M1254541 Mersenne number exponent details

Residue

Status

L-L

EA42828444EA32CC

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	23.6851	68.6567%	300000	10000000	0.0381	4.1851%	23.7232	69.9685%	1.3118%
PrimeNet	2⁵⁶	0.0077	62.5000%	5500	90000	0.0005	2.4382%	0.0081	63.4143%	0.9143%
GPU72	2⁶⁰	0.1224	65.0000%	5000	32000	0.0003	0.8561%	0.1227	65.2996%	0.2996%
Difference	+7	+23.5627	+3.6567%	+295000	+9968000	+0.0378	+3.3291%	+23.6004	+4.6689%	+4.6689%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

23.6851

68.6567%

300000

10000000

0.0381

4.1851%

23.7232

69.9685%

1.3118%

PrimeNet

2⁵⁶

0.0077

62.5000%

5500

90000

0.0005

2.4382%

0.0081

63.4143%

0.9143%

GPU72

2⁶⁰

0.1224

65.0000%

5000

32000

0.0003

0.8561%

0.1227

65.2996%

0.2996%

Difference

+23.5627

+3.6567%

+295000

+9968000

+0.0378

+3.3291%

+23.6004

+4.6689%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1254541	4588026375605865391	19	61.993	1828567729395 3² × 5 × 11² × 335825111	2011-05-09	121	335825111	0.4460	0.8409	1.5705

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1254541

4588026375605865391

61.993

1828567729395
3² × 5 × 11² × 335825111

2011-05-09

121

335825111

0.4460

0.8409

1.5705

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-24T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.239%
2003-11-28T00:00:00	eteo	v4_computers	200000	2000000		-		-	-	0.014	-	-	2.762%
2016-03-17T19:03:46	alpertron	Manual testing	300000	10000000	12	-		-	-	0.038	-	-	4.185%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.015	-	-
2003-06-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.031	-	-
2022-03-07T17:32:03	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.092	-	-
2009-02-16T00:39:00	Sturle Sunde	gonsha.ifi	2⁶⁰	2⁶¹		-	-	0.122	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.490 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	325 / 100	3.250	3.815%
25	50000	325 / 280	1.161	31.261%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	20.490 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	15.208	0.000%
25	50000	1.667	18.888%
30	250000	0.137	87.162%
35	1000000	0.009	99.076%

ECM Summary

B1	B2	factor	curves	GHz-days
		4588026375605865391	1	0.00000e+0
50000	5000000		281	10.78
250000	35000000		44	9.71

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-11-09T14:28:00	Chad Davis	Bayes	50000	5000000						1	0.038
2008-08-26T15:09:00	Sturle Sunde	v21	50000	5000000						3	0.115
2009-02-02T18:31:00	Sturle Sunde	v21	50000	5000000						3	0.115
2009-07-04T19:44:00	Lupo	yorick	50000	5000000						3	0.115
2009-10-13T14:03:00	Geoff Wing	GW1	50000	5000000						3	0.115
2010-03-22T10:29:00	sannerud.com	snap2	50000	5000000						3	0.115
2010-12-20T12:30:00	Donna Noble	PH9550v2	50000	5000000						3	0.115
2011-05-09T14:41:00	Xyzzy	Manual testing			4588026375605865391	61.993		1		1	-
2018-01-05T12:41:39	TJAOI	Manual testing	50000	5000000						121	4.642
2018-10-12T13:39:14	TJAOI	Manual testing	50000	5000000						141	5.410
2021-03-12T16:33:05	TJAOI	Manual testing	250000	35000000						44	9.71

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 = 200000, B2 = 2000000 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

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