M31667 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

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	938.3244	77.6119%	200000000	5000000000	0.3686	12.3710%	938.6930	80.3816%	2.7696%
PrimeNet	2⁴⁰	0.0000	62.5000%	500	10000	0.0000	4.1604%	0.0000	64.0601%	1.5601%
GPU72	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.7867%	0.0001	66.5182%	0.6091%
Difference	+23	+938.3243	+11.7028%	+199999500	+4999990000	+0.3686	+10.5843%	+938.6929	+13.8634%	+13.8634%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

938.3244

77.6119%

200000000

5000000000

0.3686

12.3710%

938.6930

80.3816%

2.7696%

PrimeNet

2⁴⁰

0.0000

62.5000%

500

10000

0.0000

4.1604%

0.0000

64.0601%

1.5601%

GPU72

2⁴⁴

0.0001

65.9091%

500

10000

0.0000

1.7867%

0.0001

66.5182%

0.6091%

Difference

+23

+938.3243

+11.7028%

+199999500

+4999990000

+0.3686

+10.5843%

+938.6929

+13.8634%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
31667	3038321983	10	31.501	47973 3 × 15991	-	3	15991	1.250e-8	6.981e-7	1.300e-6
31667	168149743313	12	37.291	2654968 2³ × 331871	2008-08-26	8	331871	9.646e-7	1.445e-5	2.697e-5

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

31667

3038321983

31.501

47973
3 × 15991

15991

1.250e-8

6.981e-7

1.300e-6

31667

168149743313

37.291

2654968
2³ × 331871

2008-08-26

331871

9.646e-7

1.445e-5

2.697e-5

exponent	prime factors	composite factor	digits	bits*
31667	3038321983 168149743313	510893061543695149679	21	68.792

exponent

prime factors

composite factor

digits

bits*

31667

3038321983
168149743313

510893061543695149679

68.792

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-10-09T01:59:41	kkmrkkblmbrbk	Manual testing	200000000	5000000000	12	-	skipped known factor: 3038321983 skipped known factor: 168149743313	-	-	0.369	-	-	12.371%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-10-09T01:59:41

kkmrkkblmbrbk

Manual testing

200000000

5000000000

skipped known factor: 3038321983
skipped known factor: 168149743313

0.369

-

-

12.371%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-08-26T19:59:00	ANONYMOUS	Manual testing	?	?	168149743313	37.291	12	3.86458e-7	3.91683e-5	8.67781e-7

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-08-26T19:59:00

ANONYMOUS

Manual testing

168149743313

37.291

3.86458e-7

3.91683e-5

8.67781e-7

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.172 GHz-days
Estimated T-Level:	34.537

Digits	B1	Curves	Complete	FacMiss
20	11000	2288 / 100	22.880	0.000%
25	50000	2288 / 280	8.171	0.028%
30	250000	2005 / 640	3.133	4.349%
35	1000000	1421 / 1566	0.907	40.345%

New Calculation Method

Total ECM effort:	18.172 GHz-days
Estimated T-Level:	34.537

Digits	B1	Complete	FacMiss
20	11000	300.809	0.000%
25	50000	56.599	0.000%
30	250000	8.297	0.025%
35	1000000	0.992	37.085%
40	3000000	0.098	90.629%
45	11000000	0.008	99.181%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	283	0.163
250000	25000000	584	1.678
1000000	100000000	1,421	16.33

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

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-30T14:36:00	Matthias Wurtinger	WUR_E6600	50000	5000000						30	0.017
2010-04-18T01:05:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-20T15:34:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-20T20:14:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-21T00:06:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-21T04:06:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-21T11:05:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-21T12:05:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-26T14:59:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-26T18:53:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-26T22:52:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-27T02:50:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-27T06:50:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-27T11:23:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-27T14:45:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-27T18:43:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-27T22:42:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-28T02:42:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-28T07:55:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-28T10:30:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-28T14:26:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-28T18:31:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-28T22:25:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-29T02:31:00	James Hintz	04_122109	50000	5000000						11	0.006
2011-01-20T22:06:00	James Hintz	NEW_OMFG	250000	25000000						3	0.009
2011-03-16T17:08:00	James Hintz	17_051310	250000	25000000						11	0.032
2015-06-23T17:34:00	James Hintz	08_04_2014	250000	25000000						11	0.032
2015-07-01T17:54:00	James Hintz	08_04_2014	250000	25000000						559	1.606
2015-07-01T18:35:00	James Hintz	08_04_2014	1000000	100000000						11	0.126
2018-04-12T06:37:16	kkmrkkblmbrbk	c5.large	1000000	100000000						1410	16.21