M1701509 Mersenne number exponent details

Residue

Status

L-L

74EEEE509DCC0E29

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	17.4633	68.6567%	3000000	273000000	1.2086	9.5049%	18.6718	71.6359%	2.9791%
PrimeNet	2⁵⁷	0.0113	63.1579%	8000	130000	0.0010	2.7318%	0.0123	64.1643%	1.0064%
GPU72	2⁶¹	0.1805	65.5738%	7000	100000	0.0008	1.3016%	0.1814	66.0218%	0.4481%
Difference	+6	+17.2827	+3.0829%	+2993000	+272900000	+1.2077	+8.2033%	+18.4905	+5.6140%	+5.6140%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.4633

68.6567%

3000000

273000000

1.2086

9.5049%

18.6718

71.6359%

2.9791%

PrimeNet

2⁵⁷

0.0113

63.1579%

8000

130000

0.0010

2.7318%

0.0123

64.1643%

1.0064%

GPU72

2⁶¹

0.1805

65.5738%

7000

100000

0.0008

1.3016%

0.1814

66.0218%

0.4481%

Difference

+17.2827

+3.0829%

+2993000

+272900000

+1.2077

+8.2033%

+18.4905

+5.6140%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1701509	3189947282747658574439927	25	81.400	937387719591156607 479 × 264919 × 7387043207	2014-09-19	264919	7387043207	475,157	27.482	51.296
1701509	50243016513902117747381510263	29	95.343	14764252353029610112959 3 × 1589183521 × 3096821346293	2021-05-25	1589183521	3096821346293	8.614e+9	11,616	21,505

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1701509

3189947282747658574439927

81.400

937387719591156607
479 × 264919 × 7387043207

2014-09-19

264919

7387043207

475,157

27.482

51.296

1701509

50243016513902117747381510263

95.343

14764252353029610112959
3 × 1589183521 × 3096821346293

2021-05-25

1589183521

3096821346293

8.614e+9

11,616

21,505

exponent	prime factors	composite factor	digits	bits*
1701509	3189947282747658574439927 50243016513902117747381510263	16027257400556779782464937933701072431745325062747 0801	54	176.743

exponent

prime factors

composite factor

digits

bits*

1701509

3189947282747658574439927
50243016513902117747381510263

16027257400556779782464937933701072431745325062747
0801

176.743

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-01-27T22:35:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.003	-	-	0.571%
2011-02-07T12:49:00	Carsten Kossendey	leela	90000	1507500		-		-	-	0.011	-	-	2.352%
2014-03-31T21:13:00	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.007	-	-	0.883%
2014-05-03T00:50:00	Jocelyn Larouche	Manual testing	150000	150000		-		-	-	0.010	-	-	1.108%
2016-03-16T12:29:21	alpertron	Manual testing	500000	15000000	12	-		-	-	0.088	-	-	5.024%
2021-07-15T20:18:31	Dylan Delgado	laptop-ryzen73700	3000000	273000000		-		-	-	1.209	-	-	9.505%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-02-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.011	-	-
2003-02-09T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.023	-	-
2010-04-22T12:40:00	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.090	-	-
2010-10-04T14:38:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.938	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	205.148 GHz-days
Estimated T-Level:	30.000

Digits	B1	Curves	Complete	FacMiss
20	11000	891 / 100	8.910	0.013%
25	50000	891 / 280	3.182	4.126%
30	250000	640 / 640	1.000	36.759%

New Calculation Method

Total ECM effort:

205.148 GHz-days

Digits	B1	Complete	FacMiss
20	11000	61.430	0.000%
25	50000	8.443	0.022%
30	250000	0.877	41.590%
35	1000000	0.071	93.118%
40	3000000	0.005	99.529%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		250	14.86
50000	5000000	3189947282747658574439927	1	0.059
250000	25000000		520	154.6
250000	25000000	50243016513902117747381510263	120	35.67

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-06-22T10:27:00	paulie	iMac3.4	50000	5000000						3	0.178
2009-06-17T14:13:00	James Hintz	16_060209	50000	5000000						3	0.178
2010-06-27T21:33:00	Lupo	yorick	50000	5000000						3	0.178
2011-11-22T20:18:00	Lukasz Wrobel	w-s	50000	5000000						3	0.178
2013-04-18T15:23:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2014-01-06T00:53:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2014-09-19T21:46:00	Chang Chia-Tche	exbpc13	50000	5000000	3189947282747658574439927	81.400	1	2		1	0.059
2020-03-03T14:21:17	TJAOI	Manual testing	50000	5000000						232	13.79
2021-05-25T07:03:52	Marcel PERRIN	Manual testing	250000	25000000	50243016513902117747381510263	95.343	120	2	6613210739310458	120	35.67
2021-07-09T08:06:14	Marcel PERRIN	Manual testing	250000	25000000						520	154.6

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	74EEEE509DCC0E29	0.080

date

userid

compid

res64

spent (GHz-days)

1999-03-15T00:00:00

ANONYMOUS

v4_computers

74EEEE509DCC0E29

0.080

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T03:20:26

Oliver Kruse

GTX-1

3189947282747658574439927

2EE7BAA82FA158__

2017-11-03T14:05:26

kkmrkkblmbrbk

c4.xlarge

3189947282747658574439927

2EE7BAA82FA158__

2021-05-27T00:23:09

kutens

vega

3189947282747658574439927

50243016513902117747381510263

34EFD2A54C8480AF

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 = 3000000, B2 = 273000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 90000, B2 = 1507500 (P-1 stage 2)

B1 = 150000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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