M2944231 Mersenne number exponent details

Residue

Status

L-L

083DEC66D2D3A487

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	2⁶⁸	20.2446	67.6471%	1000000	20000000	0.2512	5.5425%	20.4958	69.4402%	1.7932%
PrimeNet	2⁵⁹	0.0261	62.7119%	13000	260000	0.0033	3.0726%	0.0293	63.8576%	1.1457%
GPU72	2⁶³	0.5421	65.0794%	17000	300000	0.0040	1.9469%	0.5461	65.7592%	0.6799%
Difference	+5	+19.7026	+2.5677%	+983000	+19700000	+0.2472	+3.5956%	+19.9497	+3.6810%	+3.6810%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

20.2446

67.6471%

1000000

20000000

0.2512

5.5425%

20.4958

69.4402%

1.7932%

PrimeNet

2⁵⁹

0.0261

62.7119%

13000

260000

0.0033

3.0726%

0.0293

63.8576%

1.1457%

GPU72

2⁶³

0.5421

65.0794%

17000

300000

0.0040

1.9469%

0.5461

65.7592%

0.6799%

Difference

+19.7026

+2.5677%

+983000

+19700000

+0.2472

+3.5956%

+19.9497

+3.6810%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2944231	3569063474797121019035809	25	81.562	606111319865377584 2⁴ × 3³ × 5449 × 257484944513	2020-10-13	5449	257484944513	225,526	1,731.3	3,233.5

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2944231

3569063474797121019035809

81.562

606111319865377584
2⁴ × 3³ × 5449 × 257484944513

2020-10-13

5449

257484944513

225,526

1,731.3

3,233.5

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-12-13T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.246%
2003-12-23T00:00:00	Team Prime Rib	v4_computers	10000	10000		-		-	-	0.001	-	-	0.146%
2010-11-05T15:45:00	markr	tiny	105000	2310000		-		-	-	0.028	-	-	2.592%
2015-04-30T21:53:00	VictordeHollander	Manual testing	1000000	20000000		-		-	-	0.251	-	-	5.542%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:25	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.052	-	-
2009-02-12T23:43:00	Sturle Sunde	wright.ifi	2⁶⁰	2⁶¹		-	-	0.052	-	-
2011-12-24T16:47:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.104	-	-
2013-01-07T13:49:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.333	-	-
2015-04-27T09:54:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.667	-	-
2015-04-27T09:54:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.269	-	-
2016-02-24T09:33:38	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.538	-	-
2017-11-28T10:01:34	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.076	-	-
2018-12-24T00:53:30	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.15	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.010 GHz-days
Estimated T-Level:	1.300

Digits	B1	Curves	Complete	FacMiss
20	11000	26 / 100	0.260	77.004%
25	50000	26 / 280	0.093	91.117%

New Calculation Method

Total ECM effort:	3.010 GHz-days
Estimated T-Level:	1.300

Digits	B1	Complete	FacMiss
20	11000	0.839	43.227%
25	50000	0.076	92.700%
30	250000	0.005	99.534%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		25	2.894
50000	5000000	3569063474797121019035809	1	0.116

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-06-07T17:11:00	TeamResslerTUB	1062323	50000	5000000						3	0.347
2011-04-23T07:18:00	Martti Järvi	Tiny	50000	5000000						3	0.347
2013-07-01T07:10:00	Bruce	E6510	50000	5000000						3	0.347
2015-12-31T11:13:57	Bruce	Desk10	50000	5000000						3	0.347
2017-06-03T00:43:36	alex	newwork	50000	5000000						3	0.347
2019-09-23T21:18:49	Claude Portenier	Petit-Idiot	50000	5000000						3	0.347
2020-09-16T13:57:35	LaurV	3tits	50000	5000000						7	0.810
2020-10-13T23:34:27	daveward2005	Dave2	50000	5000000	3569063474797121019035809	81.562	1	2	5432481546508201	1	0.116

date	userid	compid	res64	spent (GHz-days)
1999-07-27T00:00:00	ANONYMOUS	v4_computers	083DEC66D2D3A487	0.251
2018-10-11T06:51:59	kkmrkkblmbrbk	old	083DEC66D2D3A487	0.251

date

userid

compid

res64

spent (GHz-days)

1999-07-27T00:00:00

ANONYMOUS

v4_computers

083DEC66D2D3A487

0.251

2018-10-11T06:51:59

kkmrkkblmbrbk

old

083DEC66D2D3A487

0.251

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-10-17T04:07:58

Sébastien Broucke

Portable_Seb

3569063474797121019035809

908E2A894669F2__

2020-10-18T02:09:19

kutens

vega

3569063474797121019035809

908E2A894669F2E1

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 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 105000, B2 = 2310000 (P-1 stage 2)

B1 = 105000 (P-1 stage 1)

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

B1 = 10000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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