M2347271 Mersenne number exponent details

Residue

Status

L-L

D15DAA7208EF2E5A

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	12.6589	67.1642%	500000	15000000	0.1264	5.2225%	12.7853	68.8790%	1.7148%
PrimeNet	2⁵⁸	0.0164	62.0690%	11000	200000	0.0021	3.0480%	0.0184	63.2251%	1.1561%
GPU72	2⁶²	0.2617	64.5161%	13000	220000	0.0024	1.8351%	0.2641	65.1673%	0.6512%
Difference	+5	+12.3972	+2.6481%	+487000	+14780000	+0.1240	+3.3874%	+12.5212	+3.7117%	+3.7117%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

12.6589

67.1642%

500000

15000000

0.1264

5.2225%

12.7853

68.8790%

1.7148%

PrimeNet

2⁵⁸

0.0164

62.0690%

11000

200000

0.0021

3.0480%

0.0184

63.2251%

1.1561%

GPU72

2⁶²

0.2617

64.5161%

13000

220000

0.0024

1.8351%

0.2641

65.1673%

0.6512%

Difference

+12.3972

+2.6481%

+487000

+14780000

+0.1240

+3.3874%

+12.5212

+3.7117%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2347271	132248607332045888936719823	27	86.773	28170715552666455841 7309 × 3854250315045349	2017-02-24	7309	3854250315045349	8,672,178	20,569,706	38,418,482

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2347271

132248607332045888936719823

86.773

28170715552666455841
7309 × 3854250315045349

2017-02-24

7309

3854250315045349

8,672,178

20,569,706

38,418,482

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-21T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.286%
2010-03-03T08:37:00	Bud	annan	500000	10000000		-		-	-	0.100	-	-	4.832%
2018-03-18T01:20:11	alpertron	Manual testing	500000	15000000	12	-		-	-	0.126	-	-	5.222%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.016	-	-
2016-02-23T16:29:12	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.049	-	-
2009-01-15T06:42:00	Sturle Sunde	celair.ifi	2⁶⁰	2⁶¹		-	-	0.065	-	-
2012-05-29T10:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.131	-	-
2013-01-23T08:26:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.418	-	-
2015-03-06T11:15:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.836	-	-
2015-03-06T11:15:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.592	-	-
2015-10-26T11:50:57	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.184	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.307 GHz-days
Estimated T-Level:	1.300

Digits	B1	Curves	Complete	FacMiss
20	11000	26 / 100	0.260	77.004%
25	50000	26 / 280	0.093	91.117%

New Calculation Method

Total ECM effort:	2.307 GHz-days
Estimated T-Level:	1.300

Digits	B1	Complete	FacMiss
20	11000	0.839	43.227%
25	50000	0.076	92.700%
30	250000	0.005	99.534%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		24	2.130
50000	5000000	132248607332045888936719823	2	0.177

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-24T14:23:00	Stun	Core2	50000	5000000						3	0.266
2010-01-28T09:33:00	mdrg	MDRG02	50000	5000000						3	0.266
2011-12-23T09:34:00	S36049	Wolle5	50000	5000000						3	0.266
2013-10-26T01:10:00	arnaud	srv-630	50000	5000000						3	0.266
2015-06-08T19:29:00	guru	w6	50000	5000000						3	0.266
2016-02-16T21:07:21	Sintax	cloud2	50000	5000000						3	0.266
2016-05-08T07:55:23	Jason U	Server7	50000	5000000						3	0.266
2016-08-28T19:07:19	Bruce	Desk6	50000	5000000						3	0.266
2017-02-24T08:51:27	Bruce	Desk6	50000	5000000	132248607332045888936719823	86.773	2	2		2	0.177

date	userid	compid	res64	spent (GHz-days)
1999-03-26T00:00:00	ANONYMOUS	v4_computers	D15DAA7208EF2E5A	0.159

date

userid

compid

res64

spent (GHz-days)

1999-03-26T00:00:00

ANONYMOUS

v4_computers

D15DAA7208EF2E5A

0.159

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-12T05:29:53

Oliver Kruse

GTX-0

132248607332045888936719823

43C735F32FE1D8__

2017-11-24T10:04:10

kkmrkkblmbrbk

c4.xlarge

132248607332045888936719823

43C735F32FE1D8__

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

B1 = 500000, B2 = 10000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

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