M2043191 Mersenne number exponent details

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M2043191

<<<

>>>

is 2 ^2043191 - 1

has 615062 decimal digits

takes 0.134 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	9C7C1C6EED679EB4	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	29.1724	69.1176%	4000000	200000000	1.3994	8.7581%	30.5719	71.8223%	2.7047%
PrimeNet	2⁵⁸	0.0188	63.7931%	9000	160000	0.0016	2.6640%	0.0204	64.7576%	0.9645%
GPU72	2⁶²	0.3007	66.1290%	9000	120000	0.0014	1.3294%	0.3021	66.5793%	0.4503%
Difference	+6	+28.8718	+2.9886%	+3991000	+199880000	+1.3980	+7.4287%	+30.2697	+5.2430%	+5.2430%

Known prime factors (1 factor, 91.5 bits, 0.00447667% 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
2043191	3422053571247618385904165377	28	91.467	837428701293128832768 2⁸ × 3² × 15619 × 205957 × 112988849	2019-07-13	205957	112988849	337,245,157	0.6055	1.0962

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	-	-	0.005%
2002-05-05T00:00:00	Jocelyn Larouche	v4_computers	2000	2000		-		-	-	0.000	-	-	0.017%
2003-01-09T00:00:00	ANONYMOUS	v4_computers	25000	418750		-		-	-	0.004	-	-	1.085%
2010-12-28T23:08:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.349%
2011-01-04T22:09:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.507%
2011-02-05T13:25:00	kurly	slice	135000	2868750		-		-	-	0.027	-	-	2.707%
2014-10-19T12:31:00	Jocelyn Larouche	Manual testing	166414	166414		-		-	-	0.016	-	-	1.058%
2015-10-06T04:05:15	Bruno Victal	4790K-windows	500000	15000000	12	-		-	-	0.123	-	-	4.662%
2019-06-29T13:04:30	BigBrother	Winston	1000000	20000000	12	-		-	-	0.194	-	-	5.316%
2019-07-13T10:56:54	mikr	MSI	4000000	200000000	12		3422053571247618385904165377	28	91.467	1.399	0.269	2.799	8.758%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-10T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-
2016-02-23T16:29:04	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.056	-	-
2009-01-03T07:14:00	Sturle Sunde	gluck.ifi	2⁶⁰	2⁶¹		-	-	0.075	-	-
2012-02-28T06:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.150	-	-
2013-08-30T08:22:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.480	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.961	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.829	-	-
2015-11-02T09:33:40	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.657	-	-
2016-08-04T22:03:49	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.315	-	-
2019-03-22T01:11:12	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	14.63	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.562 GHz-days
Estimated T-Level:	2.100

Digits	B1	Curves	Complete	FacMiss
20	11000	42 / 100	0.420	65.566%
25	50000	42 / 280	0.150	86.048%

New Calculation Method

Total ECM effort:	3.562 GHz-days
Estimated T-Level:	2.100

Digits	B1	Complete	FacMiss
20	11000	1.355	25.799%
25	50000	0.122	88.475%
30	250000	0.008	99.249%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		42	3.562

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-04T18:40:00	mognuts	hallowes	50000	5000000						3	0.254
2009-10-18T10:39:00	SubPrime	abd0	50000	5000000						3	0.254
2011-03-07T09:37:00	James Hintz	ryan	50000	5000000						3	0.254
2013-03-05T05:33:00	Syntony	Geomancer	50000	5000000						3	0.254
2014-03-22T03:27:00	Bruce	snowflake	50000	5000000						3	0.254
2015-07-09T08:09:00	guru	w6	50000	5000000						3	0.254
2016-02-19T05:08:26	Jason U	Server7	50000	5000000						3	0.254
2016-05-01T07:05:01	lettp	Home	50000	5000000						3	0.254
2016-07-16T01:02:41	Bruce	test	50000	5000000						3	0.254
2017-01-30T05:17:25	Bruce	Desk6	50000	5000000						3	0.254
2017-06-22T03:26:52	Bruce	Desk6	50000	5000000						3	0.254
2017-12-01T06:49:12	Sebastian Hornbostel	V2	50000	5000000						3	0.254
2018-03-31T22:52:42	Bruce	Desk6	50000	5000000						3	0.254
2018-09-18T20:26:59	Bruce	Desk6	50000	5000000						3	0.254

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-01-17T00:00:00	ANONYMOUS	v4_computers	9C7C1C6EED679EB4	0.134
2016-07-15T20:34:51	Mark Rose	raphael	9C7C1C6EED679EB4	0.134

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-07-14T01:59:03

Niels_Mache_Nextcloud

SuperDry-X

3422053571247618385904165377

C63267CB3DBE88AE

2019-07-14T02:18:06

ATH

ec2-PRPCFDC

3422053571247618385904165377

C63267CB3DBE88AE

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 = 4000000, B2 = 200000000 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

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

B1 = 166414 (P-1 stage 1)

B1 = 135000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 25000, B2 = 418750 (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)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2019-07-14T02:18:06+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