M2049127 Mersenne number exponent details

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M2049127

<<<

>>>

is 2 ^2049127 - 1

has 616849 decimal digits

takes 0.135 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	94C1BE5D3CB55581	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	14.5008	68.6567%	500000	15000000	0.1230	5.1380%	14.6238	70.2671%	1.6104%
PrimeNet	2⁵⁸	0.0187	63.7931%	9000	160000	0.0016	2.6654%	0.0204	64.7582%	0.9651%
GPU72	2⁶²	0.2998	66.1290%	9000	120000	0.0014	1.3302%	0.3013	66.5796%	0.4505%
Difference	+5	+14.2010	+2.5277%	+491000	+14880000	+0.1216	+3.8078%	+14.3225	+3.6876%	+3.6876%

Known prime factors (1 factor, 81.2 bits, 0.00396263% 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
2049127	2775895468088496667577351	25	81.199	677336121208811525 5² × 27093444848352461	2018-09-27	25	27093444848352461	310,643	140,730,126	262,844,685

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-04-28T00:00:00	Jocelyn Larouche	v4_computers	1000	1000		-		-	-	9.53375e-5	-	-	0.007%
2002-05-05T00:00:00	Jocelyn Larouche	v4_computers	2000	2000		-		-	-	0.000	-	-	0.022%
2003-01-16T00:00:00	ANONYMOUS	v4_computers	25000	425000		-		-	-	0.004	-	-	1.261%
2010-12-28T23:08:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.412%
2011-01-04T22:09:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.593%
2012-01-06T09:06:00	Squeeky_Squirrel	P4_2600	135000	2868750		-		-	-	0.027	-	-	3.035%
2014-10-22T23:53:00	Jocelyn Larouche	Manual testing	166323	166323		-		-	-	0.016	-	-	1.209%
2015-10-06T12:44:49	Bruno Victal	4790K-windows	500000	15000000	12	-		-	-	0.123	-	-	5.138%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-10T00:00:00	MadPoo	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-
2016-02-23T16:29:04	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.056	-	-
2009-01-03T02:41:00	Sturle Sunde	goomba.ifi	2⁶⁰	2⁶¹		-	-	0.075	-	-
2012-02-29T07:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.150	-	-
2013-08-30T08:22:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.479	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.958	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.823	-	-
2015-11-03T10:10:04	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.647	-	-
2016-08-10T20:04:42	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.294	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.393 GHz-days
Estimated T-Level:	2.000

Digits	B1	Curves	Complete	FacMiss
20	11000	40 / 100	0.400	66.897%
25	50000	40 / 280	0.143	86.666%

New Calculation Method

Total ECM effort:	3.393 GHz-days
Estimated T-Level:	2.000

Digits	B1	Complete	FacMiss
20	11000	1.290	27.518%
25	50000	0.117	88.993%
30	250000	0.007	99.284%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		39	3.309
50000	5000000	2775895468088496667577351	1	0.085

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-05T23:10:00	Matthias Eckoldt	serverSP	50000	5000000						3	0.255
2009-10-22T20:42:00	SubPrime	stor	50000	5000000						3	0.255
2011-04-02T23:40:00	Beat Bucheli	I7	50000	5000000						3	0.255
2013-03-04T20:39:00	Donna Noble	opt4820	50000	5000000						3	0.255
2014-03-22T13:06:00	Bruce	snowflake	50000	5000000						3	0.255
2015-07-11T04:22:00	guru	w1	50000	5000000						3	0.255
2016-02-18T19:13:15	Sintax	cloud2	50000	5000000						3	0.255
2016-05-03T18:14:56	Bruce	Desk6	50000	5000000						3	0.255
2016-07-16T17:13:25	Bruce	test	50000	5000000						3	0.255
2016-12-12T11:05:12	Bruce	Desk6	50000	5000000						3	0.255
2017-06-27T03:44:49	Bruce	Desk6	50000	5000000						3	0.255
2017-11-27T06:07:20	Bruce	Desk6	50000	5000000						3	0.255
2018-04-06T22:59:41	Bruce	Desk6	50000	5000000						3	0.255
2018-09-27T16:14:56	Bruce	Desk6	50000	5000000	2775895468088496667577351	81.199	1	2		1	0.085

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-01-29T00:00:00	MadPoo	v4_computers	94C1BE5D3CB55581	0.135

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-09-27T23:28:02

storm5510

7700_Kaby_Lake

2775895468088496667577351

A527F949145579__

2018-09-27T23:47:11

ANONYMOUS

2775895468088496667577351

A527F949145579__

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

B1 = 500000 (P-1 stage 1)

B1 = 135000, B2 = 2868750 (P-1 stage 2)

B1 = 166323 (P-1 stage 1)

B1 = 135000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 25000, B2 = 425000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

B1 = 25000 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

B1 = 1000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2018-09-27T23:47:11+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