M2158727 Mersenne number exponent details

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M2158727

<<<

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is 2 ^2158727 - 1

has 649842 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	4904DC1417CFB753	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	27.6111	67.6471%	5000000	5000000	0.4767	4.1581%	28.0878	68.9923%	1.3453%
PrimeNet	2⁵⁸	0.0178	62.0690%	10000	170000	0.0018	2.8099%	0.0196	63.1348%	1.0658%
GPU72	2⁶²	0.2846	64.5161%	10000	160000	0.0017	1.5191%	0.2863	65.0551%	0.5390%
Difference	+6	+27.3265	+3.1309%	+4990000	+4840000	+0.4750	+2.6391%	+27.8015	+3.9372%	+3.9372%

Known prime factors (1 factor, 98.5 bits, 0.00456073% 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
2158727	434021380836198786760726568921	30	98.454	100527158097387670316980 2² × 5 × 13 × 12601 × 18133 × 1147889 × 1474129	2019-10-03	1147889	1474129	5.355e+10	0.1111	0.2227

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	-	-	0.225%
2010-11-04T10:39:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.198%
2010-11-07T01:16:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.353%
2010-11-07T12:40:00	Jocelyn Larouche	Manual testing	45000	45000		-		-	-	0.004	-	-	0.477%
2011-01-15T02:57:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.513%
2011-01-23T11:46:00	markr	tiny	120000	2340000		-		-	-	0.023	-	-	2.546%
2014-10-03T21:04:00	Jocelyn Larouche	Manual testing	149732	149732		-		-	-	0.014	-	-	1.008%
2016-04-17T17:38:40	Jocelyn Larouche	Manual testing	240000	8840784	12	-		-	-	0.068	-	-	3.822%
2017-09-05T23:15:05	Jocelyn Larouche	low 4M	480000	4800000	6	-		-	-	0.068	-	-	3.682%
2017-09-13T23:12:02	Jocelyn Larouche	low 4M	576000	5760000	6	-		-	-	0.082	-	-	3.914%
2019-10-04T03:13:36	mikr	MSI	5000000	5000000			434021380836198786760726568921	30	98.454	0.477	0.284	0.953	4.158%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-05-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:07	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.053	-	-
2009-01-04T07:27:00	Sturle Sunde	gibsy.ifi	2⁶⁰	2⁶¹		-	-	0.071	-	-
2009-01-06T23:39:00	Sturle Sunde	ghia.ifi	2⁶¹	2⁶²		-	-	0.142	-	-
2013-01-23T08:20:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.455	-	-
2015-03-22T08:28:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.909	-	-
2015-03-22T08:28:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.731	-	-
2015-12-30T18:01:36	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.462	-	-
2016-11-04T03:09:04	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.923	-	-
2019-05-13T13:38:18	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.85	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.330 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:	3.330 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		39	3.330

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-22T08:12:00	Never Odd Or Even	Lap_Dir_1000	50000	5000000						3	0.256
2009-11-30T08:19:00	Lukasz Wrobel	cm-1	50000	5000000						3	0.256
2011-08-18T09:01:00	Bud	annan	50000	5000000						3	0.256
2013-05-02T08:28:00	hiems	Laptop	50000	5000000						3	0.256
2015-01-20T17:05:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.256
2015-09-20T02:50:00	lopper	i5-4670	50000	5000000						3	0.256
2016-03-01T09:16:20	Bruce	Desk6	50000	5000000						3	0.256
2016-06-21T09:44:01	lettp	Home	50000	5000000						3	0.256
2016-10-04T08:35:30	Bruce	Desk6	50000	5000000						3	0.256
2017-03-24T06:09:33	Bruce	Desk6	50000	5000000						3	0.256
2017-10-18T09:35:25	Bruce	Desk6	50000	5000000						3	0.256
2018-02-24T23:26:07	Bruce	Desk6	50000	5000000						3	0.256
2018-08-05T23:39:37	Bruce	Desk6	50000	5000000						3	0.256

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-10-07T00:00:00	ANONYMOUS	v4_computers	4904DC1417CFB753	0.142
2002-09-14T00:00:00	ANONYMOUS	v4_computers	4904DC1417CFB753	0.142
2018-04-10T09:31:35	kkmrkkblmbrbk	old	4904DC1417CFB753	0.142

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-10-05T19:44:34

mnd9

75211

434021380836198786760726568921

99A743D3D8784438

2019-10-05T22:09:13

Daniil Tsarkov

tsar1

434021380836198786760726568921

99A743D3D8784438

2019-10-08T14:01:49

GAN

KL-SCH09

434021380836198786760726568921

99A743D3D8784438

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 (P-1 stage 1)

B1 = 576000, B2 = 5760000 (P-1 stage 2)

B1 = 480000, B2 = 4800000 (P-1 stage 2)

B1 = 240000, B2 = 8840784 (P-1 stage 2)

B1 = 576000 (P-1 stage 1)

B1 = 480000 (P-1 stage 1)

B1 = 120000, B2 = 2340000 (P-1 stage 2)

B1 = 240000 (P-1 stage 1)

B1 = 149732 (P-1 stage 1)

B1 = 120000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 45000 (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

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2019-10-08T14:01:49+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