M1304803 Mersenne number exponent details

Residue

Status

L-L

C63171D6CBD03A6D

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	22.7727	68.6567%	1190000	34510000	0.1381	6.2151%	22.9108	70.6047%	1.9480%
PrimeNet	2⁵⁶	0.0074	62.5000%	6000	100000	0.0005	2.5955%	0.0079	63.4733%	0.9733%
GPU72	2⁶⁰	0.1177	65.0000%	5500	36000	0.0003	0.9357%	0.1180	65.3275%	0.3275%
Difference	+7	+22.6550	+3.6567%	+1184500	+34474000	+0.1378	+5.2793%	+22.7928	+5.2772%	+5.2772%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

22.7727

68.6567%

1190000

34510000

0.1381

6.2151%

22.9108

70.6047%

1.9480%

PrimeNet

2⁵⁶

0.0074

62.5000%

6000

100000

0.0005

2.5955%

0.0079

63.4733%

0.9733%

GPU72

2⁶⁰

0.1177

65.0000%

5500

36000

0.0003

0.9357%

0.1180

65.3275%

0.3275%

Difference

+22.6550

+3.6567%

+1184500

+34474000

+0.1378

+5.2793%

+22.7928

+5.2772%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1304803	53484752836444295737751231	26	85.467	20495336398078597205 5 × 2477 × 1654851546070133	2014-03-08	2477	1654851546070133	11,705,139	4,143,518	7,738,939

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1304803

53484752836444295737751231

85.467

20495336398078597205
5 × 2477 × 1654851546070133

2014-03-08

2477

1654851546070133

11,705,139

4,143,518

7,738,939

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	ANONYMOUS	v4_computers	10000	1000000		-		-	-	0.003	-	-	1.010%
2013-11-11T13:30:00	David Campeau	i5-2500k	1190000	34510000		-		-	-	0.138	-	-	6.215%
2016-03-17T19:04:42	alpertron	Manual testing	500000	15000000	12	-		-	-	0.059	-	-	4.866%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-03T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.015	-	-
2003-06-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.029	-	-
2022-03-07T17:32:09	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.088	-	-
2009-02-15T23:15:00	Sturle Sunde	goldiek.ifi	2⁶⁰	2⁶¹		-	-	0.118	-	-
2011-05-09T14:43:00	Xyzzy	Manual testing	2⁶¹	2⁶²		-	-	0.235	-	-
2013-01-03T08:41:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.752	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.683 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	298 / 100	2.980	5.004%
25	50000	298 / 280	1.064	34.432%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	20.683 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.167	0.001%
25	50000	1.348	25.975%
30	250000	0.112	89.363%
35	1000000	0.008	99.239%

ECM Summary

B1	B2	factor	curves	GHz-days
		53484752836444295737751231	1	0.00000e+0
50000	5000000		248	9.57
250000	35000000		50	11.11

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-12-09T23:16:00	Steve Scott	Epox	50000	5000000						1	0.039
2008-09-04T15:48:00	Sturle Sunde	v21	50000	5000000						3	0.116
2009-02-16T20:52:00	Sturle Sunde	v23	50000	5000000						3	0.116
2009-07-18T16:07:00	Lukasz Wrobel	WORKER-1	50000	5000000						3	0.116
2009-10-31T22:30:00	James Hintz	chris3	50000	5000000						3	0.116
2010-04-22T20:22:00	Geoff Wing	GW1	50000	5000000						3	0.116
2011-04-17T11:24:00	James Hintz	nana	50000	5000000						3	0.116
2011-11-04T02:16:00	Oscar Östlin		50000	5000000						1	0.039
2012-01-18T19:09:00	unconnected	can-01	50000	5000000						3	0.116
2012-08-30T14:34:00	soldake		50000	5000000						3	0.116
2013-06-24T12:07:00	OS1	Tina	50000	5000000						3	0.116
2014-01-13T15:47:00	OS1	Tina	50000	5000000						3	0.116
2014-03-08T15:06:00	Bruce	snowflake			53484752836444295737751231	85.467		1		1	-
2018-04-27T11:31:58	TJAOI	Manual testing	50000	5000000						216	8.339
2021-05-21T15:29:50	TJAOI	Manual testing	250000	35000000						50	11.11

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 = 1190000, B2 = 34510000 (P-1 stage 2)

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

B1 = 1190000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 10000, B2 = 1000000 (P-1 stage 2)

B1 = 10000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

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