M1104331 Mersenne number exponent details

Residue

Status

L-L

CEDD5C68189B1AF5

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	26.9067	68.6567%	5000000	200000000	0.6715	9.0736%	27.5782	71.5007%	2.8440%
PrimeNet	2⁵⁶	0.0087	62.5000%	4500	65000	0.0003	2.0293%	0.0090	63.2610%	0.7610%
GPU72	2⁶⁰	0.1391	65.0000%	4500	22000	0.0002	0.6844%	0.1393	65.2395%	0.2395%
Difference	+7	+26.7676	+3.6567%	+4995500	+199978000	+0.6712	+8.3892%	+27.4389	+6.2611%	+6.2611%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

26.9067

68.6567%

5000000

200000000

0.6715

9.0736%

27.5782

71.5007%

2.8440%

PrimeNet

2⁵⁶

0.0087

62.5000%

4500

65000

0.0003

2.0293%

0.0090

63.2610%

0.7610%

GPU72

2⁶⁰

0.1391

65.0000%

4500

22000

0.0002

0.6844%

0.1393

65.2395%

0.2395%

Difference

+26.7676

+3.6567%

+4995500

+199978000

+0.6712

+8.3892%

+27.4389

+6.2611%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1104331	52569406297886657744048833	26	85.442	23801471795089813536 2⁵ × 3² × 23 × 2221 × 19457 × 83149387	2015-02-19	19457	83149387	7,242,897	0.1955	0.3636

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1104331

52569406297886657744048833

85.442

23801471795089813536
2⁵ × 3² × 23 × 2221 × 19457 × 83149387

2015-02-19

19457

83149387

7,242,897

0.1955

0.3636

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-02-24T00:00:00	Jocelyn Larouche	v4_computers	15000	153750		-		-	-	0.001	-	-	0.683%
2012-09-25T03:20:00	kurly	smile	500000	10000000		-		-	-	0.044	-	-	4.405%
2015-02-19T08:16:00	mikr	MSI	5000000	200000000	12		52569406297886657744048833	26	85.442	0.671	0.065	1.343	9.074%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-07-12T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.009	-	-
2001-12-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.017	-	-
2022-03-07T01:57:42	firejuggler	Manual testing	2⁵⁷	2⁶⁰		-	-	0.122	-	-
2022-03-07T17:30:51	LordJulius	Manual testing	2⁵⁷	2⁶⁰		-	-	0.122	-	-
2009-02-17T03:56:00	Sturle Sunde	goomba.ifi	2⁶⁰	2⁶¹		-	-	0.139	-	-
2011-05-09T14:44:00	Xyzzy	Manual testing	2⁶¹	2⁶²		-	-	0.278	-	-
2012-10-07T08:33:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.889	-	-
2014-12-22T09:46:00	Matthias Wurtinger	Manual testing	2⁶³	2⁶⁴		-	-	1.778	-	-
2014-12-28T15:48:00	Matthias Wurtinger	Manual testing	2⁶⁴	2⁶⁵		-	-	3.383	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.645 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:	17.645 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	12.731	0.000%
25	50000	1.349	25.941%
30	250000	0.108	89.793%
35	1000000	0.007	99.295%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	9.90
250000	25000000		44	7.748

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-10-02T19:29:00	Chad Davis	Bayes	50000	5000000						1	0.035
2008-08-01T18:14:00	Sturle Sunde	v21	50000	5000000						3	0.106
2008-12-13T03:46:00	Sturle Sunde	v21	50000	5000000						3	0.106
2009-04-10T05:18:00	James Hintz	08_060209	50000	5000000						3	0.106
2009-09-05T14:56:00	JimBa	AUserv	50000	5000000						3	0.106
2009-11-26T22:14:00	Geoff Wing	GW1	50000	5000000						3	0.106
2010-04-27T22:10:00	unconnected	xp-lm	50000	5000000						3	0.106
2011-01-03T03:31:00	Boots	rchok28bo	50000	5000000						3	0.106
2011-10-03T13:03:00	Lackó	Iroda_Eva	50000	5000000						3	0.106
2012-03-19T08:30:00	Pool Party	sts	50000	5000000						3	0.106
2012-09-03T00:08:00	Pool Party	sts	50000	5000000						3	0.106
2013-03-18T07:03:00	Pool Party	sts	50000	5000000						3	0.106
2013-08-05T18:08:00	561	561	50000	5000000						3	0.106
2013-10-20T22:28:00	561	561	50000	5000000						3	0.106
2014-03-10T16:49:00	mikr	MSI	50000	5000000						20	0.704
2017-04-28T21:38:51	TJAOI	Manual testing	50000	5000000						80	2.817
2018-02-09T12:23:35	TJAOI	Manual testing	50000	5000000						141	4.966
2020-08-07T11:05:04	TJAOI	Manual testing	250000	25000000						44	7.748

date	userid	compid	res64	spent (GHz-days)
2002-04-20T00:00:00	ANONYMOUS	v4_computers	CEDD5C68189B1AF5	0.033

date

userid

compid

res64

spent (GHz-days)

2002-04-20T00:00:00

ANONYMOUS

v4_computers

CEDD5C68189B1AF5

0.033

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 = 5000000, B2 = 200000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 500000, B2 = 10000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 15000, B2 = 153750 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

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