M1187413 Mersenne number exponent details

Residue

Status

L-L

BF853C1F05766060

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	25.0241	68.6567%	300000	10000000	0.0368	4.1556%	25.0609	69.9592%	1.3025%
PrimeNet	2⁵⁶	0.0081	62.5000%	5000	80000	0.0004	2.2651%	0.0085	63.3494%	0.8494%
GPU72	2⁶⁰	0.1293	65.0000%	5000	28000	0.0003	0.8009%	0.1296	65.2803%	0.2803%
Difference	+7	+24.8947	+3.6567%	+295000	+9972000	+0.0366	+3.3547%	+24.9313	+4.6789%	+4.6789%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

25.0241

68.6567%

300000

10000000

0.0368

4.1556%

25.0609

69.9592%

1.3025%

PrimeNet

2⁵⁶

0.0081

62.5000%

5000

80000

0.0004

2.2651%

0.0085

63.3494%

0.8494%

GPU72

2⁶⁰

0.1293

65.0000%

5000

28000

0.0003

0.8009%

0.1296

65.2803%

0.2803%

Difference

+24.8947

+3.6567%

+295000

+9972000

+0.0366

+3.3547%

+24.9313

+4.6789%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1187413	480683140062703241999	21	68.704	202407730108523 701 × 288741412423	2009-09-25	701	288741412423	59.602	699.52	1,306.5

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1187413

480683140062703241999

68.704

202407730108523
701 × 288741412423

2009-09-25

701

288741412423

59.602

699.52

1,306.5

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-04-07T00:00:00	Jocelyn Larouche	v4_computers	15000	217500		-		-	-	0.001	-	-	0.777%
unknown			300000	10000000		-		-	-	0.037	-	-	4.156%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-03T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.016	-	-
2003-05-11T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.032	-	-
2022-03-07T17:31:15	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.097	-	-
2009-02-27T04:51:00	Sturle Sunde	bach.ifi	2⁶⁰	2⁶¹		-	-	0.129	-	-
2022-04-12T20:41:58	LordJulius	Manual testing	2¹	2⁶¹		-	-	0.259	-	-
2022-04-12T20:41:58	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	0.259	-	-
2022-04-12T20:41:58	LordJulius	Manual testing	2⁶²	2⁶³		-	-	0.827	-	-
2022-04-12T20:41:58	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	1.653	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.335 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	322 / 100	3.220	3.931%
25	50000	322 / 280	1.150	31.599%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	18.335 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	14.692	0.000%
25	50000	1.609	20.008%
30	250000	0.131	87.737%
35	1000000	0.009	99.133%

ECM Summary

B1	B2	factor	curves	GHz-days
		480683140062703241999	1	0.00000e+0
50000	5000000		278	10.24
250000	25000000		44	8.100

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-10-17T17:48:00	Andi47	Core2Duo	50000	5000000						1	0.037
2008-07-16T00:49:00	Sturle Sunde	v21	50000	5000000						3	0.110
2009-01-14T15:05:00	Sturle Sunde	v21	50000	5000000						3	0.110
2009-06-16T09:15:00	Lukasz Wrobel	UNIX_05	50000	5000000						3	0.110
2009-09-25T17:33:00	SubPrime	c2d0			480683140062703241999	68.704		1		1	-
2017-09-08T12:49:22	TJAOI	Manual testing	50000	5000000						127	4.676
2018-06-22T09:09:13	TJAOI	Manual testing	50000	5000000						141	5.191
2021-02-12T10:29:59	TJAOI	Manual testing	250000	25000000						44	8.100

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-29T11:27:02

Oliver Kruse

GTX-2

480683140062703241999

4385B569D7C9C8__

2017-10-17T18:00:41

Oliver Kruse

Threadripper

480683140062703241999

4385B569D7C9C8__

2018-01-03T03:49:36

ATH

ec2-8x

480683140062703241999

4385B569D7C9C8__

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 = 300000, B2 = 10000000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 15000, B2 = 217500 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

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