M1351283 Mersenne number exponent details

Residue

Status

L-L

9DEDB2A97BBE1286

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	21.9894	68.6567%	500000	15000000	0.0714	4.8862%	22.0608	70.1882%	1.5315%
PrimeNet	2⁵⁶	0.0071	62.5000%	6000	100000	0.0006	2.6135%	0.0077	63.4801%	0.9801%
GPU72	2⁶⁰	0.1137	65.0000%	5500	40000	0.0004	0.9818%	0.1141	65.3436%	0.3436%
Difference	+7	+21.8757	+3.6567%	+494500	+14960000	+0.0710	+3.9044%	+21.9468	+4.8446%	+4.8446%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

21.9894

68.6567%

500000

15000000

0.0714

4.8862%

22.0608

70.1882%

1.5315%

PrimeNet

2⁵⁶

0.0071

62.5000%

6000

100000

0.0006

2.6135%

0.0077

63.4801%

0.9801%

GPU72

2⁶⁰

0.1137

65.0000%

5500

40000

0.0004

0.9818%

0.1141

65.3436%

0.3436%

Difference

+21.8757

+3.6567%

+494500

+14960000

+0.0710

+3.9044%

+21.9468

+4.8446%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1351283	3218528222189108351	19	61.481	1190915678725 5² × 1297 × 36728317	2011-05-09	1297	36728317	0.3260	0.1109	0.2069

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1351283

3218528222189108351

61.481

1190915678725
5² × 1297 × 36728317

2011-05-09

1297

36728317

0.3260

0.1109

0.2069

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	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.001	-	-	0.798%
2016-03-17T19:05:23	alpertron	Manual testing	500000	15000000	12	-		-	-	0.071	-	-	4.886%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-04T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.014	-	-
2003-06-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.028	-	-
2022-03-07T17:32:36	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.085	-	-
2009-02-18T06:47:00	Sturle Sunde	gibus.ifi	2⁶⁰	2⁶¹		-	-	0.114	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.207 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:	25.207 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	14.654	0.000%
25	50000	1.651	19.189%
30	250000	0.141	86.866%
35	1000000	0.010	99.021%

ECM Summary

B1	B2	factor	curves	GHz-days
		3218528222189108351	1	0.00000e+0
50000	5000000		251	11.74
250000	35000000		50	13.47

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-12-25T01:59:00	Steve Scott	Abit	50000	5000000						1	0.047
2008-11-25T03:56:00	dachshund	Ann	50000	5000000						3	0.140
2009-05-02T04:37:00	ClknGo Software Corp	cngs1	50000	5000000						3	0.140
2009-08-01T22:09:00	SubPrime	c2d0	50000	5000000						3	0.140
2009-11-21T22:42:00	Lupo	yorick	50000	5000000						3	0.140
2010-06-17T21:42:00	Charles A. Morris	pulsar	50000	5000000						3	0.140
2011-03-17T11:43:00	Beat Bucheli	I7	50000	5000000						3	0.140
2011-05-09T14:43:00	Xyzzy	Manual testing			3218528222189108351	61.481		1		1	-
2018-08-10T11:21:16	TJAOI	Manual testing	50000	5000000						232	10.85
2022-02-10T10:43:45	TJAOI	Manual testing	250000	35000000						50	13.47

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 (P-1 stage 1)

B1 = 15000, B2 = 217500 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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