M1777247 Mersenne number exponent details

Residue

Status

L-L

8C7C3E112452AAD6

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	16.7191	68.6567%	2475400	86660000	0.5555	7.9636%	17.2746	71.1528%	2.4960%
PrimeNet	2⁵⁷	0.0108	63.1579%	8000	140000	0.0012	2.8107%	0.0120	64.1934%	1.0355%
GPU72	2⁶¹	0.1728	65.5738%	8000	120000	0.0011	1.4556%	0.1739	66.0749%	0.5011%
Difference	+6	+16.5462	+3.0829%	+2467400	+86540000	+0.5544	+6.5080%	+17.1006	+5.0779%	+5.0779%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.7191

68.6567%

2475400

86660000

0.5555

7.9636%

17.2746

71.1528%

2.4960%

PrimeNet

2⁵⁷

0.0108

63.1579%

8000

140000

0.0012

2.8107%

0.0120

64.1934%

1.0355%

GPU72

2⁶¹

0.1728

65.5738%

8000

120000

0.0011

1.4556%

0.1739

66.0749%

0.5011%

Difference

+16.5462

+3.0829%

+2467400

+86540000

+0.5544

+6.5080%

+17.1006

+5.0779%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1777247	12201988615847948949391	23	73.370	3432834213772185 3² × 5 × 76285204750493	2016-12-15	9	76285204750493	1,827.7	326,939	610,632

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1777247

12201988615847948949391

73.370

3432834213772185
3² × 5 × 76285204750493

2016-12-15

76285204750493

1,827.7

326,939

610,632

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-11T06:18:00	Carsten Kossendey	leela	95000	1615000		-		-	-	0.014	-	-	2.434%
2014-04-10T20:52:00	ANONYMOUS	Manual testing	100000	100000		-		-	-	0.008	-	-	0.890%
2014-05-09T20:32:00	Jocelyn Larouche	Manual testing	136114	136114		-		-	-	0.011	-	-	1.059%
2014-09-18T20:49:00	Jocelyn Larouche	Manual testing	172228	172228		-		-	-	0.014	-	-	1.202%
2015-05-23T04:17:00	mikr	MSI	2475400	86660000		-		-	-	0.556	-	-	7.964%

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	-	-
2016-02-23T16:28:51	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.065	-	-
2010-04-20T13:12:00	Architects Cubed	m1_tt	2⁶⁰	2⁶¹		-	-	0.086	-	-
2016-02-23T16:28:51	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.173	-	-
2010-12-13T03:32:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.898	-	-
2016-02-23T16:28:51	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.552	-	-
2015-05-08T04:03:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.105	-	-
2015-05-08T04:03:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.102	-	-
2015-09-11T08:33:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.205	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.280 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:	17.280 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		248	17.07
50000	5000000	12201988615847948949391	3	0.207

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-08-17T04:24:00	Scott Kurowski	UW1	50000	5000000						3	0.207
2009-07-03T08:15:00	SubPrime	abd1	50000	5000000						3	0.207
2010-12-31T08:41:00	Anu Järvi	Anu-TEMP	50000	5000000						3	0.207
2012-02-13T15:42:00	OS1	L3	50000	5000000						3	0.207
2013-06-11T03:03:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-02-17T14:57:00	Bruce	snowflake	50000	5000000						3	0.207
2015-02-08T01:39:00	codest	aliyun	50000	5000000						3	0.207
2015-09-14T18:52:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2016-01-23T01:25:19	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2016-03-26T10:47:56	Bruce	DESK3	50000	5000000						3	0.207
2016-05-10T04:27:14	Bruce	DESK3	50000	5000000						3	0.207
2016-08-06T20:53:01	Bruce	DESK3	50000	5000000						3	0.207
2016-10-13T12:15:33	Bruce	DESK3	50000	5000000						3	0.207
2016-12-15T12:38:40	Bruce	DESK3	50000	5000000	12201988615847948949391	73.370	3	2		3	0.207
2020-10-23T07:51:46	TJAOI	Manual testing	50000	5000000						209	14.39

date	userid	compid	res64	spent (GHz-days)
1998-12-06T00:00:00	ANONYMOUS	v4_computers	8C7C3E112452AAD6	0.096
2015-06-27T00:56:00	MadPoo	Manual testing	8C7C3E112452AAD6	0.096

date

userid

compid

res64

spent (GHz-days)

1998-12-06T00:00:00

ANONYMOUS

v4_computers

8C7C3E112452AAD6

0.096

2015-06-27T00:56:00

MadPoo

Manual testing

8C7C3E112452AAD6

0.096

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 = 95000, B2 = 1615000 (P-1 stage 2)

B1 = 172228 (P-1 stage 1)

B1 = 136114 (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

10¹⁴

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