M2120057 Mersenne number exponent details

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M2120057

<<<

>>>

is 2 ^2120057 - 1

has 638201 decimal digits

takes 0.139 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	E6B6BA5A74C5B963	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	28.1148	67.6471%	2500000	125000000	0.8746	7.9058%	28.9894	70.2048%	2.5578%
PrimeNet	2⁵⁸	0.0181	62.0690%	9000	160000	0.0016	2.6826%	0.0198	63.0865%	1.0175%
GPU72	2⁶²	0.2898	64.5161%	10000	140000	0.0016	1.4541%	0.2914	65.0321%	0.5160%
Difference	+6	+27.8250	+3.1309%	+2490000	+124860000	+0.8730	+6.4517%	+28.6980	+5.1727%	+5.1727%

Known prime factors (1 factor, 81.5 bits, 0.00384514% 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
2120057	3464896054216372289547857	25	81.519	817170494523584104 2³ × 157 × 635021 × 1024554229	2019-07-30	635021	1024554229	276,200	5.3790	9.940

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-07-21T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.224%
2009-08-02T20:32:00	harlee	P4_2600	20000	260000		-		-	-	0.003	-	-	0.879%
2010-12-30T22:21:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.352%
2011-01-11T22:55:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.511%
2011-01-25T17:19:00	James Heinrich	i7-920	140000	3010000		-		-	-	0.028	-	-	2.770%
2016-06-23T05:17:04	Jocelyn Larouche	Manual testing	220000	6020000	12	-		-	-	0.051	-	-	3.479%
2017-08-19T15:48:38	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.906%
2017-09-05T23:15:03	Jocelyn Larouche	low 4M	440000	4400000	6	-		-	-	0.063	-	-	3.566%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1997-11-11T00:00:00	DL	v4_computers	2¹	2⁵⁷		-	-	0.009	-	-
1999-01-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:05	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.054	-	-
2009-01-03T12:43:00	Sturle Sunde	giovanni.ifi	2⁶⁰	2⁶¹		-	-	0.072	-	-
2012-04-02T05:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.145	-	-
2013-09-06T08:31:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.463	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.926	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.762	-	-
2015-10-21T19:11:16	omylist	Manual testing	2⁶⁵	2⁶⁶		-	-	3.525	-	-
2016-10-15T17:13:25	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.050	-	-
2019-05-06T12:23:37	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	14.10	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.408 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:	3.408 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	3.323
50000	5000000	3464896054216372289547857	1	0.085

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-17T02:22:00	Luigi Morelli	AMD64x2	50000	5000000						3	0.256
2009-11-18T09:25:00	SubPrime	stor	50000	5000000						3	0.256
2011-07-14T02:41:00	S36049	Wolle5	50000	5000000						3	0.256
2013-04-15T09:00:00	Xyzzy	J	50000	5000000						3	0.256
2014-12-03T07:46:00	arnaud	srv-630	50000	5000000						3	0.256
2015-08-07T04:33:00	guru	w6	50000	5000000						3	0.256
2016-02-25T15:42:33	Bruce	Desk8	50000	5000000						3	0.256
2016-06-03T23:26:54	Bruce	Desk6	50000	5000000						3	0.256
2016-08-27T18:14:05	Bruce	test	50000	5000000						3	0.256
2017-02-25T10:32:19	Bruce	Desk6	50000	5000000						3	0.256
2017-09-08T15:13:28	Bruce	Desk6	50000	5000000						3	0.256
2018-01-23T05:35:07	Bruce	Desk6	50000	5000000						3	0.256
2018-07-06T23:10:04	Bruce	Desk6	50000	5000000						3	0.256
2019-07-30T16:28:25	Chang Chia-Tche	ex-ctcpc	50000	5000000	3464896054216372289547857	81.519	1	2	4066847199344701	1	0.085

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-11-11T00:00:00	DL	v4_computers	E6B6BA5A74C5B963	0.139
1999-01-29T00:00:00	ANONYMOUS	v4_computers	E6B6BA5A74C5B963	0.139
2018-04-04T07:18:44	kkmrkkblmbrbk	old	E6B6BA5A74C5B963	0.139

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-07-31T06:01:31

Niels_Mache_Nextcloud

SuperDry-X

3464896054216372289547857

E088A1D3D57B30D8

2019-08-01T00:25:14

marssystems

system11

3464896054216372289547857

E088A1D3D57B30D8

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 = 440000, B2 = 4400000 (P-1 stage 2)

B1 = 220000, B2 = 6020000 (P-1 stage 2)

B1 = 440000 (P-1 stage 1)

B1 = 140000, B2 = 3010000 (P-1 stage 2)

B1 = 220000 (P-1 stage 1)

B1 = 140000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 20000, B2 = 260000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

B1 = 20000 (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

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁷

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2019-08-01T00:25:14+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