M1749439 Mersenne number exponent details

Residue

Status

L-L

FFB1CDAF7667706B

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	16.9848	68.6567%	3642200	123456789	0.8000	8.6353%	17.7848	71.3633%	2.7066%
PrimeNet	2⁵⁷	0.0110	63.1579%	8000	140000	0.0012	2.8023%	0.0122	64.1903%	1.0324%
GPU72	2⁶¹	0.1756	65.5738%	8000	110000	0.0011	1.4126%	0.1767	66.0601%	0.4863%
Difference	+6	+16.8092	+3.0829%	+3634200	+123346789	+0.7989	+7.2227%	+17.6082	+5.3032%	+5.3032%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.9848

68.6567%

3642200

123456789

0.8000

8.6353%

17.7848

71.3633%

2.7066%

PrimeNet

2⁵⁷

0.0110

63.1579%

8000

140000

0.0012

2.8023%

0.0122

64.1903%

1.0324%

GPU72

2⁶¹

0.1756

65.5738%

8000

110000

0.0011

1.4126%

0.1767

66.0601%

0.4863%

Difference

+16.8092

+3.0829%

+3634200

+123346789

+0.7989

+7.2227%

+17.6082

+5.3032%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1749439	129234724835224447817593	24	76.774	36936047737367364 2² × 3 × 3301 × 932445918847	2020-07-06	3301	932445918847	14,815	3,996.2	7,463.8
1749439	800707262594856550276685977	27	89.371	228846865365084621492 2² × 3² × 97 × 5003 × 329657 × 39735431	2015-06-22	329657	39735431	110,939,571	0.1948	0.3181

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1749439

129234724835224447817593

76.774

36936047737367364
2² × 3 × 3301 × 932445918847

2020-07-06

3301

932445918847

14,815

3,996.2

7,463.8

1749439

800707262594856550276685977

89.371

228846865365084621492
2² × 3² × 97 × 5003 × 329657 × 39735431

2015-06-22

329657

39735431

110,939,571

0.1948

0.3181

exponent	prime factors	composite factor	digits	bits*
1749439	129234724835224447817593 800707262594856550276685977	10347918275501209135892513606815464164284623699336 1	51	166.146

exponent

prime factors

composite factor

digits

bits*

1749439

129234724835224447817593
800707262594856550276685977

10347918275501209135892513606815464164284623699336
1

166.146

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-07T12:41:00	Carsten Kossendey	leela	95000	1543750		-		-	-	0.014	-	-	2.401%
2014-04-08T23:00:00	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.008	-	-	0.887%
2014-05-06T10:53:00	Jocelyn Larouche	Manual testing	136688	136688		-		-	-	0.011	-	-	1.059%
2014-09-15T22:12:00	ANONYMOUS	Manual testing	173376	173376		-		-	-	0.014	-	-	1.202%
2015-04-22T02:02:00	Squeeky_Squirrel	P4_2600	130000	3640000		-		-	-	0.025	-	-	3.107%
2015-06-22T19:28:00	mikr	MSI	3642200	123456789	12		800707262594856550276685977	27	89.371	0.800	0.190	1.600	8.635%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-21T00:00:00	carlo_baffa	v4_computers	2¹	2⁵⁷		-	-	0.011	-	-
2003-01-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.022	-	-
2010-04-23T13:38:00	Architects Cubed	m1_fw	2⁶⁰	2⁶¹		-	-	0.088	-	-
2010-12-13T03:32:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.912	-	-
2015-05-13T05:09:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.122	-	-
2015-05-13T05:09:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.136	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:

20.893 GHz-days

Digits	B1	Curves	Complete	FacMiss
20	11000	304 / 100	3.040	4.711%
25	50000	304 / 280	1.086	33.700%

New Calculation Method

Total ECM effort:

20.893 GHz-days

Digits	B1	Complete	FacMiss
20	11000	9.806	0.006%
25	50000	0.886	41.218%
30	250000	0.055	94.688%
35	1000000	0.002	99.750%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		228	15.67
50000	5000000	129234724835224447817593	76	5.223

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-25T00:12:00	James Heinrich	Q6600	50000	5000000						3	0.206
2009-06-24T04:34:00	Lupo	yorick	50000	5000000						3	0.206
2010-10-21T22:04:00	Lupo	yorick	50000	5000000						3	0.206
2012-01-01T17:43:00	S36049	Wolle5	50000	5000000						3	0.206
2013-05-18T23:47:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2014-02-14T14:39:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2014-12-22T13:10:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2020-05-24T23:35:07	-Anonymous-	aws-nano	50000	5000000						3	0.206
2020-07-06T08:24:30	TJAOI	Manual testing	50000	5000000	129234724835224447817593	76.774	76	2		76	5.223
2020-07-06T08:24:30	TJAOI	Manual testing	50000	5000000						154	10.58
2020-07-07T12:17:48	Oliver Kruse	IOS-1	50000	5000000						50	3.436

date	userid	compid	res64	spent (GHz-days)
1998-12-06T00:00:00	carlo_baffa	v4_computers	FFB1CDAF7667706B	0.095

date

userid

compid

res64

spent (GHz-days)

1998-12-06T00:00:00

carlo_baffa

v4_computers

FFB1CDAF7667706B

0.095

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:24:43

alpertron

Manual testing

800707262594856550276685977

994499E171B95C__

2017-10-19T16:05:00

Oliver Kruse

Threadripper

800707262594856550276685977

994499E171B95C__

2020-07-06T13:51:49

mrh.org

129234724835224447817593

800707262594856550276685977

FDBED91387456805

2020-07-08T10:37:30

oodaira

com1

129234724835224447817593

800707262594856550276685977

FDBED91387456805

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 = 3642200, B2 = 123456789 (P-1 stage 2)

B1 = 3642200 (P-1 stage 1)

B1 = 130000, B2 = 3640000 (P-1 stage 2)

B1 = 95000, B2 = 1543750 (P-1 stage 2)

B1 = 173376 (P-1 stage 1)

B1 = 136688 (P-1 stage 1)

B1 = 130000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 95000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

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