M2409469 Mersenne number exponent details

Residue

Status

L-L

5DFE8EC532EECEFB

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	12.3321	67.1642%	2000000	60000000	0.5055	7.6183%	12.8376	69.6657%	2.5015%
PrimeNet	2⁵⁹	0.0319	62.7119%	10000	180000	0.0019	2.5203%	0.0338	63.6517%	0.9398%
GPU72	2⁶³	0.6624	65.0794%	10000	140000	0.0017	1.2759%	0.6641	65.5249%	0.4455%
Difference	+4	+11.6698	+2.0848%	+1990000	+59860000	+0.5038	+6.3425%	+12.1735	+4.1408%	+4.1408%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

12.3321

67.1642%

2000000

60000000

0.5055

7.6183%

12.8376

69.6657%

2.5015%

PrimeNet

2⁵⁹

0.0319

62.7119%

10000

180000

0.0019

2.5203%

0.0338

63.6517%

0.9398%

GPU72

2⁶³

0.6624

65.0794%

10000

140000

0.0017

1.2759%

0.6641

65.5249%

0.4455%

Difference

+11.6698

+2.0848%

+1990000

+59860000

+0.5038

+6.3425%

+12.1735

+4.1408%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2409469	294285859347849155405907892231	30	97.893	61068612907625944846335 3 × 5 × 11 × 751 × 39929 × 1044569 × 11815949	2014-03-07	1044569	11815949	1.475e+10	0.1598	0.2082

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2409469

294285859347849155405907892231

97.893

61068612907625944846335
3 × 5 × 11 × 751 × 39929 × 1044569 × 11815949

2014-03-07

1044569

11815949

1.475e+10

0.1598

0.2082

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.288%
2010-11-09T10:51:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.244%
2010-11-16T23:08:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.311%
2010-12-21T11:32:00	markr	tiny	95000	1923750		-		-	-	0.019	-	-	2.660%
2014-03-07T00:44:00	mikr	MSI	2000000	60000000			294285859347849155405907892231	30	97.893	0.505	0.326	1.011	7.618%
2018-09-28T16:26:33	alpertron	Manual testing	2000000	60000000	12	-	skipped known factor: 294285859347849155405907892231	-	-	0.505	-	-	7.618%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-07-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.032	-	-
2022-03-09T16:37:59	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.064	-	-
2009-01-16T20:22:00	Sturle Sunde	gicy.ifi	2⁶⁰	2⁶¹		-	-	0.064	-	-
2012-06-03T17:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.127	-	-
2013-12-04T21:14:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.407	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.069 GHz-days
Estimated T-Level:	0.600

Digits	B1	Curves	Complete	FacMiss
20	11000	12 / 100	0.120	88.638%
25	50000	12 / 280	0.043	95.797%

New Calculation Method

Total ECM effort:	1.069 GHz-days
Estimated T-Level:	0.600

Digits	B1	Complete	FacMiss
20	11000	0.387	67.903%
25	50000	0.035	96.562%
30	250000	0.002	99.785%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.069

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-19T03:26:00	youli	ALCHEMY	50000	5000000						3	0.267
2010-02-23T15:09:00	BobbyMK	Quaddl	50000	5000000						3	0.267
2012-02-26T03:19:00	S36049	Wolle5	50000	5000000						3	0.267
2013-12-03T12:10:00	Andy Incline	Office-PC	50000	5000000						3	0.267

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-14T01:25:15

kkmrkkblmbrbk

c4.xlarge

AAD53B6CA31C83__

2017-11-03T16:50:15

Oliver Kruse

GTX-2

294285859347849155405907892231

AAD53B6CA31C83__

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 = 2000000, B2 = 60000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 95000, B2 = 1923750 (P-1 stage 2)

B1 = 95000 (P-1 stage 1)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

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