M2016967 Mersenne number exponent details

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M2016967

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is 2 ^2016967 - 1

has 607168 decimal digits

takes 0.133 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	54907FF3E1737E7B	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	14.7320	68.6567%	640000	14080000	0.1308	5.2101%	14.8628	70.2897%	1.6330%
PrimeNet	2⁵⁸	0.0190	63.7931%	9000	150000	0.0016	2.6112%	0.0206	64.7385%	0.9454%
GPU72	2⁶²	0.3046	66.1290%	8000	120000	0.0013	1.2729%	0.3059	66.5602%	0.4311%
Difference	+5	+14.4274	+2.5277%	+632000	+13960000	+0.1295	+3.9371%	+14.5569	+3.7295%	+3.7295%

Known prime factors (1 factor, 70.9 bits, 0.00351334% 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
2016967	2147244562392658380671	22	70.863	532295412466505 5 × 113 × 431 × 2185883467	2017-12-12	431	2185883467	217.14	11.354	21.206

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	2000	2000		-		-	-	0.000	-	-	0.022%
2002-05-05T00:00:00	Jocelyn Larouche	v4_computers	3000	3000		-		-	-	0.000	-	-	0.040%
2003-02-02T00:00:00	ANONYMOUS	v4_computers	30000	547500		-		-	-	0.006	-	-	1.426%
2010-12-07T03:13:00	Jocelyn Larouche	Manual testing	201696	201696		-		-	-	0.019	-	-	1.331%
2013-10-16T12:22:00	David Campeau	i5-2500k	640000	14080000		-		-	-	0.131	-	-	5.210%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-02T00:00:00	kbutler	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-
2016-02-23T16:29:03	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.057	-	-
2009-01-02T22:06:00	Sturle Sunde	doak.ifi	2⁶⁰	2⁶¹		-	-	0.076	-	-
2012-02-03T20:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.152	-	-
2013-06-06T07:18:00	David Campeau	Manual testing	2⁶²	2⁶³		-	-	0.487	-	-
2015-03-15T12:12:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.973	-	-
2015-03-15T12:12:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.852	-	-
2015-10-28T09:42:37	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.705	-	-
2016-07-16T16:15:45	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.410	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.657 GHz-days
Estimated T-Level:	2.750

Digits	B1	Curves	Complete	FacMiss
20	11000	55 / 100	0.550	57.535%
25	50000	55 / 280	0.196	82.137%

New Calculation Method

Total ECM effort:	4.657 GHz-days
Estimated T-Level:	2.750

Digits	B1	Complete	FacMiss
20	11000	2.115	12.059%
25	50000	0.196	82.223%
30	250000	0.012	98.773%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		33	2.794
50000	5000000	2147244562392658380671	22	1.863

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-02T09:08:00	Luigi Morelli	AMD64x2	50000	5000000						3	0.254
2009-09-07T07:40:00	JimBa	E5400	50000	5000000						3	0.254
2011-02-18T16:35:00	argusdusty	argusdusty-PC	50000	5000000						3	0.254
2013-02-04T17:04:00	butera	CSAct	50000	5000000						3	0.254
2014-03-17T10:57:00	Bruce	snowflake	50000	5000000						3	0.254
2015-07-01T05:25:00	guru	w1	50000	5000000						3	0.254
2015-09-22T16:58:00	mikr	MSI	50000	5000000						12	1.016
2017-05-04T16:30:45	Bruce	Desk6	50000	5000000						3	0.254
2017-12-12T06:12:10	Sid & Andy	Pterodactyl	50000	5000000	2147244562392658380671	70.863	22	2		22	1.863

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-01-17T00:00:00	kbutler	v4_computers	54907FF3E1737E7B	0.133
2016-07-15T12:04:08	Mark Rose	donatello	54907FF3E1737E7B	0.133

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-12-16T12:30:52

Oliver Kruse

GTX-2

2147244562392658380671

7F6530D4C7C6A0__

2017-12-16T20:01:26

kkmrkkblmbrbk

c4.xlarge

2147244562392658380671

7F6530D4C7C6A0__

2017-12-25T15:33:57

YarBer

Manual testing

2147244562392658380671

7F6530D4C7C6A0__

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 = 640000, B2 = 14080000 (P-1 stage 2)

B1 = 640000 (P-1 stage 1)

B1 = 201696 (P-1 stage 1)

B1 = 30000, B2 = 547500 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

B1 = 3000 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2017-12-25T15:33:57+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