M1771717 Mersenne number exponent details

Residue

Status

L-L

AA6F2B4261A5DE0D

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	16.7713	68.6567%	2475400	86660000	0.5555	7.9611%	17.3268	71.1520%	2.4953%
PrimeNet	2⁵⁷	0.0108	63.1579%	8000	140000	0.0012	2.8090%	0.0120	64.1928%	1.0349%
GPU72	2⁶¹	0.1734	65.5738%	8000	120000	0.0011	1.4547%	0.1745	66.0746%	0.5008%
Difference	+6	+16.5979	+3.0829%	+2467400	+86540000	+0.5544	+6.5064%	+17.1523	+5.0774%	+5.0774%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.7713

68.6567%

2475400

86660000

0.5555

7.9611%

17.3268

71.1520%

2.4953%

PrimeNet

2⁵⁷

0.0108

63.1579%

8000

140000

0.0012

2.8090%

0.0120

64.1928%

1.0349%

GPU72

2⁶¹

0.1734

65.5738%

8000

120000

0.0011

1.4547%

0.1745

66.0746%

0.5008%

Difference

+16.5979

+3.0829%

+2467400

+86540000

+0.5544

+6.5064%

+17.1523

+5.0774%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1771717	7809606385274348003219047	25	82.692	2203965527585485719 3 × 11 × 151 × 317 × 88001 × 15855029	2015-05-15	88001	15855029	1,038,540	0.0745	0.1269
1771717	684454810766986146151904449	27	89.145	193161439091848795872 2⁵ × 3 × 182857 × 253751 × 43364051	2015-05-15	253751	43364051	80,136,646	0.2047	0.3471

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1771717

7809606385274348003219047

82.692

2203965527585485719
3 × 11 × 151 × 317 × 88001 × 15855029

2015-05-15

88001

15855029

1,038,540

0.0745

0.1269

1771717

684454810766986146151904449

89.145

193161439091848795872
2⁵ × 3 × 182857 × 253751 × 43364051

2015-05-15

253751

43364051

80,136,646

0.2047

0.3471

exponent	prime factors	composite factor	digits	bits*
1771717	7809606385274348003219047 684454810766986146151904449	53453226605976005648220494852798239995861015608401 03	52	171.837

exponent

prime factors

composite factor

digits

bits*

1771717

7809606385274348003219047
684454810766986146151904449

53453226605976005648220494852798239995861015608401
03

171.837

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-07T12:40:00	Carsten Kossendey	leela	95000	1615000		-		-	-	0.014	-	-	2.433%
2014-04-08T23:03:00	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.008	-	-	0.889%
2014-05-09T20:31:00	Jocelyn Larouche	Manual testing	136227	136227		-		-	-	0.011	-	-	1.059%
2014-09-18T20:49:00	Jocelyn Larouche	Manual testing	172454	172454		-		-	-	0.014	-	-	1.202%
2015-05-15T13:15:00	mikr	MSI	2475400	86660000	12		7809606385274348003219047 684454810766986146151904449	52	171.837	0.556	0.192	1.111	7.961%
2016-03-16T12:31:22	alpertron	Manual testing	500000	15000000	12	-		-	-	0.101	-	-	5.049%

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	-	-
2010-04-20T13:12:00	Architects Cubed	m1_tt	2⁶⁰	2⁶¹		-	-	0.087	-	-
2010-12-13T03:32:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.901	-	-
2015-05-01T11:45:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.108	-	-
2015-05-01T11:45:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.109	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.274 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	17.274 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.097	0.030%
25	50000	0.732	48.105%
30	250000	0.045	95.594%
35	1000000	0.002	99.794%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		251	17.27

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-08-11T09:50:00	paulie	iMac3.4	50000	5000000						3	0.206
2009-10-13T00:11:00	Piepen	T41-2000	50000	5000000						3	0.206
2010-12-19T10:42:00	Lupo	yorick	50000	5000000						3	0.206
2012-02-06T15:42:00	OS1	L3	50000	5000000						3	0.206
2013-06-05T07:15:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2014-02-17T11:06:00	Bruce	snowflake	50000	5000000						3	0.206
2015-02-01T20:14:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2020-06-30T09:00:50	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						3	0.206
2020-07-28T02:54:54	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						3	0.206
2020-10-02T07:43:10	TJAOI	Manual testing	50000	5000000						224	15.42

date	userid	compid	res64	spent (GHz-days)
1998-11-28T00:00:00	ANONYMOUS	v4_computers	AA6F2B4261A5DE0D	0.096

date

userid

compid

res64

spent (GHz-days)

1998-11-28T00:00:00

ANONYMOUS

v4_computers

AA6F2B4261A5DE0D

0.096

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T11:48:59

Oliver Kruse

GTX-3

7809606385274348003219047

684454810766986146151904449

827526C4846FD568

2017-10-05T21:44:02

Oliver Kruse

Manual testing

7809606385274348003219047

684454810766986146151904449

827526C4846FD5__

2017-11-10T22:28:23

kkmrkkblmbrbk

c4.xlarge

7809606385274348003219047

684454810766986146151904449

827526C4846FD5__

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 = 1615000 (P-1 stage 2)

B1 = 172454 (P-1 stage 1)

B1 = 136227 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 95000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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