M2165039 Mersenne number exponent details

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M2165039

<<<

>>>

is 2 ^2165039 - 1

has 651742 decimal digits

takes 0.142 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	8D9ABBAD7352B578	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	13.7244	67.1642%	2500000	125000000	0.8746	8.5915%	14.5991	69.9853%	2.8211%
PrimeNet	2⁵⁸	0.0177	62.0690%	10000	180000	0.0018	2.8546%	0.0196	63.1518%	1.0828%
GPU72	2⁶²	0.2838	64.5161%	10000	160000	0.0017	1.5200%	0.2855	65.0555%	0.5393%
Difference	+5	+13.4407	+2.6481%	+2490000	+124840000	+0.8729	+7.0715%	+14.3136	+4.9298%	+4.9298%

Known prime factors (1 factor, 73.2 bits, 0.00338135% 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
2165039	10906621845030996540409	23	73.208	2518804937239236 2² × 3² × 4561 × 15340233241	2018-08-10	4561	15340233241	1,154.3	79.681	148.82

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.279%
2010-11-04T10:39:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.238%
2010-11-07T12:40:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.417%
2011-01-15T02:57:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.599%
2011-01-22T03:16:00	markr	tiny	120000	2370000		-		-	-	0.023	-	-	2.869%
2014-10-05T22:22:00	Jocelyn Larouche	Manual testing	149646	149646		-		-	-	0.014	-	-	1.155%
2016-03-04T02:35:05	Jocelyn Larouche	Manual testing	224468	4040424	6	-		-	-	0.041	-	-	3.576%
2017-09-05T23:15:04	Jocelyn Larouche	low 4M	448936	4489360	6	-		-	-	0.064	-	-	3.988%
2018-01-03T06:58:25	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	8.591%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:07	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.053	-	-
2009-01-04T09:04:00	Sturle Sunde	morovan.ifi	2⁶⁰	2⁶¹		-	-	0.071	-	-
2009-01-06T22:34:00	Sturle Sunde	homilius.ifi	2⁶¹	2⁶²		-	-	0.142	-	-
2013-09-08T17:50:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.453	-	-
2015-03-25T10:09:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.907	-	-
2015-03-25T10:09:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.726	-	-
2015-12-30T18:01:38	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.452	-	-
2016-11-11T01:20:36	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.903	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.332 GHz-days
Estimated T-Level:	1.950

Digits	B1	Curves	Complete	FacMiss
20	11000	39 / 100	0.390	67.573%
25	50000	39 / 280	0.139	86.976%

New Calculation Method

Total ECM effort:	3.332 GHz-days
Estimated T-Level:	1.950

Digits	B1	Complete	FacMiss
20	11000	1.258	28.420%
25	50000	0.114	89.252%
30	250000	0.007	99.302%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		36	3.075
50000	5000000	10906621845030996540409	3	0.256

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-09T14:02:00	Johan Koolwaaij	C0B5A3B75	50000	5000000						3	0.256
2009-12-01T04:57:00	James Hintz	ryan	50000	5000000						3	0.256
2011-09-02T21:44:00	Lukasz Wrobel	WORK_lupo	50000	5000000						3	0.256
2013-05-06T16:04:00	hiems	Laptop	50000	5000000						3	0.256
2015-02-01T16:03:00	arnaud	CHAMOT22	50000	5000000						3	0.256
2015-10-02T23:53:47	Wolfgang Fluck	C91F72025	50000	5000000						3	0.256
2016-03-07T12:36:56	S36049	Wolle5	50000	5000000						3	0.256
2016-06-20T00:43:49	Bruce	Desk6	50000	5000000						3	0.256
2016-10-10T10:48:09	Bruce	Desk6	50000	5000000						3	0.256
2017-03-27T07:14:47	Bruce	Desk6	50000	5000000						3	0.256
2017-10-22T23:18:56	Bruce	Desk6	50000	5000000						3	0.256
2018-02-28T23:56:21	Bruce	Desk6	50000	5000000						3	0.256
2018-08-10T22:55:39	Bruce	Desk6	50000	5000000	10906621845030996540409	73.208	3	2		3	0.256

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	8D9ABBAD7352B578	0.142
2018-04-11T07:09:04	kkmrkkblmbrbk	old	8D9ABBAD7352B578	0.142

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-08-12T02:16:28

Chang Chia-Tche

homura

10906621845030996540409

68EBBEC46DB463__

2018-08-13T10:12:50

arnaud

stm-11-010

10906621845030996540409

68EBBEC46DB463__

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 = 2500000, B2 = 125000000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 448936, B2 = 4489360 (P-1 stage 2)

B1 = 448936 (P-1 stage 1)

B1 = 224468, B2 = 4040424 (P-1 stage 2)

B1 = 120000, B2 = 2370000 (P-1 stage 2)

B1 = 224468 (P-1 stage 1)

B1 = 149646 (P-1 stage 1)

B1 = 120000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (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

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2018-08-13T10:12:50+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