M13043603 Mersenne number exponent details

Residue

Status

L-L

68190B6C822D5E37

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	2⁶⁹	9.1529	65.2174%	255000	6566250	0.3547	4.1484%	9.5076	66.6603%	1.4429%
PrimeNet	2⁶⁴	0.2729	62.5000%	60000	1700000	0.0885	4.3393%	0.3613	64.1272%	1.6272%
GPU72	2⁶⁸	4.5697	64.7059%	90000	2400000	0.1278	3.1704%	4.6975	65.8248%	1.1190%
Difference	+1	+4.5832	+0.5115%	+165000	+4166250	+0.2268	+0.9780%	+4.8101	+0.8355%	+0.8355%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

9.1529

65.2174%

255000

6566250

0.3547

4.1484%

9.5076

66.6603%

1.4429%

PrimeNet

2⁶⁴

0.2729

62.5000%

60000

1700000

0.0885

4.3393%

0.3613

64.1272%

1.6272%

GPU72

2⁶⁸

4.5697

64.7059%

90000

2400000

0.1278

3.1704%

4.6975

65.8248%

1.1190%

Difference

+4.5832

+0.5115%

+165000

+4166250

+0.2268

+0.9780%

+4.8101

+0.8355%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
13043603	40227308876859001223257	23	75.091	1542032093312676 2² × 3² × 7 × 6119174973463	2019-10-28	9	6119174973463	1,002.6	197,462	368,803

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

13043603

40227308876859001223257

75.091

1542032093312676
2² × 3² × 7 × 6119174973463

2019-10-28

6119174973463

1,002.6

197,462

368,803

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-07-17T00:00:00	ANONYMOUS	v4_computers	200000	200000		-		-	-	0.118	-	-	1.399%
2001-10-25T00:00:00	ANONYMOUS	v4_computers	150000	1912500		-		-	-	0.146	-	-	2.924%
2012-04-23T09:05:00	James Heinrich	i7-920	255000	6566250		-		-	-	0.355	-	-	4.148%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-05-05T00:00:00	korva	v4_computers	2¹	2⁶⁴		-	-	0.273	-	-
2013-05-27T20:16:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.286	-	-
2014-05-19T10:19:00	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.573	-	-
2015-07-04T23:27:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	1.146	-	-
2017-12-22T13:48:53	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	2.292	-	-
2018-01-09T16:37:27	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	4.583	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.242 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:	1.242 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	0.621
50000	5000000	40227308876859001223257	1	0.621

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-05-17T12:33:45	XZT	Laptop2	50000	5000000						1	0.621
2019-10-28T06:55:12	Keysarecool	HPLaptop	50000	5000000	40227308876859001223257	75.091	1	2	3213263092156510	1	0.621

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-01-02T00:00:00	ANONYMOUS	v4_computers	68190B6C822D5E37	5.328
2004-10-18T00:00:00	ANONYMOUS	v4_computers	68190B6C822D5E37	5.328

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 = 255000, B2 = 6566250 (P-1 stage 2)

B1 = 255000 (P-1 stage 1)

B1 = 150000, B2 = 1912500 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 150000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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