85000	1508750		-		-	-	0.033	-	-	2.437%
2017-02-13T18:39:08	Squeeky_Squirrel	i5-5250U_1600	300000	9375000	12	-		-	-	0.160	-	-	4.456%
2018-06-06T04:43:13	mikr	Color	3600000	120000000	12		1119428951822542798364656510601	31	99.821	1.998	1.388	3.996	8.778%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-03-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.061	-	-
2016-02-23T16:39:06	Mark Rose	Manual testing	2⁶¹	2⁶³		-	-	0.257	-	-
2014-08-29T14:16:00	kracker	Manual testing	2⁶³	2⁶⁴		-	-	0.392	-	-
2014-08-30T11:46:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.746	-	-
2015-04-20T08:58:00	Gordon Spence	Manual testing	2⁶⁵	2⁶⁶		-	-	1.493	-	-
2016-05-13T12:13:08	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.986	-	-
2017-10-11T18:30:04	mikr	Manual testing	2⁶⁷	2⁶⁸		-	-	5.971	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.897 GHz-days
Estimated T-Level:	0.450

Digits	B1	Curves	Complete	FacMiss
20	11000	9 / 100	0.090	91.352%
25	50000	9 / 280	0.032	96.831%

New Calculation Method

Total ECM effort:	1.897 GHz-days
Estimated T-Level:	0.450

Digits	B1	Complete	FacMiss
20	11000	0.290	74.802%
25	50000	0.026	97.410%
30	250000	0.002	99.839%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	1.897

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-06-21T20:16:00	oodaira	Linux03	50000	5000000						3	0.632
2014-05-07T10:11:00	bunddog	debian	50000	5000000						3	0.632
2017-06-12T18:32:55	bayanne	iMac	50000	5000000						3	0.632

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2000-04-05T00:00:00	ANONYMOUS	v4_computers	E94AC20A3B077E__	0.694
2001-06-30T00:00:00	delta_t	v4_computers	DE182E09A0F2554F	0.694

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-06-06T21:16:48

storm5510

HP-Z220-CMT

1119428951822542798364656510601

7C5F8E3F0F9508__

2018-06-07T16:09:02

Battlemaxx

Work-3

1119428951822542798364656510601

7C5F8E3F0F9508__

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 = 3600000, B2 = 120000000 (P-1 stage 2)

B1 = 3600000 (P-1 stage 1)

B1 = 300000, B2 = 9375000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 85000, B2 = 1508750 (P-1 stage 2)

B1 = 55000, B2 = 907500 (P-1 stage 2)

B1 = 85000 (P-1 stage 1)

B1 = 55000 (P-1 stage 1)

B1 = 25000, B2 = 200000 (P-1 stage 2)

B1 = 25000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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