M25 243 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

-unknown-

-unknown-

Cofactor is a certified prime

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	1,177.1151	77.6119%	500000000	500000000	0.3283	8.5751%	1,177.4434	79.5317%
Target	2⁴⁴	0.0001	65.9091%	500	50000	0.0000	1.6713%	0.0001	66.4788%
Difference	+23	+1,177.1150	+11.7028%	+499999500	+499950000	+0.3283	+6.9038%	+1,177.4433	+13.0529%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

2⁶⁷

1,177.1151

77.6119%

500000000

0.3283

8.5751%

1,177.4434

79.5317%

Target

2⁴⁴

0.0001

65.9091%

500

50000

0.0000

1.6713%

0.0001

66.4788%

Difference

+23

+1,177.1150

+11.7028%

+499999500

+499950000

+0.3283

+6.9038%

+1,177.4433

+13.0529%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
25243	252431	6	17.946	5 5	-	1	5	6.925e-13	7.996e-10	1.336e-9
25243	403889	6	18.624	8 2³	2008-08-26	8	8	1.386e-12	5.252e-9	1.069e-8
25243	43014073	8	25.358	852 2² × 3 × 71	2008-08-26	4	71	2.097e-10	5.023e-9	5.345e-9
25243	449245236879223161338352589831	30	98.503	8898412171279625269150905 3² × 5 × 2711 × 258659 × 11588783 × 24333527	2016-12-05	11588783	24333527	2.898e+12	0.0081	0.0155
25243	hide decimal representation P7551 click to show decimal representation	7,551	25,082.569		2016-12-05

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

25243

252431

17.946

5
5

6.925e-13

7.996e-10

1.336e-9

25243

403889

18.624

8
2³

2008-08-26

1.386e-12

5.252e-9

1.069e-8

25243

43014073

25.358

852
2² × 3 × 71

2008-08-26

2.097e-10

5.023e-9

5.345e-9

25243

449245236879223161338352589831

98.503

8898412171279625269150905
3² × 5 × 2711 × 258659 × 11588783 × 24333527

2016-12-05

11588783

24333527

2.898e+12

0.0081

0.0155

25243

P7551

click to show decimal representation

7,551

25,082.569

2016-12-05

exponent	prime factors	composite factor	digits	bits*
25243	252431 403889	101954104159	12	36.569
25243	252431 43014073	10858085461463	14	43.304
25243	403889 43014073	17372910929897	14	43.982
25243	252431 403889 43014073	4385461278944829607	19	61.927
25243	252431 449245236879223161338352589831	113403424390659181839801682603629161	36	116.449
25243	403889 449245236879223161338352589831	181445209477912563409785889154252759	36	117.127
25243	43014073 449245236879223161338352589831	19323867414025197245098675998729691663	38	123.862
25243	252431 403889 449245236879223161338352589831	45802395673718946294095661785097178207129	41	135.073
25243	252431 43014073 449245236879223161338352589831	4877943175189794565777503881035334796182753	43	141.807
25243	403889 43014073 449245236879223161338352589831	7804697485983222890125659150450936436077407	43	142.485
25243	252431 403889 43014073 449245236879223161338352589831	1970147591084230937377310265007480335495455926417	49	160.431

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-12-05	kkmrkkblmbrbk	Manual testing	500000000	500000000			449245236879223161338352589831	30	98.503	0.328	2.28589e-5	0.657	8.575%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-12-05

kkmrkkblmbrbk

Manual testing

500000000

449245236879223161338352589831

98.503

0.328

2.28589e-5

0.657

8.575%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-08-26	ANONYMOUS	Manual testing	?	?	403889	18.624	6	2.39558e-15	0.000	2.43905e-14
2008-08-26	ANONYMOUS	Manual testing	?	?	43014073	25.358	8	3.26565e-11	0.000	3.32490e-10

ECM factoring results:

Total ECM effort:	1.617 GHz-days
Estimated T-Level:	29.672

Digits	B1	Complete	FacMiss
20	11000	43.171	0.000%
25	50000	7.191	0.075%
30	250000	0.934	39.282%
35	1000000	0.101	90.416%
40	3000000	0.009	99.081%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	138	0.065
250000	25000000	213	0.503
1000000	100000000	111	1.049

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-06	Matthias Wurtinger	AMD_Funzel	50000	5000000						30	0.014
2009-05-10	Matthias Wurtinger	WUR_E6600	250000	25000000						30	0.071
2009-07-21	James Hintz	newestmember	50000	5000000						105	0.050
2010-05-13	Rob_Dee	twopc	50000	5000000						1	0.000
2010-05-14	Rob_Dee	twopc	50000	5000000						1	0.000
2010-05-14	Rob_Dee	twopc	50000	5000000						1	0.000
2010-05-15	Rob_Dee	twopc	250000	25000000						1	0.002
2010-05-16	Rob_Dee	twopc	250000	25000000						1	0.002
2010-05-20	Rob_Dee	twopc	250000	25000000						1	0.002
2010-05-21	Rob_Dee	twopc	250000	25000000						1	0.002
2010-05-22	Rob_Dee	twopc	250000	25000000						1	0.002
2010-05-23	Rob_Dee	twopc	250000	25000000						1	0.002
2011-01-18	James Hintz	NEW_OMFG	250000	25000000						11	0.026
2011-03-25	James Hintz	17_051310	250000	25000000						11	0.026
2013-04-03	Sergiosi	Manual testing	1000000	100000000						100	0.945
2014-10-30	James Hintz	08_04_2014	250000	25000000						155	0.366
2014-10-30	James Hintz	08_04_2014	1000000	100000000						11	0.104

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 = 500000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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