M2909747 Mersenne number exponent details

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M2909747

<<<

>>>

is 2 ^2909747 - 1

has 875922 decimal digits

takes 0.225 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	4BF3907F017A396D	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	20.4846	67.6471%	5000000	200000000	1.7498	9.1909%	22.2343	70.6206%	2.9735%
PrimeNet	2⁵⁹	0.0264	62.7119%	13000	260000	0.0030	3.0661%	0.0294	63.8552%	1.1433%
GPU72	2⁶³	0.5485	65.0794%	16000	300000	0.0035	1.9102%	0.5520	65.7464%	0.6671%
Difference	+5	+19.9360	+2.5677%	+4984000	+199700000	+1.7463	+7.2807%	+21.6823	+4.8742%	+4.8742%

Known prime factors (1 factor, 77.4 bits, 0.00266112% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2909747	203861093972941034126599	24	77.432	35030725003400817 3 × 19 × 947 × 648969506723	2020-08-14	947	648969506723	11,742	3,959.8	7,395.8

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-12-02T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.246%
2009-07-03T00:43:00	Carsten Kossendey	leela	15000	168750		-		-	-	0.003	-	-	0.736%
2010-12-24T02:50:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.273%
2011-01-27T12:24:00	markr	tiny	105000	2283750		-		-	-	0.025	-	-	2.581%
2015-04-25T17:20:00	VictordeHollander	Manual testing	1000000	20000000		-		-	-	0.228	-	-	5.535%
2020-03-27T13:31:02	masser	Manual testing	5000000	200000000	12	-		-	-	1.750	-	-	9.191%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:24	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.053	-	-
2009-02-14T17:11:00	Sturle Sunde	dittersdorf.ifi	2⁶⁰	2⁶¹		-	-	0.053	-	-
2011-12-16T15:15:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.106	-	-
2013-01-10T21:10:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.337	-	-
2015-04-25T17:15:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.675	-	-
2015-04-25T17:15:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.284	-	-
2016-02-22T09:35:52	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.568	-	-
2017-11-19T23:57:49	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.136	-	-
2018-12-17T01:16:49	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.27	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.992 GHz-days
Estimated T-Level:	0.950

Digits	B1	Curves	Complete	FacMiss
20	11000	19 / 100	0.190	82.617%
25	50000	19 / 280	0.068	93.428%

New Calculation Method

Total ECM effort:	1.992 GHz-days
Estimated T-Level:	0.950

Digits	B1	Complete	FacMiss
20	11000	0.613	54.178%
25	50000	0.055	94.611%
30	250000	0.003	99.659%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		18	1.887
50000	5000000	203861093972941034126599	1	0.105

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-28T08:11:00	Smurgs	Praca	50000	5000000						3	0.315
2011-03-26T01:21:00	Thomas N	ubuntu	50000	5000000						3	0.315
2013-05-27T07:28:00	Richard Kint	xps	50000	5000000						3	0.315
2015-12-23T05:03:27	Bruce	Desk7	50000	5000000						3	0.315
2016-09-18T13:24:46	Bruce	test	50000	5000000						3	0.315
2019-07-12T13:02:58	furkell	furkell1	50000	5000000						3	0.315
2020-08-14T22:00:57	GAN	LMS-01	50000	5000000	203861093972941034126599	77.432	1	2	7722535508839286	1	0.105

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-11-24T00:00:00	ANONYMOUS	v4_computers	4BF3907F017A396D	0.225
2018-10-02T18:49:13	kkmrkkblmbrbk	old	4BF3907F017A396D	0.225

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-08-15T19:06:31

Massimo Cappelli (ik5pwa)

maxlinux_8

203861093972941034126599

F60999168A604746

2020-08-16T15:51:28

kutens

spica

203861093972941034126599

F60999168A604746

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

B1 = 1000000 (P-1 stage 1)

B1 = 105000, B2 = 2283750 (P-1 stage 2)

B1 = 105000 (P-1 stage 1)

B1 = 15000, B2 = 168750 (P-1 stage 2)

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)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-08-16T15:51:28+00:00

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