M1747063 Mersenne number exponent details

Residue

Status

L-L

45E2F23A3ED8CB85

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	17.0079	68.6567%	2475400	86660000	0.5555	7.9499%	17.5634	71.1485%	2.4918%
PrimeNet	2⁵⁷	0.0110	63.1579%	8000	140000	0.0012	2.8016%	0.0122	64.1901%	1.0322%
GPU72	2⁶¹	0.1758	65.5738%	8000	110000	0.0011	1.4122%	0.1769	66.0599%	0.4862%
Difference	+6	+16.8321	+3.0829%	+2467400	+86550000	+0.5544	+6.5377%	+17.3865	+5.0886%	+5.0886%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.0079

68.6567%

2475400

86660000

0.5555

7.9499%

17.5634

71.1485%

2.4918%

PrimeNet

2⁵⁷

0.0110

63.1579%

8000

140000

0.0012

2.8016%

0.0122

64.1901%

1.0322%

GPU72

2⁶¹

0.1758

65.5738%

8000

110000

0.0011

1.4122%

0.1769

66.0599%

0.4862%

Difference

+16.8321

+3.0829%

+2467400

+86550000

+0.5544

+6.5377%

+17.3865

+5.0886%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1747063	567079747121563813987777	24	78.908	162295162544671776 2⁵ × 3² × 83 × 6789456264419	2020-07-06	83	6789456264419	44,414	29,098	54,347
1747063	3588105631160274354492239881	28	91.535	1026896463138499972380 2² × 3³ × 5 × 468463 × 543877 × 7463747	2015-04-22	543877	7463747	376,514,606	0.0724	0.0871

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1747063

567079747121563813987777

78.908

162295162544671776
2⁵ × 3² × 83 × 6789456264419

2020-07-06

6789456264419

44,414

29,098

54,347

1747063

3588105631160274354492239881

91.535

1026896463138499972380
2² × 3³ × 5 × 468463 × 543877 × 7463747

2015-04-22

543877

7463747

376,514,606

0.0724

0.0871

exponent	prime factors	composite factor	digits	bits*
1747063	567079747121563813987777 3588105631160274354492239881	20347420339638275029109104858695827869023074859345 37	52	170.443

exponent

prime factors

composite factor

digits

bits*

1747063

567079747121563813987777
3588105631160274354492239881

20347420339638275029109104858695827869023074859345
37

170.443

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-09T06:18:00	Carsten Kossendey	leela	95000	1543750		-		-	-	0.014	-	-	2.401%
2014-04-05T13:21:00	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.008	-	-	0.887%
2014-05-06T10:53:00	Jocelyn Larouche	Manual testing	136738	136738		-		-	-	0.011	-	-	1.059%
2014-09-15T22:12:00	ANONYMOUS	Manual testing	173476	173476		-		-	-	0.014	-	-	1.203%
2015-04-22T11:19:00	mikr	MSI	2475400	86660000	12		3588105631160274354492239881	28	91.535	0.556	0.190	1.111	7.950%
2016-03-16T12:35:09	alpertron	Manual testing	500000	15000000	12	-		-	-	0.101	-	-	5.040%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.022	-	-
2010-04-20T22:46:00	Architects Cubed	m1_fw	2⁶⁰	2⁶¹		-	-	0.088	-	-
2010-11-18T02:51:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.914	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.454 GHz-days
Estimated T-Level:	24.536

Digits	B1	Curves	Complete	FacMiss
20	11000	254 / 100	2.540	7.786%
25	50000	254 / 280	0.907	40.302%

New Calculation Method

Total ECM effort:	17.454 GHz-days
Estimated T-Level:	24.536

Digits	B1	Complete	FacMiss
20	11000	8.194	0.028%
25	50000	0.741	47.686%
30	250000	0.046	95.542%
35	1000000	0.002	99.791%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		185	12.71
50000	5000000	567079747121563813987777	69	4.742

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-22T03:12:00	Team_Bundu	bundu4	50000	5000000						3	0.206
2009-10-02T23:39:00	Samoflan	Parker	50000	5000000						3	0.206
2010-08-26T13:07:00	James Hintz	terri_castor	50000	5000000						3	0.206
2011-12-28T15:43:00	Wojciech Florek	gafel	50000	5000000						3	0.206
2013-05-16T22:42:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2014-02-13T02:59:00	Bruce	snowflake	50000	5000000						3	0.206
2014-12-18T22:51:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2020-05-18T04:08:13	-Anonymous-	aws-nano	50000	5000000						3	0.206
2020-06-22T23:22:45	nordi	sweet16	50000	5000000						3	0.206
2020-07-06T08:24:21	TJAOI	Manual testing	50000	5000000	567079747121563813987777	78.908	69	2		69	4.742
2020-07-06T08:24:21	TJAOI	Manual testing	50000	5000000						158	10.86

date	userid	compid	res64	spent (GHz-days)
1998-12-21T00:00:00	ANONYMOUS	v4_computers	45E2F23A3ED8CB85	0.095

date

userid

compid

res64

spent (GHz-days)

1998-12-21T00:00:00

ANONYMOUS

v4_computers

45E2F23A3ED8CB85

0.095

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T05:41:51

Oliver Kruse

GTX-3

3588105631160274354492239881

0FA0C6A27E0A53__

2017-11-03T18:06:42

kkmrkkblmbrbk

c4.xlarge

3588105631160274354492239881

0FA0C6A27E0A53__

2020-07-06T13:39:35

mrh.org

567079747121563813987777

3588105631160274354492239881

2AB874439BCCCDA8

2020-07-07T12:17:37

marssystems

SYSTEM01

567079747121563813987777

3588105631160274354492239881

2AB874439BCCCDA8

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 = 2475400, B2 = 86660000 (P-1 stage 2)

B1 = 2475400 (P-1 stage 1)

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

B1 = 500000 (P-1 stage 1)

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

B1 = 173476 (P-1 stage 1)

B1 = 136738 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 95000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

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