M1543207 Mersenne number exponent details

Residue

Status

L-L

AF3020FC8BD1C5A0

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	19.2547	68.6567%	945000	27405000	0.1546	5.9452%	19.4092	70.5201%	1.8634%
PrimeNet	2⁵⁷	0.0124	63.1579%	6500	110000	0.0008	2.4184%	0.0132	64.0489%	0.8910%
GPU72	2⁶¹	0.1991	65.5738%	6500	55000	0.0006	1.0161%	0.1996	65.9236%	0.3498%
Difference	+6	+19.0556	+3.0829%	+938500	+27350000	+0.1540	+4.9290%	+19.2096	+4.5965%	+4.5965%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

19.2547

68.6567%

945000

27405000

0.1546

5.9452%

19.4092

70.5201%

1.8634%

PrimeNet

2⁵⁷

0.0124

63.1579%

6500

110000

0.0008

2.4184%

0.0132

64.0489%

0.8910%

GPU72

2⁶¹

0.1991

65.5738%

6500

55000

0.0006

1.0161%

0.1996

65.9236%

0.3498%

Difference

+19.0556

+3.0829%

+938500

+27350000

+0.1540

+4.9290%

+19.2096

+4.5965%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1543207	42664513229964533489	20	65.210	13823328053192 2³ × 7 × 227 × 1087423541	2015-01-06	227	1087423541	5.5787	3.8372	7.1667

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1543207

42664513229964533489

65.210

13823328053192
2³ × 7 × 227 × 1087423541

2015-01-06

227

1087423541

5.5787

3.8372

7.1667

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-29T00:00:00	Team Prime Rib	v4_computers	20000	290000		-		-	-	0.002	-	-	0.993%
2011-02-03T03:56:00	James Heinrich	WHS	80000	1340000		-		-	-	0.010	-	-	2.196%
2013-11-20T05:24:00	David Campeau	i5-2500k	945000	27405000		-		-	-	0.155	-	-	5.945%
2016-03-17T19:16:08	alpertron	Manual testing	500000	15000000	12	-		-	-	0.084	-	-	4.965%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-10-18T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.012	-	-
2003-08-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.025	-	-
2010-04-28T15:20:00	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.100	-	-
2010-05-19T19:30:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	1.034	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	31.233 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	301 / 100	3.010	4.855%
25	50000	301 / 280	1.075	34.064%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	31.233 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.263	0.000%
25	50000	1.390	24.916%
30	250000	0.116	89.004%
35	1000000	0.008	99.198%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		248	13.86
50000	5000000	42664513229964533489	3	0.168
250000	40000000		50	17.21

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-02-27T10:37:00	Steve Scott	Music-2	50000	5000000						3	0.168
2009-06-18T00:42:00	James Hintz	01_060309	50000	5000000						3	0.168
2010-04-22T19:57:00	SubPrime	stor	50000	5000000						3	0.168
2011-05-14T13:08:00	Bud	annan	50000	5000000						3	0.168
2012-11-18T13:57:00	Donna Noble	CCI-i7-3770s-XP	50000	5000000						3	0.168
2013-09-15T01:01:00	AdolfNor	PC1	50000	5000000						3	0.168
2014-03-17T10:50:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.168
2015-01-06T12:36:00	Chang Chia-Tche	exbpc13	50000	5000000	42664513229964533489	65.210	3	2		3	0.168
2019-07-19T09:17:31	TJAOI	Manual testing	50000	5000000						227	12.68
2022-05-12T09:16:07	TJAOI	Manual testing	250000	40000000						50	17.21

date	userid	compid	res64	spent (GHz-days)
1998-11-07T00:00:00	ANONYMOUS	v4_computers	AF3020FC8BD1C5A0	0.069

date

userid

compid

res64

spent (GHz-days)

1998-11-07T00:00:00

ANONYMOUS

v4_computers

AF3020FC8BD1C5A0

0.069

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 = 945000, B2 = 27405000 (P-1 stage 2)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 945000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 80000, B2 = 1340000 (P-1 stage 2)

B1 = 80000 (P-1 stage 1)

B1 = 20000, B2 = 290000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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